**Kuralay Yesmakhanova**, Eurasian National University, Higher Mathematics, Kazakhstan

**Abstract:**In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdVMB) equations. Lax pairs of cmKdVMB equations are presented. Using the Lax pair, we construct a Darboux transformation and namely one-fold transformations. The soliton solutions are obtained from the different ”seeds” by using this Darboux transformation.

**Acknowledgements:**The work of K.Y., G.B., G.Sh. and M.R. is supported by the Ministry of Education and Science of Republic of Kazakhstan (the base part of the state task No.0888/GF4)

1

**Sergey Gladkov**, Moscow aviation institute (national research university) (MAI), Mathematical modelling , Russian Federation

**Sophie Bogdanova**, Moscow Aviation Institution (National Research University) (MAI), mathematic simulation, Russian Federation

**Abstract:**In the article solved the problem of calculation the intensity of the electromagnetic waves radiation by the revolving ferromagnetic sphere with a constant angular velocity . Decision of the problem was find in the general form at condition that all three vectors of magnetizations , external magnetic field and the frequency of rotation not complanare. It is shown that the radiation intensity has strongly anisotropic and nonstationary nature relatives to the angular dependence. The graphic interpretation of the intensity distribution was illustrated due to the numerical methods of the calculation.

2

**Ramin Zahedi**, Hokkaido University, , Japan

**Abstract:**This article is an expanded version of my previous publication [, 2015]. In part I (pp. 1-10) of this article, I provide an analysis and overview concerning discrete physics. In Part II (the main part, pp.11-97) of this article I present a new axiomatic matrix approach based on the ring theory (including the integral domains) and the generalized Clifford algebra. On the basis of this (primary) mathematical approach, by linearization (and simultaneous parameterization, as necessary algebraic conditions), followed by first quantization of the relativistic energy-momentum relation (defined algebraically for a single particle with invariant mass m_0), a unique and original set of the general relativistic (single-particle) wave equations are derived directly. These equations are shown to correspond uniquely to certain massive forms of the laws governing the fundamental forces of nature, including the Gravitational (Einstein), Electromagnetic (Maxwell) and Nuclear (Yang-Mills) field equations (formulated solely in (1+3) dimensional space-time), in addition to the (half-integer spin) single-particle wave equations such as the Dirac equation (which are formulated solely in (1+2) dimensional space-time). In particular, a unique massive form of the general theory of relativity – with a definite complex torsion – is shown to be obtained solely by first quantization of a special relativistic algebraic matrix relation. In addition, it is shown that the "massive " Lagrangian density of the obtained Maxwell and Yang- Mills fields could be also locally gauge invariant – where these fields are formally re-presented on a background space-time with certain complex torsion which is generated by the invariant mass of the gauge field carrier particle. Subsequently, in agreement with certain experimental data, the invariant mass of a particle (that actually would be identified as massive photon) has been specified ( m_γ ≈ 1.4070696×10 *-41 kg), which is coupled with background space-time geometry. Moreover, based on the unique structure of general relativistic particle wave equations derived and also the assum ption of chiral symmetry as a basic discrete symmetry of the source-free cases of these fields, it has been proven that the universe cannot have more than four space-time dimensions. In addition, an argument for the asymmetry of left and right handed (interacting) particles is presented. Furthermore, on the basis of definite mathematical structure of the field equations derived, it is also shown that magnetic monopoles (in contrast with electric monopoles) could not exist in nature.

**Acknowledgements:**Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A . Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to continue this work as a new unorthodox (primary) mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research.

3

**Constantinos Vayenas**, University of Patras, LCEP , School of Engineering, Greece

**Athanasios Fokas**, University of Cambridge, Department of Applied Mathematics and Theoretical Physics, United Kingdom

**Dimitrios Grigoriou**, University of Patras, LCEP, Greece

**Abstract:**Abstract. We compute analytically the masses, binding energies and free energies of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton’s relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles [1, 2]. The model also accounts for the electrostatic charge-induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons [3]. It is found that gravitationally bound states comprising three relativistic neutrinos have masses in the baryon mass range (∼ 0.9 to 2 GeV/c2), whereas states comprising two neutrinos have masses in the meson mass range (∼ 0.2 to 0.8 GeV/c2) [1, 2]. It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (∼ 81 GeV/c2) corresponds

4

**Adrian Sotomayor**, Antofagasta University, Department of Mathematics, Chile

**Alvaro Restuccia**, Antofagasta University, Physics Department, Chile

**Abstract:**We present a local Bäcklund Wahlquist-Estabrook type supersymmetric transformation for the Korteweg-de Vries equation. As in the scalar case, such type of transformation generates infinite hierarchies of solutions by himself and also implicitly gives the associated (local) conserved quantities. A nice property is that every of such hierarchies admits a nonlinear superposition principle, starting for a initial solution, including as a particular case the multisolitonic solutions of the system. We comment about on a particular non-local of such transformations and also about on the related algebra of the non-local conserved quantities.

5

**Vaitsa Tsakstara**, University of Ioannina, Deapartment of Physics, Greece

**Theocharis Kosmas**, University of Ioannina, Deapartment of Physics, Greece

**John Sinatkas**, TEI of Western Makedonia, Department of Informatics Engineering, Greece

**Abstract:**In various cross section calculations of lepton-nucleus reactions performed up to now, the required reduced nuclear matrix elements have been formulated as analytical compact expressions containing an exponential multiplied by a definite polynomial with simple coefficients, both functions of the momentum transfer to the target (detector) nucleus. Original results for specific neutral current (NC) lepton-nucleus processes have been obtained through appropriate codes of old FORTRAN versions constructed for such purposes. In the first part of the present work, we replace these obsolete codes and provide them with the advantage to be used for charged current (CC) lepton-nucleus reactions. In the second part of the paper, the new codes are employed in order to evaluate cross sections for the concrete CC reaction $^{128,130}Te(\nu_\ell, \ell)^{128,130}I$ which is of current experimental interest for the CUORE experiment operating at Gran Sasso, Italy.

6

**Ioannis Mathioudakis**, National Technical University of Athens, School of Chemical Engineering, Greece

**Georgios G. Vogiatzis**, National Technical University of Athens, School of Chemical Engineering, Greece

**Christos Tzoumanekas**, National Technical University of Athens, School of Chemical Engineering, Greece

**Doros N. Theodorou**, National Technical University of Athens, , Greece

**Abstract:**The interaction energetics, molecular packing, entanglement network properties, segmental dynamics, and elastic constants of atactic polystyrene – amorphous silica nanocomposites, in molten and glassy state are studied via molecular simulations using two interconnected levels of representation: (a) A coarse – grained level, wherein each polystyrene repeat unit is mapped onto a single “superatom” and the silica nanoparticle is viewed as a single sphere. Equilibration at all length scales at this level is achieved via connectivity – altering Monte Carlo simulations. (b) An atomistic level, where the polymer chains are represented in terms of a united – atom forcefield and the silica nanoparticle is represented in terms of a simplified, fully atomistic model. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse – grained configurations. By analyzing microcanonical atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. An estimate of the enthalpy of mixing between polymer and nanoparticles, derived from the atomistic simulations, compares favorably with available experimental values. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation and dihedral angle time autocorrelation functions. At low concentration in the molten polymer matrix, silica nanoparticles are found to bring about a slight deceleration of the segmental dynamics close to their surface relative to the bulk polymer. Well – equilibrated coarse – grained long – chain configurations are reduced to entanglement networks via topological analysis with the CreTA algorithm, yielding a slightly lower density of entanglements in the filled than in the neat systems. Atomistic melt configurations are glassified by MD cooling. The Young’ and bulk moduli of the resulting glassy nanocomposites are computed through an analysis of stress fluctuations in the undeformed state and through explicit mechanical deformation by MD, showing a stiffening of the polymer in the presence of nanoparticles. Atomistic simulation results for the elastic constants are compared to the predictions of continuum micromechanical calculations invoked in homogenization models of the overall mechanical behavior of heterogeneous materials.

**Acknowledgements:**Part of this work was funded by the European Union through the project NanoModel under the grant number 211778.

7

**Tatiana Petrova**, Southern Federal University , Institute of Mathematics, Mechanics and Computer Sciences them. I.I. Vorovich, Russian Federation

**Roman Gerasimov**, Southern Federal University, I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Russian Federation

**Olga Maksimova**, Cherepovets State University, Physics, Russian Federation

**Andrei Maksimov**, Cherepovets State University, Physics, Russian Federation

**Abstract:**Absorption of energy of electromagnetic field in liquid crystal system occures due to periodic changes in molecular orientational order. Molecular mechanisms of quadrupole polarization of the nematic phase in electric fields are associated with the rotation of rod-shaped molecules around long and short axes. To describe liquid-crystal systems the lattice model is used, in which each node has anisotropic elongated particle possessing only rotational (orientation) degrees of freedom. This model has the potential of the quadrupole type, Tsvetkov factor is selected as the order parameter. Calculation is carried out by the dynamic Monte Carlo method. The behavior of these systems in alternating external fields is investigated; hysteresis curves are obtained (dependencies of the order parameter on the value of the external field at different parameters). The curves obtained are not symmetrical and have the form of "butterfly". The dependencies of the area of the hysteresis curves on the frequency of the external field, at various values of temperature, amplitude of external field and constants of interaction are researched. It is shown that at a certain frequency near the phase transition point, there is a maximum area of the hysteresis curve. The position of maximum and the peak height depending on the temperature and the constants of intermolecular interactions are investigated.

**Acknowledgements:**The work is performed within the framework of the grant by the Russian Science Foundation “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No 15-19-10008).

8

**Flora Koukiou**, Cergy-Pontoise University, Physics, France

**Abstract:**A family of models involving Gaussian Random Fields is studied in a unified manner and the freezing phenomenon and its relation with the behaviour of the entropy of the Gibbs measure is described in terms of the variational principle. The analysis includes the Gaussian Multiplicative Chaos, Random Energy Model, Spin Glass Mean-Field, Random Polymers on Trees and the Branching Brownian Motion models.

9

**Gisele Helena Miranda**, University of São Paulo (USP), Institute of Mathematics and Computer Science, Computer Science, Brazil

**Jeaneth Machicao**, Instituto de Física de São Carlos, Computação Interdisciplinar, Brazil

**Odemir Bruno**, University of São Paulo (USP), São Carlos Institute of Physics, Department of Physics and Materials Science, Brazil

**Abstract:**Different network models have been proposed along the last years inspired by real-world topologies. The characterization of these models implies the understanding of the underlying network phenomena, which accounts structural and dynamic properties. Several mathematical tools can be employed to characterize such properties as Cellular Automata (CA), which are dynamical systems of discrete nature composed by spatially distributed units governed by deterministic rules. We have proposed a method based on the modeling of one specific CA over distinct network topologies in order to perform the classification of the network model. The proposed methodology consists in the modeling of a binary totalistic CA over a network. The transition function that governs each CA cell is based on the density of living neighbors. Secondly, the distribution of the Shannon entropy is obtained from the evolved spatio-temporal pattern of the referred CA and used as a network descriptor. The experiments were performed using a dataset composed of different types of networks including random, small-world and scale-free, and, cross-validation for training purposes. The accuracy of network classification was analyzed as a function of the initial number of living neighbors and, also, as a function of a threshold parameter regarding the density of living neighbors. For specific combinations of these conditions, we obtained accuracies greater than 90% indicating the feasibility of the proposed method.

**Acknowledgements:**This research was supported by the São Paulo State Research Foundation (FAPESP) under grant: 2015/05899-7 and by Coordination for the Improvement of Higher Education Personnel (CAPES)

10

**Mayken Espinoza - Andaluz**, Lund University, Department of Energy Sciences, Sweden

**Martin Andersson**, Lund University, Department of Energy Sciences, Sweden

**Bengt Sunden**, Lund University, Department of Energy Sciences, Sweden

**Abstract:**The lattice Boltzmann method (LBM) is a suitable tool for solving transport phenomena that occur in gas- and liquid phases at different length scales, especially when complex geometries such as porous media are involved. However, investigations about applications of LBM in the solid-phase material have not been carried out yet. Since in fuel cells (FCs) the multifunctional layers play an important role during the energy conversion process, and such layers are mostly built of porous materials, the ohmic resistance of porous materials represents a crucial characteristic to be studied to predict the internal ohmic losses. The purpose of this paper is to show the feasibility of LBM to determine the ohmic resistance of conducting materials whose dimensions are modified considering the cross sectional area and length. Characteristics, limitations and recommendations of LBM applied to the solid phase for calculating the ohmic resistance are presented considering the coupling of the methodology with the Ohm’s Law. Additionally, the behavior prediction of the ohmic resistance for a given porous material is presented based on the methodology considered in this study.

11

**A. Zaidi**, Universiti Teknologi MARA, Mathematics, Malaysia

**Khairul Rasmani**, Universiti Teknologi MARA, Mathematics, Malaysia

**Abstract:**Demand for clean and treated water is increasing all over the world. Therefore it is crucial to conserve water for better use and to avoid unnecessary, excessive consumption or wastage of this natural resource. Classification of excessive domestic water consumption is a difficult task due to the complexity in determining the amount water usage per activity, especially as the data is known to vary between individuals. In this study, classification of excessive domestic water consumption is carried out using a well-known Fuzzy C-Means (FCM) clustering algorithm. Consumer data containing information on daily, weekly and monthly domestic water usage was employed for the purpose of classification. The result produced by the FCM clustering algorithm is compared with the result obtained from a statistical control chart which demonstrates the potential use of FCM clustering algorithm for the classification of domestic consumer water consumption data.

**Acknowledgements:**This research work is funded by the Ministry of Higher Education, Malaysia under the Fundamental Research Grant Scheme (FRGS) with reference number 600-RMI/FRGS TD 5/3 (1/2015). The authors also would like to thank the Institute of Research Management and Innovation (IRMI), Universiti Teknologi MARA, Malaysia.

12

**Roman Gerasimov**, Southern Federal University, I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Russian Federation

**Victor Eremeev**, Southern Federal University, I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Russian Federation

**Tatiana Petrova**, Southern Federal University , Institute of Mathematics, Mechanics and Computer Sciences them. I.I. Vorovich, Russian Federation

**Vladislav Egorov**, Cherepovets State University, Information Technology Institute, Russian Federation

**Olga Maksimova**, Cherepovets State University, Physics, Russian Federation

**Andrei Maksimov**, Cherepovets State University, Physics, Russian Federation

**Abstract:**For mixed discrete-continual model consisting of an elastic substrate and a polymer coating we performed computer analysis of mechanical properties for various levels of deformations. For the substrate we used the classic elastic material described by the Hooke law. The polymer coating is modelled using discrete approach. We used the Stockmayer potential which is a Lennard-Jones potential with additional term which is responsible for dipole interactions between neighboring elements of polymeric chains, that is the Keesom energy. Using the Monte-Carlo method and the Metropolis algorithm for a given temperature we obtained the equilibrium state of the system. In particular, we derived dependencies of the energy, stresses, Young's modulus on the relative strains. We shown that for stretching increase of the system the influence of the surface coating on the material parameters decreases. In addition we compared the presented analysis with experimental data on deformations of crystalline polymers such as gutta-percha, etc.

**Acknowledgements:**The work is performed within the framework of the grant by the Russian Science Foundation “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No 15-19-10008).

13

**Dimitri Petritis**, Universite de Rennes 1, Mathematics, France

**Abstract:**Let $\mathbb{X}$ be an abstract space and $\mathbb{A}$ a denumerable (finite or infinite) alphabet. Suppose that $(p_a)_{a\in\mathbb{A}}$ is a family of functions $p_a:\mathbb{X}\to\mathbb{R}_+$ such that for all $x\in\mathbb{X}$ we have $\sum_{a\in\mathbb{A}} p_a(x)=1$ and $(S_a)_{a\in\mathbb{A}}$ a family of transformations $S_a:\mathbb{X}\to\mathbb{X}$. The pair $ ((S_a)_a, (p_a)_a)$ is termed an \textit{iterated function system with place dependent probabilities}. Such systems can be thought as generalisations of random dynamical systems. As a matter of fact, suppose we start from a given $x\in\mathbb{X}$; we pick then randomly, with probability $p_a(x)$, \text{the} transformation $S_a$ and evolve to $S_a(x)$. We are interested in the behaviour of the system when the iteration continues indefinitely. Random walks of the above type are omnipresent in both classical and quantum Physics. To give a small sample of occurrences we mention: random walks on the affine group, random walks on Penrose lattices, random walks on partially directed lattices, evolution of density matrices induced by repeated quantum measurements, quantum channels, quantum random walks, etc. In this article, we review some basic properties of such systems.

14

**Jun Cao**, Ryerson University, Mechanical and Industrial Engineering, Canada

**Abstract:**As a typical form of disastrous weather, a tornadic wind is essentially considered as an airflow that simultaneously translates and rotates. Numerical simulations of this kind of hybrid flow remain inadequate due to many numerical difficulties, one of the major challenges consisting in the establishment of a set of boundary conditions that are, for the tornado-obstacle interaction scenario, both rational in physics and simple in numerical implementation. Inspired by the success of immersed-boundary (IB) lattice Boltzmann method (LBM) for simulations of fluid-structure interaction problems, this study proposes a new outlet of the IB-LBM framework for investigation of tornadic wind effects, featuring a reformed interpretation of the Rankine-Combined Vortex Model (RCVM) that considerably facilitates the boundary condition setup. Moreover, the main purpose of this study is to examine the tornadic wind loadings in relation to the rotation intensity of a tornado, and presents a practical Newton’s bi-section-like method for determining the critical rotation intensity beyond which the aerodynamic coefficients no longer increase when Reynolds number rises. This critical rotation intensity serves to characterize tornadic winds, such that the tornado with a rotation density below its critical value can be considered as mainly dominated by the translation part and, otherwise, the dominance no longer belongs only to the translational component of the tornado. Since it has been rather conventional that, when studying tornadoes, Reynolds number is determined using only the translation velocity as characteristic velocity, the present tornado study intends to suggest, through a number of numerical test series, that more attention be paid to the insufficiently explored rotational component, which physically tends to play a more dominant role when an intensive rotation is present in a tornado scenario.

15

**Viktor Dezhin**, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

**Igor Bataronov**, Voronezh State Technical University, , Russian Federation

**Abstract:**Oscillations of a dislocation segment dependence on the external forces are considered. Expressions are obtained for matrix elements which are expressed by means of the generalized susceptibilities matrix of dislocation oscillators. Elimination of non-physical features in the range of large wave numbers was made within the Peierls dislocation model. An expression was obtained describing the low-frequency asymptotic behavior of the diagonal and non-diagonal elements of the generalized susceptibilities matrix of dislocation oscillators.

16

**Omar Mansouri**, ESIEE, Amiens, , France

**Kamal MEGHRICHE**, Yvelines Institute of Sciences and Technology, University of Versailles Saint-Quentin-en-Yvelines, Mechatronics, France

**Abderrezzak Cherifi**, IUT Mantes-en-Yvelines, University of Versailles Saint-Quentin-en-Yvelines, Industrial Engineering and Maintenance, France

**Abstract:**This paper presents a mathematical modeling of a three-phase power inverter by Fourier analysis. The Fourier coefficients (harmonics) are calculated in terms of the switching angles. The objective of the proposed model is to minimize the number of switching states while reducing the total harmonic distortion (THD) rate. To optimize the number of canceled harmonics, we assume that the inverter output voltage has the same symmetry properties as the output voltage of a perfect and balanced three-phase system. This symmetry property allows canceling all even-ranked harmonics and all harmonics whose rank is a multiple of three. Voltage setting becomes possible only aver 1/6 period (/3). The obtained general inverter model allows modulating both the pulse width (PWM) as well as the multilevel. The rank of the first non-canceled harmonic depends on the number of the switching states. The model has been tested on a three-level PWM inverter. The obtained simulation and experimental results have shown a substantial reduction of the THD rate at the inverter output, while minimizing the switching stress.

17

**Daniel Rodríguez-Pérez**, Universidad Nacional de Educación a Distancia (UNED), Física Matemática y de Fluidos, Spain

**María Desco**, Universidad Nacional de Educación a Distancia (UNED), Física Matemática y de Fluidos, Spain

**J. Carlos Antoranz**, UNED, Física Matemática y de Fluidos, Spain

**Abstract:**Chemo- and radiotherapy are the two most often used treatments to deal with cancer tumors. Although these two treatments can remove tumors on their own, they are also used in coadjuvancy: chemotherapy, administered globally, may improve the effects of local radiotherapy. The effects of radiotherapy is well modeled by linear-quadratic (LQ) models currently in use that predict cell survival fractions for low and fractionated doses. However, for higher doses, such as those used in hypofractionated therapy, better predictions are obtained using a model derived from non-extensive Tsallis entropy [1]. In a previous paper [2] the former model was discretized and new predictions emerged, describing unusual behaviors of some types of tumors (e.g. prostate cancer) under radiotherapy, not well predicted by LQ model without introducing further hypotheses. The goal of this work is to model the interaction between chemo- and radiotherapy. Our hypothesis is that, although both treatments haven different mechanisms, both affect similar key points of cell metabolism and regulation, that lead to cellular death. Hence, we will consider a discrete model where chemotherapy may affect a fraction of the same targets destroyed by radiotherapy. Although radiotherapy reaches all cells equally, chemotherapy diffuses through an spherical tumor attaining lower concentration in its center and higher in its surface. With our simulations we study the enhanced effect of combined therapy treatment and how it depends on the tissue critical parameters (the parameters of the non-extensive radiobiological model), the number of “targets” aimed by chemotherapy, and the concentration and diffusion rate of the drug inside the tumor. The results show that an equivalent chemo-radio-dose can be computed that allows the prediction of the lower radiation dose that causes the same effect than a radio-only treatment. References: [1] Oscar Sotolongo-Grau, Daniel Rodriguez-Perez, José Carlos Antoranz, Oscar Sotolongo-Costa (2010). Tissue radiation response with maximum Tsallis entropy. Physical Review Letters, 105(15):158105. [2] D. Rodriguez-Perez, O. Sotolongo-Grau, M.M. Desco, J.C. Antoranz (2015). Stochastic effects in a discrete RT model with critical behaviour. Journal of Physics: Conference Series, 633:012089.

**Acknowledgements:**The authors acknowledge the financial support of the Spanish Ministerio de Ciencia e Innovación under research contract FIS2012-37408.

18

**Antonina Fedorova**, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation

**Michael Zeitlin**, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation

**Abstract:**We present the applications of the multiresolution analysis approach in the constrained variational framework for calculation of dynamical aperture for particle/beam motion in accelerators. We construct an exact multiscale representation by decomposition via nonlinear high-localized eigenmodes, which allows to control contributions to motion from the whole underlying hidden multiscale structure. We consider a qualitative approach to the aperture problem based on the analysis of smoothness classes in the underlying functional space.

19

**Hemwati Nandan**, Gurukula Kangri Vishwavidyalaya, Haridwar Uttarakhand, Department of Physics, India

**Abstract:**We investigate the evolution of timelike geodesics, in the background of a charged black hole spacetime surrounded with the quintessence. The weak and the strong energy conditions for the focusing of timelike geodesic congruences are also analysed. The Raychaudhuri equations for the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and then solved numerically. The effect of the normalisation constant and equation of state (EOS) parameter on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation along with the justification of corresponding energy conditions. It is observed that there always exists a critical value of the initial expansion below which we have focusing with smaller values of the normalisation constant and EOS parameter. As the corresponding values of both of these parameters are increased, no geodesic focusing is observed. The results obtained are also compared with those of the Reissener-Nordtrom (RN) and Schwarzschild black hole spacetimes as well as their de-Sitter black hole analogues accordingly.

20

**Antonina Fedorova**, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation

**Michael Zeitlin**, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation

**Abstract:**We present applications of methods of nonlinear local harmonic analysis in variational framework for a description of multiscale representations in polynomial/rational approximations (up to any order) for nonlinear motions in arbitrary n-pole fields. Our approach is based on the methods allowed to consider dynamical beam/particle localization in phase space and provided exact multiscale representions via nonlinear high-localized eigenmodes for observables with exact control of contributions to motion from each underlying hidden scale.

21

**Evangelos Bakalis**, University of Bologna, Dipartimento di Chimica "G. Ciamician", Italy

**Francesco Zerbetto**, Universita di Bologna, Dipartimento di Chimica "G. Ciamician", Italy

**Abstract:**The anomalous diffusion of a particle that moves in complex environment is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a particle caused either by a uniform external field or by short-range interactions in the form of a delta spike is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M-Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the models to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.

22

**RAVI SHANKAR KUNIYAL**, GURUKULA KANGRI VISHVAVIDYALAYA, HARIDWAR, PHYSICS, India

**Abstract:**We study the geodesic motion of the massless test particles in the background of a magnetically charged black hole spacetime arising in dilaton-Maxwell gravity in four dimensions. The behaviour of effective potential and possible photon orbits in view of the different values of black hole parameters are analysed in detail. The results obtained for above black hole spacetime are then compared with its dual counterpart i.e. the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime in GR.

23

**Rashmi Uniyal**, Government Degree College, Narendranagar, Tehri Garhwal Uttarakhand, Physics, India

**Abstract:**String theory is one of the leading candidate theories to unify gravity with other fundamental forces in nature. In the present study, we consider time-like geodesic congruences around a Black Hole (BH) spacetime which arises in low energy heterotic string theory, popularly known as Sen BH. Most of the BH solutions in string theory are characterized by one or more charges associated with the Yang-Mills fields or the anti-symmetric tensor gauge field. The Sen BH carries a finite amount of charge, angular momentum and magnetic dipole moment and it could be produced by twisting method and starting from a rotating BH having no charge, i.e. the Kerr BH in GR and sometimes referred as twisted Kerr BH or Kerr-Sen BH. In order to analyse the properties of BHs using geodesics, the separability and integrability of the geodesic equations are essential and based on these standpoints, we have analysed the complete orbit structure for both the timelike and null geodesics in view of the corresponding effective potential. In addition to the orbits in the equatorial plane, we have also obtained the approximate solution for the radius of spherical photon orbits in non-equatorial plane. The results obtained for Sen BH are also compared with those of various charged/rotating/uncharged/non-rotating solutions such as Kerr-Newman (KN), Kerr, Reissner-Nordstrom (RN) and Schwarzschild class solutions in GR.

24

**Igor Levchenko**, Queensland University of Technology, School of Chemistry, Physics, and Mechanical Engineering, Australia

**Abstract:**The Hall thruster, sometimes named the stationary plasma thruster, is the most promising type of plasma sources and spacecraft low-thrust devices. The main distinguishing feature of this thruster is high density of thrust current that is not limited by the space charge in the acceleration channel. This provides high efficiency and small geometrical dimensions of the device, as compared with the ion thrusters. The cross-field transport in the electrical field (E) and magnetic field (B), as well as closed electron drift are the characteristic features of the Hall thruster physics. In this work we examine the processes in a stationary plasma thrusters paying special attention to the near-wall processes and spatial distribution of the plasma parameters in the thruster channel.

25

**Maxim Stolyarchuk**, ITMO University, , Russian Federation

**Alexander Sidorov**, ITMO University, , Russian Federation

**Abstract:**Silicate glasses containing subnanometer-sized noble metal particles exhibit novel and unusual optical properties and find various applications in photonics, helioenergetics and sensor technologies. Here we present first-principles study of the electronic structure, stability and optical properties of silver atom and dimer at point defects in silicate glasses investigated by means of a finite cluster approximation using density functional theory. Two defects have been explored as representative of amorphous silicon dioxide: negatively charged non-bridging oxygen (NBO) and non-bridging oxygen hole center (NBOHC). Optically allowed electronic transitions of the bounded silver atoms have been compared with those of the corresponding free gas-phase units. The considered defects bind strongly the silver atoms forming stable complexes. Our results give insight into the nature of optical absorption patterns due to the interaction between the silver species and the defects.

26

**Elena Ivanova**, Far Eastern Federal University , School of Natural Sciences, Russian Federation

**Abstract:**One of the major contradictions in subject teaching is the contradiction between the unity of the world and the discrete separated generalized content of natural sciences that study natural phenomena. These are physics, chemistry, biology and more. One can eliminate the conflict if opens the content’s inter-subject links set by the events that are studied by different disciplines. The corresponding contexts of the phenomenon content arise depending on the discipline, and they are not enough coordinated. Obviously, we need a mechanism that allows establishing inter-subject links in the content quickly and without losing the logic of the material and assess their coherence in academic disciplines. This article uses a quantitative method of coherence assessment elaborated by T.N. Gnitetskaya. The definition of the concept of the semantic state introduced by the authors is given in this article. The method is applied to coherence assessment of physics and chemistry textbooks. The coherence of two pairs of chemistry and physics textbooks by different authors in different combinations was calculated. The most cohered pairs of textbooks (chemistry-physics) were identified. One can recommend using the pair of textbooks for eighth grade that we offered that favors the development of holistic understandings of the world around us.

27

**Alexandros Kyrtsos**, Boston University, Electrical and Computer Engineering, United States

**Gerrit De Young**, Boston University, Department of Psychology, United States

**Enrico Bellotti**, Boston University, Electrical and Computer Engineering, United States

**Abstract:**The economic crisis of 2007 made apparent that a cascade of events in a system with interconnected institutions like the banking system can have catastrophic results. In addition to market crashes, other physical phenomena such as brain seizures in neuroscience can be modeled using networks. In our studies, we simulate a system as a population of interacting and static nodes in a network. We assign a quantitative attribute to each node which indicates the health of the node at any given time. We assume that a node can fail either independently (internal failure) with probability p dt in the interval between t and t+dt or due to the influence of its neighbors (external failure) if it happens to be in a damaged neighborhood of nodes. We also take into account the case in which a node recovers from failure. We perform numerical simulations for regular, random and scale-free networks and we examine different sets of interactions.

**Acknowledgements:**We acknowledge the help and the fruitful discussions with Dr Eugene H. Stanley and Dr Jianxi Gao.

28

**Viktor Dezhin**, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

**Vladimir Nechaev**, Voronezh State Technical University, , Russian Federation

**Abstract:**The system of equations describing the bending vibrations of the dislocation in the ferromagnetic crystal is written. Elastic and magnetostrictive properties of the ferromagnetic crystals are considered isotropic. The linearization of the resulting system produced a relatively small contribution to the magnetization from the influence of dislocation. In the linear approximation of the dislocation displacement system of equation describing vibrations of a ferromagnetic crystal with an edge dislocation is obtained. The equation of motion of an edge dislocation in a ferromagnetic crystal is found.

29

**Lyudmila Prokudina**, South Ural State University, applied mathematics , Russian Federation

**Abstract:**Nonlinear mathematical model of free surface fluid film is presents. Increment, frequency, phase velocity for thin layers of viscous liquids at low Reynolds numbers are calculated. The instability region is found. Optimal flow regimes of films of water and alcohol, corresponding to the maximum values of increment, are calculated.

30

**Olga Karpova**, Turin Polytechnic university in Tashkent, Laboratory for Advanced Studies, Uzbekistan

**Abstract:**Wave propagation in absorbing or transparent media is a problem having practical applications in acoustics, optics, fluid dynamics and geology. The main complication appearing is solving such problems is correct formulation of the boundary conditions which are called absorbing or transparent boundary conditions [1-3]. Also, both, wave equation and boundary conditions require using of effective grids and tricks providing simplification of the numerical solutions. So far, different wave equations have been studied in the context of absorbing boundary conditions. However, extension of such studies to relativistic wave equations such as Klein-Gordon and Dirac equations are remaining still less-studied. Relativistic waves in transparent media appears in many systems such as plasma, graphene, nuclear and quark-gluon matter [4]. All these cases require solving of the Dirac equation with absorbing boundary conditions. In this work we develop simple approach for solving of the Dirac equation with absorbing boundary conditions. In particular, using relativistic extension of the methods developed in [5] we derive absorbing boundary conditions for the one-dimensional Dirac equation in finite interval. Also, we develop effective numerical method for solving such equation. Application of the results to relativistyic electron motion in laser field, plasma waves and graphene is discussed. References 1. V.A. Baskakov and A.V. Popov, Wave Motion 14 123 (1991). 2. X. Antoine, et.al, Commun.Comput. Phys. 4 729 (2008) 3. X. Antoine, C. Besse, P. Klein , J. Comput. Phys., 228 312 (2009) 4. G.A. Mourou, T. Tajima, S.V. Bulanov, Rev.Mod.Phys., 78, 309 (2006) 5. J.P. Kuska, Phys.Rev.B., 46 5000 (1994)

31

**JORGE GARCIA BELLO**, INSTITUTO POLITÉCNICO NACIONAL, FÍSICA MATEMÁTICA, Mexico

**Abstract:**In this paper, we do a statistical analysis about the data reported by the Daya Bay collaboration, we propose a statistics χ 2 for the analysis that offer confidence regions consistent with those reported by the collaboration. Is possible noted that the statistical errors dominant in the results. We obtain sin 2 2θ 13 = 0.08387 and m 2 ee = (2.507 × 10 −3 )eV 2 , within a framework of three neutrinos.

32

**Yulia Maslennikova**, Kazan federal university, Institute of Physics, Russian Federation

**Ildus Nugmanov**, Kazan federal university, Radiophysics, Russian Federation

**Abstract:**The problem of probability density function estimation for a random process is one of the most common in practice. There are several methods to solve this problem. Presented laboratory work uses methods of the mathematical statistics to detect patterns in the realization of random process. On the basis of ergodic theory we construct algorithm for estimating univariate probability density distribution function for a random process. Correlational analysis of realizations is applied to estimate the necessary size of the sample and the time of observation. Hypothesis testing for two probability distributions (normal and Cauchy) is used on the experimental data, using χ2 criterion. To facilitate understanding and clarity of the problem solved, we use ELVIS II platform and LabVIEW software package that allows us to make the necessary calculations, display results of the experiment and, most importantly, to control the experiment. At the same time students are introduced to a LabVIEW software package and its capabilities.

33

**Radka Keslerova**, Czech Technical University in Prague, Faculty of Mechanical Engineering, Dep. of Technical Mathematics, Czech Republic

**David Trdlicka**, Czech Technical University in Prague, Dep. of Technical Mathematics, Czech Republic

**Hynek Reznicek**, Czech Technical University in Prague, Dep. of Technical Mathematics, Czech Republic

**Abstract:**Branching of pipes occurs in many technical or biological applications. In biomedical applications, it is the complex branching system of blood vessels in human body. The blood can be characterized by shear-thinning viscoelastic property. The aim of this paper is to describe and discuss the results of numerical simulation of steady and unsteady fluids flow. Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta time integration. In the case of unsteady computation an artificial compressibility method is considered.

**Acknowledgements:**This work was supported by grant SGS16/206/OHK2/3T/12 of the Czech Science Foundation.

34

**Stanislav Khristoforov**, Kazan (Volga region) Federal University, Physics, Russian Federation

**Vladimir Bochkarev**, Kazan federal university, Radiophysics, Russian Federation

**Abstract:**The problem of increasing of optimization speed of some objective function is one of the most important tasks in the areas of science such as physical processes simulation, machine learning, or in problems of the decision-making. The presence of a huge number of gradient optimization methods of different complexities allows investigators to find a local minimum of the objective function as quickly as possible. However, we offer the opportunity to increase speed of solving this problem based on using frames while the calculation the direction of the next step of optimization. Frames are coordinate systems with an excess of the coordinate axes. Translation the N-dimensional space of the arguments of objective function to the frame-space of dimension M (M>N), calculation and generation the magnitude and direction of the optimization step and then returning to the function arguments space of the original dimension using the inverse transform lead us to getting the motion direction of the decision point that is slightly different from the normal. For algorithms that depend on the basis orientation (such as Rprop) this process can have a significant impact on the convergence speed of the algorithm because the greater number of axes provides geting the most optimal coordinate system that leads to the fastest convergence of algorithm. For algorithms that don't depend on the basis orientation(eg ADAgrad, ADAdelta) this process will help to suppress the noise that there is in all the real target functions just due to using larger number of axes in calculations. We verified the performance increase of the above method in the optimization problem of multidimensional version of Rosenbrock's function, as well on multidimensional quadratic function adding Gaussian noise of constant and non-constant dispersion. Frames gives the speed increasing of convergence. For example, the use of frames in Rprop algorithm much stronger accelerates optimization (up to 40 times faster) than in the case of ADAdelta type algorithms (double acceleration)

35

**Anna Wawrzynczak-Szaban**, Siedlce University, , Poland

**Renata Modzelewska-Lagodzin**, Siedlce University, Institute of Math and Physics, Poland

**Abstract:**We present the stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. The model is created based on the numerical solution of the Parker transport equation (PTE) describing the non-stationary transport of charged particles in the turbulent medium. We present the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary PTE. Among the employed methods are the strong order Euler-Maruyama, Milstein and stochastic Runge-Kutta methods. We perform the selection of the method resulting in the highest agreement of the model of the 27-day variation of the GCR intensity with the experimental observations.

36

**Viktor Dezhin**, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

**Vladimir Nechaev**, Voronezh State Technical University, , Russian Federation

**Abstract:**The amplitude of the electric fields around the vibrating edge dislocation on the distance from the dislocation line is found. The law of decrease modulus of the amplitude of the electric fields at the distance from the dislocation line is determined.

37

**Rıza Erdem**, Akdeniz University, Department of Physics, Turkey

**Ekrem Aydiner**, Istanbul University, Department of Physics, Turkey

**Abstract:**Ion channel systems are a class of proteins that reside in the membranes of all biological cells and forms conduction pores that regulate the transport of ions into and out of cells [1]. They are solved in the microcanonical formalism since the number of accessible states can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials [2]. In this work, we have solved the two-state channel system without any approximation, using gamma function (Gamma(N)). Exact values are calculated for the open probability ( Po^ex) and the relative error between our exact solution and the approximate one using Stirling formula (Po^app-Po^ex)/Po^ex. This error is significant for small channel systems. [1] B. Hille, Ionic Channels of Excitable Membranes _Sinauer Associates, Sunderland, MA, 1992. [2] R. Erdem, C. Ekiz, Phys. Lett. A 331 (2004) 28.

38

**Klaus Lieutenant**, Helmholtz-Zentrum Berlin, EM-AMCT, Germany

**Tommy Hofmann**, Helmholtz-Zentrum Berlin, , Germany

**Carolin Zendler**, European Spallation Source ERIC, , Sweden

**Christian Schulz**, Helmholtz-Zentrum Berlin, , Germany

**Emad Aziz**, Helmholtz-Zentrum Berlin, , Germany

**Klaus Habicht**, Helmholtz-Zentrum Berlin, , Germany

**Abstract:**At Helmhotz-Zentrum Berlin (HZB) the end-station PEAXIS (Photo Electron Analysis and X-ray resonant Inelastic Spectroscopy) combining Angle-dependent Photoelectron Spectroscopy (AdXPS) and Resonant Inelastic X-ray Scattering (RIXS) is currently built. The latter method uses a spherical variable line space (VLS) grating to focus the beam to the detector. Working in first order diffraction allows resolving photon energy by transferring the energy-dependent signal to a position-dependent focal spot on the detector. Fosusing requires a precise combination of various parameters of the VLS grating and the geometry of the RIXS spectrometer. The VLS grating was optimized by calculating the dependent geometry parameters for different photon energies, simulating the instrument and evaluating the pattern on the detector. As figure of merit the intensity times the square of the resolution power averaged over the photon energies was chosen.

39

**Georgios Kritikos**, Aristotle University of Thessaloniki, Chemical Engineering, Greece

**Aris Sgouros**, National Technical University of Athens, School of Chemical Engineering, Greece

**Georgios G. Vogiatzis**, National Technical University of Athens, School of Chemical Engineering, Greece

**Doros N. Theodorou**, National Technical University of Athens, , Greece

**Abstract:**In macromolecules before the liquid to solid transition the viscosity and the relaxation times increase dramatically. In some cases, extreme confinement (interwall distance comparable to the chain dimensions) has been related to a non-Einstein-like decrease in viscosity [1]. Moreover it has been shown [2, 3] that attractive confining walls introduce one more mechanism (in addition to the caging effect and intramolecular conformational barriers) for time scale separation of glass forming polymers. This mechanism is the slow desorption kinetics of monomers from the surface, leading to slow layer exchange dynamics on the length scale of (at least) the radius of gyration of the chains. Several experimental works [3] have supported the idea that the confined/bounded layer is immobilized above the major Tg, in such a way that finally it does not participate in the glass transition. We present results concerning the dynamics and the structure (trains, loops and tails) of an adsorbed layer of polyethylene (PE) between two graphite surfaces. The molecular weight of the chosen monodisperse PE chains reaches the entanglement regime. We study three cases of interwall distance, equal to two, three and four times the radius of gyration of PE chains. The confined system is equilibrated [2] with the use of an efficient Monte Carlo algorithm [4]. By the use of molecular dynamics simulation we reveal the distribution of relaxation times as a function of the distance from the graphite walls at the temperature of 450 K. From the atomic-level stresses we calculate the adhesion tension. Although the gap between the two walls is comparable to the width of the adsorbed layer, we do not record the formation of 'glassy bridges'. The diffusion of polymer chains in the middle layer is not inhibited significantly by the existence of the two adsorbed layers. The presented results seem to justify a reduction in the calorimetric (heat capacity step) glass transition temperature (Tg). References [1] Mackay ME, Dao TT, Tuteja A, Ho DL, Van Horn B, Kim HC, et al. Nanoscale effects leading to non-Einstein-like decrease in viscosity. Nat Mater. 2003;2(11):762-766. [2] Theodorou DN, Vogiatzis GG, Kritikos G. Self-Consistent-Field Study of Adsorption and Desorption Kinetics of Polyethylene Melts on Graphite and Comparison with Atomistic Simulations. Macromolecules. 2014;47(19):6964-6981. [3] Kritikos G. Transition of the bounded polymer layer to a rigid amorphous phase: A computational and DSC study. Polymer. 2014;55(18):4658-4670. [4] Karayiannis NC, Mavrantzas VG, Theodorou DN. A novel Monte Carlo scheme for the rapid equilibration of atomistic model polymer systems of precisely defined molecular architecture. Phys Rev Lett. 2002;88(10):1055031-1055034.

40

**Vladimir Oskomov**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Alexandr Sedov**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Nurzhan Saduyev**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Orazaly Kalikulov**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Aisha Naurzbayeva**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Nazgul Alimgazinova**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Inesh Kenzhina**, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan

**Abstract:**Experimental studies of estimation the mutual influence of humidity and flux of cosmic rays in first approximation were carried out. Normalized cross-correlation function of time series of neutron monitors count rate and level of relative atmosphere humidity near cosmic rays registration point is studied. Corrected and uncorrected on pressure minute and hour data of 6NM64 neutron monitor count rate were used for the study. Neutron monitor is located in Al-Farabi Kazakh National University, at an altitude of 850 m above sea level. Also, data from NM64 neutron monitor of Tien Shan mountain research station of Institute of Ionosphere, located at an altitude of 3340 m above sea level were used. Uncorrected on pressure cosmic rays intensity better reflects the changes in relative atmosphere humidity. Average and sometimes strong relationship is often observed by time changes of atmosphere humidity near the point of cosmic rays detection and their intensity: the value of normalized cross-correlation function of respective signals, even in case of their long duration and a large number of data (eg, for minute changes at intervals of up to several months) covers 0.5 - 0.75 range, sometimes falling to ~ 0.4.

**Acknowledgements:**The study was carried out under the support of grant #3842/GF4 of Ministry of Education and Science of Kazakhstan.

41

**Olga Baruzdina**, Cherepovets state university, Physics, Russian Federation

**Olga Maksimova**, Cherepovets State University, Physics, Russian Federation

**Andrei Maksimov**, Cherepovets State University, Physics, Russian Federation

**Abstract:**The purpose of this work is to study the influence of the substrate on structural phase transitions from an ordered state to disordered one in ferroelectric thin films. Three-dimensional anisotropic Heisenberg’s classic model has been used. The constants of this model are determined by the chemical structure of the ferroelectric. The temperature dependences of the susceptibility and the long-range orientation order parameter (the mean cosine of the angle between the dipole and the direction of their preferred orientation) were calculated. Dependences of temperature of structural phase transitions in the volume and on a free surface of the ferroelectric film on its thickness by means of Monte-Carlo method were obtained. Four cases were investigated: 1) Infinitely extended ferroelectric. In this case, calculations shown that the order parameter changes jump wise, and the susceptibility is maximal at a certain temperature Tc. The value of this temperature depends on the chemical structure of the substance. 2) Freely - suspended film. Temperature of phase transition decreases at decreasing of the film thickness. For ultrathin films, the phase transition is absent that corresponds to Mermin-Wagner-Hohenberg's theorem [1]. 3) Ferroelectric film between two electrodes. The point of phase transition is shifted in area of more high temperatures. 4) Ferroelectric film on the metal surface at high adhesion. In the simulation, one party of the film has the fixed boundary conditions, and another party has periodic ones. Temperature of phase transition in this case doesn't depend on the film thickness. References 1. N. Mеrmin, H.Wagner Phys. Rev. Lett. 17, 1133 (1966) 2. Hohenberg, P.C. Phys. Rev. 158, 383 (1967)

**Acknowledgements:**The study was performed in frame of the State Contract No. 2014/267, project No. 1715

42

**Lei Yang**, Nanjing University of Aeronautics and Astronautics, Civil Aviation, China

**Abstract:**Characteristics analysis of air traffic flow is an essential part of air traffic flow theory, and also the important basis of air traffic management. In this article, based on hybrid dynamic characteristics of traffic flow, a Fuzzy Logic method is adopted to present dynamic separation control strategy to reflect controller’s decision behavior, “stimulation-reflection” aircraft-following theory and local FCFS rules are used to establish generalized aircraft-following model of arriving flow in terminal airspace. To deduce and analyze emergence behavior of air traffic system, multi-agent simulation system is setup using NetLogo tool to simulate the arriving flow of ZGGG 02R. The inter-relations of traffic flow parameters: velocity, density and flow rate are revealed in this article and five phases in arriving air traffic flow evolvement are discovered: free, unimpeded, metastable, Pseudo congestion and synchronization. Further, air traffic flow influence mechanism is analyzed under traffic organizations, separation standards and ATFM strategies variations. The results of this paper may have positive impact on air traffic flow theory perfection.

43

**Constantin Meis**, CEA-Saclay , National Institute for Nuclear Science and Technology, France

**Pierre Dahoo**, Université de Versailles-St. Quentin en Yvelines, LATMOS, France

**Abstract:**The quantization procedure of the vector potential is enhanced at a single photon state revealing the possibility for a simultaneous representation of the wave-particle nature of the photon. Its relationship to the quantum vacuum results naturally. A vector potential amplitude operator is defined shoing the parallelism with the Hamiltonian of a massless particle. It is further shown that the quantized vector potential satisfies both the wave propagation equation and a linear time-dependent Schrödinger-like equation. References: 1/ C.Meis "Light & Vacuum". World Scientific. 2015 2/C.Meis. Physics Research International Volume 2014, Article ID 187432

44

**Alexandre Zakharov**, Saint Petersburg Institute for Machine Sciences, Russian Academy of Sciences, Laboratory of Micromechanics of Materials , Russian Federation

**Anna Vakulenko**, Saint Petersburg Institute for Machine Sciences, Russian Academy of Sciences, Laboratory of Micromechanics of Materials , Russian Federation

**Sergey Pasechnik**, Moscow Technological University, Problem Laboratory of Molecular Acoustics, Russian Federation

**Abstract:**The peculiarities in the dynamics of the director reorientation in confined nematic liquid crystals (LCs) under the influence of a strong electric field E have been investigated theoretically based on the hydrodynamic theory including the director motion with appropriate boundary and initial conditions [1,2]. Analysis of the numerical results for the turn-on process provides an evidence for the appearance of the spatially periodic patterns in confined LC film, only in response to the suddenly applied strong E. It has been shown that there is a threshold value of the amplitude of the thermal fluctuations of the director over the LC sample which provides the nonuniform rotation mode rather than the uniform one, whereas the lower values of the amplitude dominate the uniform mode. During the turn-off process, the reorientation of the director to the direction preferred by the surfaces is characterized by the complex destruction of the initially periodic structure to a monodomain state. [1] A. A. Vakulenko and A. V. Zakharov, Phys. Rev. E88, 022505 (2013); [2] A. V. Zakharov and A. A. Vakulenko, J. Chem. Phys. 139, 244904 (2013)

**Acknowledgements:**This work was partially supported by the Ministry of Education and Science of the Russian Federation [grant no. 3.1921.2014/K] and the RFBR [project no. 16-02-00041].

45

**Svetlana Absalyamova**, Kazan (Volga Region) Federal University, Institute of Management, Economics and Finance, Russian Federation

**Timur Absalyamov**, Kazan (Volga Region) Federal University, Institute of Management, Economics and Finance, Russian Federation

**Chulpan Mukhametgalieva**, Kazan (Volga Region) Federal University, Institute of Management, Economics and Finance, Russian Federation

**Asiya Khusnullova**, Kazan Cooperation Institute (branch) of the Russian University of Cooperation, , Russian Federation

**Abstract:**The article explains the use of the human capital sustainable development index (HCSDI) to assess the quality of the reproduction of human capital. The paper provides the algorithm for calculating HCSDI and its components. Authors estimated cross-country differences of HCSDI and developed econometric model of the impact of corruption on HCSDI. The use of this model has allowed to reveal the mechanism and assess the impact of corruption on HCSDI and its components. The results of econometric analysis revealed a negative multiplier effect: an increase in the corruption of the socio-economic system of the state by 1% caused HCSDI reduce by more than 1%. The results and conclusions may be proxy-assessments of the socio-economic consequences of violations of the stability of reproduction of human capital in the conditions of the growth of corruption in the country.

46

**Tetsuya Takaishi**, Hiroshima University of Economics, Faculty of Economics, Japan

**Ting Ting Chen**, Hiroshima University, , Japan

**Abstract:**We examine the relationship between trading volumes, number of transaction and volatility using daily stock data on the Tokyo Stock Exchange. Under the mixture of distributions hypothesis the trading volumes and number of transactions are used as a proxy for the number of information arrivals which affects stock volatility. The impact on volatility from trading volumes or number of transactions is measured in the GARCH model. We find that the GARCH effects, i.e. persistence of volatility is not completely removed by adding the trading volumes or number of transactions, which might indicate that the trading volumes and number of transactions do not adequately represent the number of information arrivals.

47

**Sergey Pasechnik**, Moscow Technological University, Problem Laboratory of Molecular Acoustics, Russian Federation

**Alexandre Zakharov**, Saint Petersburg Institute for Machine Sciences, Russian Academy of Sciences, Laboratory of Micromechanics of Materials , Russian Federation

**Dina Shmeleva**, Moscow Technological University (MIREA), Problem Laboratory of Molecular Acoustics, Russian Federation

**Anton Chopic**, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation

**Anna Vakulenko**, Saint Petersburg Institute for Machine Sciences, Russian Academy of Sciences, Laboratory of Micromechanics of Materials , Russian Federation

**Abstract:**The dynamics of the director reorientation in nematic liquid crystals (NLC) confined by cylindrical cavities of porous polymeric films under strong electric field E have been investigated theoretically. Two modes of electric field application were considered. The first (traditional) mode corresponds to the application of high frequency radio pulses, which induces strong dielectric moment, acting on a director. This mode was considered on the base of a hydrodynamic theory with appropriate boundary and initial conditions [1]. The ‘’turn on” and “ turn off” times were obtained and analyzed as functions of applied voltage and pore`s radius. The second mode corresponds to the periodical abrupt changes of a of the applied voltage’s polarity. In experiments with porous films filled with a liquid crystal 5CB [2] such mode resulted in appearance of strong peak –like decreasing of an optical transparence of the films. Two mechanisms of such unusual response based on assumption of electrically induced motion of ions and overall motion of a liquid were considered and applied to explain experimental results. 1. A. A. Vakulenko and A. V. Zakharov, Phys. Rev. E88, 022505 (2013) 2. Chopik A.P., Pasechnik S.V., Semerenko D.A., Shmeliova D.V., Dubtsov A.V., Srivastava A., Chigrinov V.G. Electro-optical effects in porous PET films filled with liquid crystal: new possibilities for fiber optics and THz applications // Optics Letters, Vol. 39, Issue 6, pp. 1453-1456 (2014).

**Acknowledgements:**This work was partially supported by the Ministry of Education and Science of the Russian Federation [grant no. 3.1921.2014/K] and the RFBR [project no. 16-02-00041].

48

**Samuel Akintunde**, University of Pretoria, Physics, South Africa

**Abstract:**A number of experimental works has shown the feasibility of a compound layer formation especially at the interface of two immiscible solid layers under the influence of radiation at a low irradiation temperature. Most of the reported works were carried out independently with either ion or electron beam irradiation technique. The reports shown that the compound layers were formed via cascade mixing during ion irradiation However, this explanation is not applicable to electron irradiation due to mass differences between the irradiating electrons and target atoms. An alternative approach is, therefore, proposed which intend to explain the compound layer formation process from the viewpoint of radiation induced process which is fundamental to all irradiation techniques. Radiation induced processes are many and they occur only for a very short time during the course of irradiation. Examples of such process includes radiation induced heating, radiation induced defect mediated process, radiation induced excitation and ionization process, radiation induced recombination and annihilation of defects, radiation induced defect clusters etc. Due to a number of these processes under irradiation, it is unclear which of them actually responsible for compound layer formation at the interface of bilayer system, such as metal-silicon system. In the course of our investigation on this subject, we developed a theoretical approach that take into account the contribution of radiation induced heating and radiation induced defects (both are central to other radiation induced processes) independently under a separate circumstance at a low irradiation temperature. The results obtained from this investigation show that the temperature associated with radiation induced heating is not high enough to activate the diffusion of lattice atoms in the irradiated layers. If lattice atoms remain in their respective bulk layers, the chance of compound formation at the reaction interface become zero. In other words, radiation induced heating is not a viable process for a compound layer formation under irradiation. However, the radiation induced defect mediated process proved effective for the compound layer formation process. The results show that the defect creation rate is directly proportional to the diffusivity of atoms in each irradiated layer. A substantial number of atoms diffuse from the irradiated layers as the defect creation rate rises in the target layers. The diffusion of lattice atoms to the reaction interface increases the chance of chemical transformation at the reaction sites and make the formation of compound layer more likely at the reaction interface. The results of this investigation is in good agreement with experiment.

49

**Inna Petrova**, Kazan Federal University, Institute of Phisics, Russian Federation

**Vladimir Bochkarev**, Kazan federal university, Radiophysics, Russian Federation

**Adel Akchurin**, Kazan Federal University, , Russian Federation

**Abstract:**The study of Earth's atmosphere is an acute problem due to global climate change. Modeling of global atmospheric circulation is one of the main tasks. The ionosphere is an important element in the vertical atmosphere coupling. Manifestations of atmospheric waves in the ionosphere can be detected as traveling ionosphere disturbances (TID) which dynamics should be taken into account in the atmospheric models. As a rule, the studies of TID are based on the analysis of ionosphere parameter variations (the critical frequency and maximum height) of ionospheric layers. These data, in turn, are obtained via processing of ionograms (height-frequency characteristic of the HF signal reflected from the ionosphere). In this paper, we suggest a method, which allows detection of wave disturbances throughout the whole height interval of the E and F regions, not only in the region of the layer maximum. To do this, similar variations are determined in time series of virtual reflection height for neighbor sounding frequencies. The estimation of direction and vertical projection of the disturbance propagation velocity is conducted using the delay of the similar variations at different frequencies from each other. To perform this analysis, we use data obtained from the "Cyclone" ionosonde of Kazan Federal University working in a mode with a higher temporal resolution, which provides favorable conditions for observation of small-scale perturbations. To interpret the experimental data, modeling of the ionospheric ionograms is performed taking into account ionospheric disturbances. Also, in this study the accuracy of determining the parameters of the wave indignation is estimated using statistical modeling.

50

**José Juan Peña Gil**, Universidad Autónoma Metropolitana Azc., Ciencias Básicas, Mexico

**Alberto Rubio Ponce**, Universidad Autónoma Metropolitana - Azcapotzalco, Ciencias Básicas, Mexico

**Jesús Morales**, Universidad Autónoma Metropolitana Azc., Ciencias Básicas, Mexico

**Abstract:**In statistical thermodynamics, the canonical partition function is fundamental for finding the most important properties of a system because from there the internal energy, entropy, specific heat and others thermodynamic functions are derived. In this work, we propose a non linear differential equation of Riccati-type with the aim of using the standard partition function Z(T) as its particular solution to obtain their corresponding generalization Zg(T); from there, others thermodynamic properties are generalized. As an useful application, we study the generalized thermodynamic functions that correspond to the internal energy, heat capacity, Helmholtz free energy and entropy, associated to the model of the ideal monatomic gas in D-dimensions. According to our results, the treatment of the thermodynamic properties using the standard partition functions by means of the ordinary statistical mechanics, is incomplete. As will be shown, in addition of that generalized statistical thermodynamic functions, asymptotically with the increasing of temperature are reduced to the standard ones, the generalization contains an extra term which is dominant at very low temperature. This fact and other findings will be discussed in detail.

**Acknowledgements:**This work was supported by the UAM-Azc., México, through the research project UAM-A-CB-2232004-09 and also by the SNI-Conacyt México.

51

**Michal Petru**, Technical University of Liberec, Institute for Nanomaterials, Advanced Technologies and Innovation, Czech Republic

**Abstract:**Currently, traditional materials (e.g. iron, steel, aluminium, wood) are very often replaced by composite materials in many industrial areas. The advantages of these materials consist mainly in their lightweight, high strength and flexibility, corrosion resistance and a long lifespan. The use of composites reaches its large development in the field of aerospace. This article discusses quality of the manufacturing process technology of a specially shaped composite frame in 3D space. The used technology is based on a winding of carbon, glass, organic filament rovings on a polyurethane core. Polyurethane core which is a geometry of frame with and without a circular cross section (this type of final composites frames is used for example to reinforce the doors and windows of airplanes). Quality production of said type of composite frame depends primarily on the correct winding of fibers on a polyurethane core. It is especially needed to ensure the correct angles of the fibers winding on the polyurethane core and the homogeneity of individual winding layers. The quality of fibers winding also depends on the material properties of polyurethane core and fibers (especially on adhesion of the fiber to the core). The article describes mathematical model for use an industrial robot in filament winding and how to calculate the trajectory of the robot. When winding fibers on the polyurethane core which is fastened to the robot-end-effector so that during the winding process goes through a fibre-processing head on the basis of the suitably determined robot-end-effector trajectory. We use the described numerical model and matrix calculus to enumerate the trajectory of the robot-end-effector to determine the desired passage of the frame through the fibre-processing head. The calculation of the trajectory was programmed in the Delphi development environment. Relations of the numerical model are important for use a real solving of the passage of a polyurethane core through fibre-processing head.

**Acknowledgements:**The results of this project No. LO1201 were obtained through the financial support of the Ministry of Education, Youth and Sports, Czech Republic in the framework of the targeted support of the “National Programme for Sustainability I”, the OPR&DI project Centre for Nanomaterials, Advanced Technologies and Innovation No. CZ.1.05/2.1.00/01.0005

52

**Rustem Sakhapov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Muhammat Gatiyatullin**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Marat Makhmutov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Regina Nikolaeva**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Abstract:**In this article the mathematical model of the motor grader. To study the dynamics of the system chassis grader in accordance with its kinematics built its mathematical dynamic model. On the basis of the d'Alembert-Lagrange equations formulated and solved a system of nonlinear differential equations of motion of the running motor grader system. The numerical values of the transfer function coefficients for the motor grader determined from the experimentally obtained curve acceleration, processed by area. The experimental curves were transient grader running system. These calculations of the mathematical modeling of the dynamics chassis graders were tested by comparing the transient, the calculated and experimentally obtained. These expressions of transfer functions grader suspension system dynamics simulation confirmed by experimental studies and with sufficient accuracy to be used in the design and development of new machines. Analyzing the results of the simulation can be said that the difference between the coordinate and calculated curves starting transients do not exceed 4% in average, indicating a sufficiently accurate description of the process. Investigation of the dynamics of the system chassis grader showed that the mathematical model it is described by a differential equation of the third order.

**Acknowledgements:**Kazan State University of Architecture and Engineering

53

**Rustem Sakhapov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Muhammat Gatiyatullin**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Regina Nikolaeva**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Marat Makhmutov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Abstract:**Transport is an important part of the global economy. Efficient road transport is crucial to economic and social development of countries. The development of road transport has a number of negative consequences: increase in the level of motorization, disparities in the development of the road network, unevenness of the road load, growth of road accidents, socio-economic losses. Therefore, the development of transport systems in terms of structural reforms of the economy should be carried out with the safety position. To prevent dangerous traffic situations using a variety of methods of modeling and forecasting of indicators of traffic safety. Indicators of road safety are a function of many variables: the number of traffic accidents, the number of victims of road accidents, the number of vehicles, the length of the road network, and the number of residents. For the assessment and prediction of accident models take into account the dynamics of change of indicators of safety of traffic in time determined by mutual some other indicators and impact indicators on changes in the level of road safety. Modern technologies of information processing methods of mathematical modeling are used to manage road safety. Modeling of transport processes makes it possible to understand the mechanisms of road accidents, the options for its development, ways to eliminate it. Mathematical models are the basis for planning increase road safety. The necessary parameters at the same time may be: the risk of accidents for some time; the expectation of delay time delivery of passengers and cargo, violations of traffic safety; expectation to prevent costs and lessen the effects of road accidents. As a result of mathematical modeling and the determination of measures to improve road safety held calculation of socio-economic efficiency.

**Acknowledgements:**Kazan State University of Architecture and Engineering

54

**George Alexandru Nemnes**, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), The Department of Computational Physics and Information Technologies, Romania

**Camelia Visan**, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), The Department of Computational Physics and Information Technologies, Romania

**Dragos-Victor Anghel**, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 077126 Magurele-Ilfov, Romania, The Department of Theoretical Physics, Romania

**Andrei Manolescu**, Reykjavik University, School of Science and Engineering, Iceland

**Abstract:**Motivated by recent developments in achieving highly defined patterns in hybrid graphene - hexagonal boron nitride (G-hBN) materials [1,2] we investigate the structural, electrical and vibrational properties of halogenated G-hBN nanoribbons. Having a lattice mismatch of less than 2%, graphene and hBN form an ideal mixture of materials with rather different conductive properties: while graphene has a high electrical and thermal conductance, hBN has insulating properties. We analyze here graphene-hBN nanorribons [3] with respect to the electrical and thermal conductance changes induced by passivating with different halogen atoms, of different mass and electronegativity. Our computational methodology combines molecular dynamics with density functional theory (DFT) at the atomic level. The results indicate the type of the halogen passivating atoms may constitute an important aspect to be considered in the future design of thermoelectric devices based on 2D materials. [1] Li Song, Lijie Ci, Hao Lu et al., Nanolett. 10, 3209 (2010). [2] Yongji Gong, Gang Shi, Zhuhua Zhang et al., Nature Communications 5, 3193 (2014). [3] G.A. Nemnes and S. Antohe, Mater. Sci. Eng. B 178, 1347 (2013).

**Acknowledgements:**This work was supported by the National Authority for Scientific Research and Innovation (ANCSI) under grant PN16420202.

55

**George Alexandru Nemnes**, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), The Department of Computational Physics and Information Technologies, Romania

**Dragos-Victor Anghel**, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 077126 Magurele-Ilfov, Romania, The Department of Theoretical Physics, Romania

**Abstract:**The concept of fractional exclusion statistics (FES) was first proposed by Haldane [1], based on a generalization of the Pauli exclusion principle and subsequently, the thermodynamics of the ideal FES gas was developed. We propose a drift-diffusion model for systems which obey fractional exclusion statistics (FES), in a framework where the species include classical degrees of freedom such as positions [3-5]. The transition rates are calculated and the relation between the step and acceptance probabilities on one hand and the diffusion and drift processes on the other hand are established. A Monte Carlo scheme is implemented for a system of particles with screened Coulomb interactions. In our approach the properties of interacting quantum gases are locally included using the FES methodology. The model is suitable to describe transient as well as stationary regimes for nanoelectronic device simulation. [1] F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991) [2] G. A. Nemnes and D.-V. Anghel, J. Stat. Mech. P09011 (2010) [3] G. A. Nemnes and D.-V. Anghel, J. Phys.: Conf. Series 410, 012120 (2013) [4] D.V. Anghel, G.A. Nemnes and F. Gulminelli, Phys. Rev. E 88, 042150 (2013) [5] G. A. Nemnes and D.-V. Anghel, Rom. J. Phys. 60, 691 (2015)

**Acknowledgements:**This work was supported by the National Authority for Scientific Research and Innovation (ANCSI) under grant PN16420202.

56

**Andrey LUGOVSKOY**, NUST MISIS, Department of theroetical physics and quantum technology, Russian Federation

**Oleg Krasilnikov**, NUST MISIS, Department of theroetical physics and quantum technology, Russian Federation

**Yuri Vekilov**, NUST MISIS, Department of theroetical physics and quantum technology, Russian Federation

**Abstract:**In the present work we investigate the elastic properties of the loaded crystals. The general method of the n-order (n≥2) elastic constants calculations for a loaded crystal is given in the framework of the nonlinear elasticity theory. The two calculation methods are realized using the relations: energy-finite deformations, and stress-finite deformations. The energy and the mechanical stresses at different deformations are defined in the framework of density functional theory. The second and third order elastic constants of bcc Nb, Ta, Mo, W are calculated in the pressure interval 0-600 GPa. The Gruneisen parameters for the long-wavelength acoustic modes are estimated in this interval, using the obtained results. The second and third order Lame constants of polycrystalline samples are estimated in the pressure interval 0-600 GPa. Note that the data for the Lame constants were absent in the literature.

57

**Eleonora Koltsova**, D. Mendeleyev University of Chemical Technology of Russia , Informational and Computer Technologies, Russian Federation

**Andrey Kostin**, D. Mendeleyev University of Chemical Technology of Russia, ICT, Russian Federation

**Irina Soboleva**, D. Mendeleyev University of Chemical Technology of Russia, ICT, Russian Federation

**Abstract:**On the basis of heterogeneous media mechanics, the equations for conservation of mass, momentum and energy for continuous and dispersed phases taking into account dispersed phase particles aggregation were obtained in the work involved. Based on these equations and using the apparatus of particles thermodynamics, the expression for system entropy production in which particle aggregation occurs was found. From the analysis of entropy production, the ratio for thermodynamic aggregation driving force and thermodynamic aggregation flow (using the Onsager relations) were obtained. The expression for the aggregation "constant" was defined in the form of: K=LXag=L(U2-U1), where K – the aggregation "constant", L – phenomenological factor, Xag – aggregation driving force, U2 – the proportion of particles interaction kinetic energy in the aggregation, dissipated in the system internal energy, U1 – the particles interaction energy consisting of three elements: electrostatic repulsive energy, molecular attraction energy, the structural component (arising due to the interface layers overlap). On the basis of minimum entropy production variational principle two equations are obtained: Xag=0 , dXag/dh=0 (1) (where h – distance between particles) to determine the limitary sustainable size under aggregation. For alko-oxide sol-gel method to the process of titanium dioxide obtaining with the stabilizer - nitric acid on the basis of equations (1), the range of nitric acid concentration changes was calculated [0.1-0.4 mol/l], with which it is possible to receive the aggregate stable TiO2 particles in the size range (14-60 nm). To improve aggregation mechanisms of alko-oxide sol-gel method for TiO2 production, the mathematical model was developed for aggregation process based on particles distribution function not only in size but also in clusters structural components of the particles: titanium atoms, oxygen atoms, hydrogen atoms and alkyl groups. This is such a representation of distribution function that has made it possible to prove that the aggregation mechanism OH-OH prevails over the aggregation mechanism OH-OR. The software package has been developed to solve the model equations with application of parallel computation technology (which allowed to calculate the clusters with containing titanium atoms ~ 1 million). Based on the investigations conducted, optimal conditions for titanium dioxide nanoparticles production were found.

**Acknowledgements:**This work was carried on with partial support of the Russian Foundation for Basic Research (RFBR) grant № 14-07-00960.

58

**Stam Nicolis**, CNRS-LMPT Tours, Département de Physique, Université de Tours, France

**Abstract:**We study the dynamics of nanomagnets, in contact with stochastic external fields, whose statistics is described by colored noise. We deduce the hierarchy of evolution equations to equilibrium, for the moments of the magnetization and focus on the conditions that allow us to close the hierarchy consistently and to distinguish Gaussian from non-Gaussian fluctuations.

59

**Vasilii Zubkov**, St. Petersburg State Electrotechnical University, Department of Micro- and nanoelectronics, Russian Federation

**Abstract:**Owing to the intense advancement of nanotechnology in the recent decades, the impressive results have been attained in the design and fabrication of quantum-confinement heterostructures and devices based on them. Continuing technological progress requires the development of modern techniques for deep analysis of nanoscale structures. We consider the achievement in comprehensive characterization of electronic properties of semiconductor device by mutual experimental measurements and numerical simulation with subsequent fitting.

**Acknowledgements:**This work was supported by Act 220 of the Russian Government (Agreement No. 14.B25.31.0021 with the host organization IAP RAS).

60

**Andrey Gorshenin**, FRC CSC RAS, Institute of Informatics Problems, Russian Federation

**Victor Korolev**, Lomonosov MSU, Computational mathematics and cybernetics, Russian Federation

**Abstract:**The paper presents a methodology for the stochastic analysis of random processes based on the method of moving separation of finite normal mixtures. Within the framework of our approach, the one-dimensional distributions of observed processes are approximated by finite location-scale mixtures of normal distributions. The theoretical background of these models is based on that finite normal mixtures are convenient approximations to general location-scale normal mixtures or normal variance-mean mixtures which are limit laws for the distributions of sums of a random number of independent random variables or non-homogeneous and non-stationary random walks and hence, are reasonable asymptotic approximations to the statistical regularities in observed real processes. We show that this approach can be also applied to positive time series, if the initial data is primarily noised by adding i.i.d. normal random variables with known parameters. This approach allows to analyze the regularities in the variation of the parameters and capturing the low-term variability in the case of complex internal structure of data.

**Acknowledgements:**The research is supported by the Russian Foundation for Basic Research (projects 15-07-04040, 15-37-20851).

61

**Aicha Guenachi**, Université d'Oran des Sciences et de la Technologie, Faculté de Physique - Département de Physique Energétique, Algeria

**Siham Zenak**, Université d'Oran des Sciences et de la Technologie, Faculté de Physique - Département de Physique Energétique, Algeria

**Sid Ahmed Sabeur**, Université d'Oran des Sciences et de la Technologie , Faculté de Physique - Département de Physique Energétique, Algeria

**Abstract:**In this work, we have studied the adsorption of a single flexible star polymer chain by a flat surface. The molecular dynamics simulation has been validated for the case of a free star polymer chain using the diffusion experiment. The scaling laws found are in agreement with the Flory theory predictions and the Rouse model. For the adsorption, preliminary results were obtained for chains of different sizes N=31 to N=199 and different functionalities (f=3,4,6,8,10). For the case of semi-flexible star polymer chains, further investigation is needed to locate the critical point of adsorption when varying the potential interaction strength between the chain and the surface.

**Acknowledgements:**The authors thank Professor Andrey Milchev for fruitful discussions and insights. The computation was made possible on IBN BAJA supercomputer in the HPC Center at USTOMB.

62

**Derya Gemici Deveci**, İstanbul Kemerburgaz University, Physics, Opticianry, Turkey

**Ekrem Aydiner**, Istanbul University, Department of Physics, Turkey

**Abstract:**In this study we consider modified Pöschl-Teller potential because of these potentials widely appear in the analysis of soliton bearing nonlinear equations, e.g., Bose-Einstein condensates and in quantum problems on curved background. Firstly we obtain radial wave function of ground and excited states for modified Pöschl-Teller potential and we plot probability of wave function in position and momentum spaces. We obtain non-extensive [2] entropies and show that these entropies satisfy the non-extensive uncertainty relation [3]. We also deal with non-extensive complexity measure which is depending on disequilibrium. We compute statistical complexity depend on entropy index q by using Lopez-Ruiz, Mancini and Calbet [4] measure to analyze the structural behavior of probability distributions for the modified Pöschl-Teller potential. We show that complexity increases for decreasing q, which indicates that number of equiprobable states are growing in the system. [1] G. Pöschl and E. Teller, "Bemerkungen zur Quantenmechanik des anharmonischen Oszillators". Zeitschrift für Physik Vol: 83 (1933) 143. [2] C. Tsallis, "Possible generalization of Boltzmann-Gibbs statistics". Journal of Statistical Physics Vol: 52 (1988) 479487. [3] A. K. Rajagopal, "The Sobolev inequality and the Tsallis entropic uncertainty relation". Physics Letters A Vol: 205 (1995) 32. [4] R. Lopez-Ruiz, H. L. Mancini, X. Callbet, “A statistical measure of complexity”. Physics Letters A Vol: 209 (1995) 321.

63

**Violetta Vasilenko**, D. Mendeleev University of Chemical Technology of Russia, Informational Computer Technologies, Russian Federation

**Andrei Scherbakov**, D. Mendeleyev University of Chemical Technology of Russia , Informational and Computer Technologies, Russian Federation

**Eleonora Koltsova**, D. Mendeleyev University of Chemical Technology of Russia , Informational and Computer Technologies, Russian Federation

**Abstract:**In this paper we used CFD software FLUENT ANSYS to simulate phenomena occurring in membrane-electrode assembly of hydrogen-air fuel cell (MEA). Besides that the mathematical model was complemented with the equations describing decrease of catalysts electrochemical surface area (ECSA) due to coalescence of platinum nanoparticles. With the help of a mathematical model we have obtained and compared discharge curves data of two MEA’s by using the Pt/C commercial catalyst and catalytic system synthesized on carbon nanotubes (CNT). The calculated values are in good agreement with the experimental data. In order to determine ECSA of the cathode catalyst a cyclic voltammetry test has been taken. Cathodes of two types were subjected to accelerated stress testing in order to determine the characteristics of the degradation and electrochemical parameters changes depending on CNT amount in support. Comparison of calculated voltage curves for two catalysts shows that before cycling the characteristics of CNT-based catalyst are similar to the commercial catalyst in high-voltage area, and in the area of high current density they are lower only by 8-10% compared to commercial one. However, predicted by mathematical modeling the voltage characteristics of the synthesized catalyst are significantly higher than those for commercial one after 5000 cycles. The predicted reduction of discharge characteristics of the synthesized CNT catalyst at high current density area is about 10% after 5000 cycles. Thus, the results of experimental studies and mathematical modeling has showed that synthesized CNT-based catalyst systems have higher stability and can be a good alternative to the commercial catalysts.

64

**Guzel Bulgakova**, Ufa State Aviation Technical University, Department of Mathematics, Russian Federation

**Abstract:**Extensive man-made fractures are formed in productive reservoirs as a result of their long -term development under high depression. Such main fractures can extend over long distances comparable to distances between injection and production wells that leads to catastrophic water cut in the produced liquid. For the isolation of high-permeability channels, nonlinear-viscous and plastic non-Newtonian fluids are injected into the fractures. A mathematical modeling of the non-Newtonian agent injection into the main fracture is very important for predicting an ultimate injected volume distribution and for creating stable gel barriers. This paper describes a mathematical model of the main fracture isolation in porous media by water-based gels (gelant). While modeling injection, water infiltration from gel pack through fracture walls is taking into account, due to which the polymer concentration changes and the residual water resistance factor changes as a consequence. The salutation predicts velocity and pressure fields of the non-Newtonian incompressible fluid filtration for conditions of a non-deformable formation as well as a gel front trajectory in the fracture. The mathematical model of agent injection into the main fracture is based on the fundamental laws of continuum mechanics conservation describing the flow of non-Newtonian and Newtonian fluids separated by a interface plane in a flat channel of width and length with permeable walls of porosity (fracture porosity) equal to . The mathematical model is based on a one-dimensional isothermal approximation, with dynamic parameters - pressure and velocity - averaged over the fracture section. This study was supported by the Ministry of Education and Science of the Russian Federation as the base part of the state orders for higher educational institutions in 2016 and the Russian Foundation for Basic Research (Project 14-01-97012_r_povolzh’e.a).

65

**Yuliya Zhiganshevna Pchelkina**, Samara State Aerospace University (SSAU), Applied Mathematics, Russian Federation

**Abstract:**We considered the new equation of distribution of optical impulses in silica fibers. We also found its exact solitonic solution and analyzed extreme cases.

66

**Tatyana Gnitetskaya**, Far Eastern Federal University, School of Natural Sciences , Russian Federation

**Elena Ivanova**, Far Eastern Federal University , School of Natural Sciences, Russian Federation

**Abstract:**An application of the graph model of inter-subject links to University courses of Physics and Chemistry is presented in this article. A part of inter-subject space with directions of inter-subject links from Physics to Chemistry in the group of physical concepts has been shown. The graph model of inter-subject links includes quantitative indicators. Its numerical values are given in the article. The degree of connectedness between the data of Physics and Chemistry courses is discussed for the courses considered. The effect of the courses placement within a curriculum on the value of their connectedness is shown. The placement of courses within a curriculum can provide the study of the courses at the same time or consecutive study, when one course precedes another.

67

**Greg Anderson**, Bhaktivedanta Institute, Chemistry, India

**Raghu Behera**, Birla Institute of Technology and Science, Pilani - K. K. Birla Goa Campus, Chemistry, India

**Ravi Gomatam**, Bhaktivedanta Institute, , United States

**Abstract:**Density function theory, a subfield of quantum mechanics (QM), in combination with molecular mechanics (MM) has opened the way to engineer new artificial enzymes [1-2]. Herein, we report calculations done using QM/MM to examine whether the regioselectivity and rate of chlorination of the enzyme chloroperoxidase can be improved by replacing the vanadium of this enzyme with niobium in the active site. Our calculations show that a niobium substituted chloroperioxidase will be able to enter the initial steps of the catalytic cycle for chlorination. Although the protonation state of the niobium substituted ligand of the putative enzyme is calculated to be different than that of the natural vanadium substituted enzyme, our calculations show that the catalytic cycle can still proceed forward. Using natural bond orbitals, we analyze the electronic differences between the niobium substituted enzyme and the natural enzyme. We conclude by briefly examining how good of a model QM/MM provides for understanding the mechanism of catalysis in haloperoxidases. [1] Friesner, R.A.; Guallar, V.: Annu. Rev. Phys. Chem. Vol. 56 (2005), p. 389. [2] Breslow, R. (ed): Artificial Enzymes (Wiley-VCH: Weinheim, 2005).

68

**Sergey Gladkov**, Moscow aviation institute (national research university) (MAI), Mathematical modelling , Russian Federation

**Abstract:**It has been proved that the solution of the quasi-classical kinetic equation for Bose and Fermi statistics can be represented in the general form, using the relaxation time approximation. The general solution found for the distribution function helps calculate any non – equilibrium characteristics of metals, magnets, and dielectrics in any order of the perturbation theory according to the relaxation time.

69

**Yulia Maslennikova**, Kazan federal university, Institute of Physics, Russian Federation

**Vladimir Bochkarev**, Kazan federal university, Radiophysics, Russian Federation

**Abstract:**In recent years significant advanced have been made in the development of nonlinear data processing techniques. Such techniques are widely used in digital data filtering and image enhancement. Many of the most effective nonlinear filters based on order statistics. The widely used median filter is the best known order statistic filter. Generalized form of these filters could be presented based on Lloyd’s statistics. Filters based on order statistics have excellent robustness properties in the presence of impulsive noise. In this paper, we present special approach for synthesis of order statistics filters using artificial neural networks. Optimal Lloyd’s statistics are used for selecting of initial weights for the neural network. Adaptive properties of neural networks provide opportunities to optimize order statistics filters for data with asymmetric distribution function. Different examples demonstrate the properties and performance of presented approach.

70

**Daniel Kraft**, University of Graz, Institute of Physics, Austria

**Willibald Plessas**, University of Graz, Institute of Physics, Austria

**Abstract:**The stochastic variational method (SVM) as elaborated, e.g., by Suzuki and Varga [1] has proven to be a very efficient and accurate tool to calculate bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenergies of Hermitean Hamiltonians. From molecular, to atomic, nuclear, and particle physics there is a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be described by non-Hermitean quantum Hamiltonians. They correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the energy expectation value provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies. [1] Y. Suzuki and K. Varga: Lect. Notes in Phys. M54 (1998) 1-310

71

**Carolina Ribeiro**, Minho University, Department of Mathematics and Applications and Centre of Mathematics, Portugal

**Abstract:**In this work we consider an epidemic model of pneumococcal infection (lung infection) dynamics in a population that include a class of quarantined individuals. The objective is, using control optimal, to control the rate in-hospital transmission of pneumococcal infections with educational campaign to increase hand hygiene.

72

**Alain Michez**, Université Montpellier, Institut d'Electronique et des Systèmes, France

**Jérôme Boch**, Université Montpellier, Institut d'Electronique et des Systèmes, France

**Antoine Touboul**, Université Montpellier, Institut d'Electronique et des Systèmes, France

**Frédéric Saigné**, Université Montpellier, Institut d'Electronique et des Systèmes, France

**Abstract:**Mesh generation for TCAD modeling is challenging. Because densities of carriers can change by several orders of magnitude in thin areas, a significant change of the solution can be observed for two very similar meshes. The mesh must be defined at best to minimize this change. To address this issue, a criterion based on polynomial interpolation on adjacent nodes is proposed that adjusts accurately the mesh to the gradients of Degrees of Freedom. Furthermore, a dynamic mesh that follows changes of DF in DC and transient mode is a powerful tool for TCAD users. But, in transient modeling, adding nodes to a mesh induces oscillations in the solution that appears as spikes at the current collected at the contacts. This paper proposes two schemes that solve this problem. Examples show that using these techniques, the dynamic mesh generator of the TCAD tool ECORCE handle semiconductors devices in DC and transient mode.

73

**Regina Kleinhappel**, University of Graz, Institute of Physics, Austria

**Willibald Plessas**, University of Graz, Institute of Physics, Austria

**Abstract:**The description of hadron resonances represents a big challenge in all current approaches to quantum chromodynamics (QCD). Hitherto the spectroscopy of mesons, usually considered as quark-antiquark systems, and of baryons, usually considered as three-quark systems, has been treated through excitation spectra of bound states (namely, confined few-quark systems), corresponding to poles of the quantum-mechanical resolvent at real negative values in the complex energy plane. As a result the wave functions, i.e. the residua of the resolvent, have not exhibited the behaviour as required for hadron resonances with their multiple decay modes. This has led to disturbing shortcomings in the description of hadronic resonance phenomena. We have aimed at a more realistic description of hadron resonances within relativistic constituent-quark models taking into account explicitly meson-decay channels. The corresponding coupled-channels theory is based on a relativistically invariant mass operator capable of producing hadron ground states with real energies and hadron resonances with complex energies, the latter corresponding to poles in the lower half-plane of the unphysical sheet of the complex energy plane. So far we have demonstrated the feasibility of the coupled-channels approach to hadron resonances along model calculations producing indeed the desired properties. The corresponding spectral properties will be discussed in this contribution. More refined studies are under way towards constructing a coupled-channels relativistic constituent-quark model for meson and baryon resonances.

74

**Federico Grasselli**, Università degli Studi di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Italy

**Andrea Bertoni**, CNR-Nano S3, , Italy

**Guido Goldoni**, Università degli Studi di Modena e Reggio Emilia / CNR-Nano S3, , Italy

**Abstract:**When composite particles –such as excitons, small molecules, nuclei – are scattered by an external potential, energy may be transferred between the center-of-mass (CoM) and internal degrees of freedom (DoF).[1] Despite the broad range of applications, the development of numerical methods is recent and, due to computational load, applications are limited to few degrees of freedom, and/or uncontrolled approximations are performed. In this contribution we discuss the exact quantum dynamics of a composite particle through numerical unitary evolution of the time-dependent Schroedinger equation, taking fully into account its internal structure. We have implemented a numerical approach which relies on the Fourier split-step algorithm, whereby the evolution operator is expressed as the product of terms which are diagonal either in real or Fourier space. The core of the algorithm reduces to switching between real and reciprocal space representation of the wave-packet, and the wave-packet evolution reduces to array-by-array multiplications, allowing for very good scaling on parallel architectures. We have simulated the exact dynamics of a Mott exciton in semiconductor nanostructures, an electron-hole pair interacting through the long-range Coulomb interaction, scattering in prototypical potential landscapes, such as barriers, wells, single/double slits, anti-dots, impurities.[2] Depending on the scattering potential strength and shape, the exciton can be accelerated, reflected, transmitted, or dissociate. Besides, the internal dynamics may give rise to complex phenomena in the scattering region, and complex scattering phenomena, which are unique to complex systems, may arise. Using combinations of exact and mean-field propagations,[3] we disclose, in particular, the role of internal virtual dynamics in determining scattering resonances and diffraction patterns which are unique to quantum complexes. Furthermore, a systematic way to improve mean-field calculations, which reduces the computational load by orders of magnitude, will be discussed. Application to other fields, such as scattering phenomena in molecular systems, will also be discussed. [1] N. Saito, and Y. Kayanuma. Resonant tunnelling of a composite particle through a single potential barrier. Journal of Physics: Condensed Matter, 6(20):3759, 1994. [2] F. Grasselli, A. Bertoni, and G. Goldoni. Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures. The Journal of Chemical Physics, 142(3):034701, 2015. [3] F. Grasselli, A. Bertoni, and G. Goldoni. Exact two-body quantum dynamics of an electron-hole pair in semiconductor coupled quantum wells: a time-dependent approach. Submitted.

75

**Lukas Valasek**, Institute of Informatics of Slovak Academy of Sciences, Department of Numerical Methods and Algorithms, Slovakia

**Abstract:**Current HPC clusters are capable to reduce execution time of parallelized tasks significantly. This paper deals with a comparison of impact of computing resources allocation strategies on efficiency of fire simulation modelled by Fire Dynamics Simulator and parallelized by MPI model. Two selected strategies, the --map-by core, --bind-to core and the --map-by socket, --bind-to socket are tested using an example of corridor fire simulation. The tests were performed on the HPC cluster at Institute of Informatics of Slovak Academy of Sciences in Bratislava (Slovakia) and realized on selected number of cluster computing cores. The results confirmed a great potential of parallelization to reduce the execution time of simulation. However, the tests also showed that increasing number of cores about one computing core does not necessarily reduce the execution time of simulation. The simulation results also indicate different efficiency of parallelization in regard of the used strategy for cluster computing resources allocation.

76

**Narek Martirosyan**, Yerevan Physics Institute(YerPhi), Computational Physics and IT Department, Armenia

**Abstract:**The Kolmogorov-Smirnov (K-S) test is used to compare how well the empirical cumulative distribution function of a data sample fits the cumulative distribution function of the reference distribution. The K-S test is also widely used as a powerful statistical test to check the quality of pseudo-random number generators. We propose a new approximate approach for the numerical estimation of the multidimensional K-S test. It uses a using binning technique and does reduce essentially the time and memory requirements.

77

**Svetlana Zubkova**, Frantsevich Institute for Problems of Materials Science NASU, Department of functional oxide materials, Ukraine

**Abstract:**. Based on data of scanning tunneling microscopy, ab initio calculations of the electronic structure were performed for the first time for four variants of Te-terminated polar CdTe(111)B surface, namely, ideal, relaxed, reconstructed, and reconstructed with the subsequent relaxation. In the approximation of a layered superlattice, the surfaces were simulated by a film with a thickness of 12 atomic layers and a vacuum gap of ~16 Å. Dangling bonds of Cd - atoms were closed by adding, on the opposite side of the film, 24 fictitious hydrogen atoms, each having a charge of 1.5 electrons. Ab initio calculations were performed with the ESPRESSO QUANTUM program based on the density functional theory. In each of the variants, the equilibrium coordinates of the upper four free - standing layers were determined. It has been shown that the reconstruction splitted the 4 upper free - standing layers into 22 layers on 2 atoms in each layer. For four variants of the surfaces, the band structures were calculated and analyzed, as well as the total densities of states of the surfaces and densities of states of individual layers.

**Acknowledgements:**All the calculations were performed on the Computing Grid Cluster at the Institute for Problems of Materials Science of the National Academy of Sciences of Ukraine.

78

**Evangelos Melas**, Central Greece University of Applied Sciences, Engineering Informatics, Greece

**Abstract:**The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space$-$times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. For this purpose McCarthy constructed generalisations of $B$ appropriate to these other signatures and complex space$-$times. Here, we follow this programme for 3-dim G.R. and construct for this case, for all signatures and complex space-times, all possible asymptotic symmetry groups in all asymptotic directions with all possible notions of asymptotic flatness. There are such groups. The relationships between these various groups are described. Strongly continuous unitary irreducible representations (IRs) of B(2,1), the analogue of B in three space-time dimensions, are analysed in the Hilbert topology. It is proved that that all induced IRs of B(2,1) arise from IRs of compact `little groups'. It follows that some IRS of B(2,1) are controlled by the IRs of the finite symmetry groups of regular polygons in ordinary euclidean 2-space. It is proved that all IRS of B(2,1) are obtained by Mackey's semi-direct product theory notwithstanding the fact that B(2,1) is not locally compact in the employed Hilbert topology. The paper closes with the explicit construction of the IRs of B(2,1).

79

**Seung-Yeon Kim**, Korea National University of Transportation, School of Liberal Arts and Sciences, Korea, Republic of

**Abstract:**Understanding the folding of a protein into its three-dimensional tertiary native structure only with its one-dimensional amino-acid sequence information is one of the most important problems in modern science. Simplified model proteins have been popularly used to understand the physical principles of protein folding. The HP model is the most simplified model for protein folding, consists of two types of amino acids, the hydrophobic (A) and hydrophilic (B) monomers, and is configured as self-avoiding walks on lattices. A more generalized off-lattice AB protein model is based on a realistic potential energy including the bending energy and the van der Waals interaction energy. Here, we study the C-terminal beta-hairpin of protein G in an off-lattice AB protein model using conformational space annealing, a global optimization method.

80

**Sanasar Babajanyan**, Yerevan Physics Institue , Theoretical Physics Department, Armenia

**Abstract:**The functioning of many heat-engines (e.g. car engines) demands either on-line control with external fields, or externally imposed fitting between internal parameters and temperatures of the thermal baths. We study a stochastic model for heat engine that is described via coupled Markov processes. The heat-engine functions without external on-line control and does not require external fitting, i.e. the overall Markov process is autonomous. The structure of the engine adapts to a given non-equilibrium thermal environment due to a feedback from its functional part. Such engines can be useful for fuelling devices employing unknown and/or scarce resources; e.g. they can adapt to results of they own activity that makes the bath temperatures closer. Our study is motivated by the physics of photosynthesis, which is a complex heat-engine also demonstrating adaptive features.

81

**Mohamed BOUALEM**, Research Unit LaMOS, University of Bejaia, Departement of Technology, 06000 Bejaia, Algeria

**Abstract:**This paper deals with the study of M/M/1/N and M/M/c/N queueing models with server vacations, bernoulli feedback, balking, reneging and retention of reneged items, the steady state solutions of our queueing models are derived, many performance measures are carried out.

82

**Alexey Sukhinin**, Southern Methodist University, Mathematics, United States

**Alejandro Aceves**, Southern Methodist University, Mathematics, United States

**Jean-Claude Diels**, University of New Mexico, Electrical and Computer Engineering, United States

**Ladan Arissian**, University of New Mexico, Electrical and Computer Engineering, United States

**Abstract:**We present numerical simulations of co-propagation of a nanosecond UV pulse and femtosecond IR pulse. The model proposed assumes the long UV pulse to act as a guide. We explore the effect of such guiding in suppressing known IR spatio-temporal instabilities.

**Acknowledgements:**This work was supported by ARO MURI Light Filamentation Science, contract No W911NF1110297 and partly by US Department of Energy grant, contract No DE-SC0011446.

83

**Georgios Lukes-Gerakopoulos**, Charles University in Prague, institute of theoretical physics, Czech Republic

**Abstract:**The Mathisson-Papapetrou (MP) equations are describing the motion of a spinning particle in a curved spacetime. Thus, these equation can approximate the motion of a stellar compact object moving in the spacetime background of a supermassive Kerr black hole. For defining the wordline along which the MP equations evolve the body, we need a spin supplementary condition (SSC). There are various SSCs and each of them define a different worldline for a compact object. We will discuss the impact of the SSCs on the dynamics and on the gravitational wave production of circular equatorial orbits.

84

**Hovik Matevossian**, Moscow Aviation Institute (National Research University - MAI), Mathematical Modeling, Russian Federation

**Abstract:**We study the asymptotic behavior of solution $u(x,t)$ of the Cauchy problem for the one-dimensional second-order hyperbolic equation with periodic coefficients at $t\to\infty$.

85

**Yannick Carissan**, Aix Marseille Université - CNRS, Chemistry, France

**Nicolas Goudard**, Aix Marseille Université, Institut des Sciences Moléculaires de Marseille (iSm2) UMR 7313, France

**Denis Hagebaum-Reignier**, Aix Marseille Université, Institut des Sciences Moléculaires de Marseille (iSm2) UMR 7313, France

**Stéphane Humbel**, Aix Marseille Université, Institut des Sciences Moléculaires de Marseille (iSm2) UMR 7313, France

**Abstract:**The HuLiS program is presented as a tool to decompose a delocalized wave function as a linear combination of localized electronic structures. The principles of the energy based HL-CI and the overlap based schemes HL-P are developed. The results obtained for a set of 10 relevant organic molecules are shown to compare very well with high level quantum chemistry calculations. A trust factor τ is introduced and its use is shown on the allyl radical case where symmetry must be taken into account.

86

**Sergo Gotoshia**, Ivane Javakhishvili Tbilisi State University, R. Aglaze Institute of Inorganic Chemistry and Electrochemistry, Laser Center, Georgia

**Abstract:**Abstract: Thiosemicarbazon (TSC) is known as one the of active complex-productive ligands with different metals. TSC and its derivatives are known as antibacterial, antiviral, antifunginal, antinevrological, biologically active compounds. The complex-productivity ability of TSC with transition metals enhances their pharmacological activity . We have recorded the IR spectrum of TSC on the Fourier IR spectrometer Varian 660 and The Raman spectrum – on the homemade Raman-system, with the excitation wavelength 632.8 nm. For quantum-chemical computations the semi-empirical program MOPAC 8 Ultra has been used. On the basis of theory AM1 the geometrical parameters of optimized molecular structures- bound lengths and angles have been computed. Also the theoretical spectrum and normal frequencies have been computed. The experimental and theoretical data are in satisfactory fit.

87

**Dimitrios Vlachos**, University of Peloponnese, Department of Informatics and Telecommunications, Greece

**Amanda Mavrogianni**, Ionideios Model School, , Greece

**Abstract:**A family of path fitted methods in the numerical scheme is formulated for the solution of discrete Lagrangian and Hamilton differential equations using variational integrators techniques. In our new formulation the action integral is approximated with appropriate choices of functions. The method is applied to the 2-body problem with high eccentricity and to the 5-outer planet system. The results exhibit an improved behavior of the calculated solutions, especially in the case of total energy of the integrated systems.

88

**Hyunju Lee**, Ewha Womans University, Department of Statistics, Korea, Republic Of

**Ji Hwan Cha**, Ewha Womans University, Department of Statistics, Korea, Republic Of

**Abstract:**A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. Cascading failures usually begin when one part of the system fails. When this happens, remaining components must then take up the slack for the failed component. This in turn overloads these components, causing them to fail as well, prompting additional components to fail one after another. In this paper, we discuss the lifetimes of systems composed of components having interdependence and cascading effect. For this, a class of bivariate distributions is constructed based on the notion of conditional failure rate. We show that the members in a suitably defined subclass of the developed bivariate distributions satisfy the bivariate lack of memory property. Based on the developed class of distributions, we study the lifetimes of systems having interdependence and cascading effect. We compare the lifetimes of systems having interdependence and cascading effect with those of systems having independent components.

**Acknowledgements:**This work was supported by the BK21 Plus Project through the National Research Foundation of Korea (KRF) funded by the Ministry of Education (22A20130011003).

89

**Omar Pavón**, Universidad Autónoma del Estado de México, Física, Mexico

**Abstract:**The internal dynamics of the DNA base pairs is studied starting from the generalized coupled plane base-rotator model of DNA's B-form, earlier obtained by Yomosa and later improved by Takeno and Homma. The generalized hamiltonian expressed in terms of quasi-spin operators is averaged over the generalized coherent states in the Perelomov's sense in order to obtain the classical nonlinear evolution equations of this molecular system. This approach provide us with the equation of motion reduced to a nonlinear Schrodinger equation with a saturable nonlinearity. This equation under certain restrictions in the parametric space, support traveling periodic triangular, bell, bubble and kink like solutions.

90

**Maximo Aguero Granados**, Universidad Autónoma del Estado de México, Física, Mexico

**Omar Pavón**, Universidad Autónoma del Estado de México, Física, Mexico

**Abstract:**The internal dynamics of the DNA base pairs is studied starting from the generalized coupled plane base-rotator model of DNA's B-form, earlier obtained by Yomosa and later improved by Takeno and Homma. The generalized hamiltonian expressed in terms of quasi-spin operators is averaged over the generalized coherent states in the Perelomov's sense in order to obtain the classical nonlinear evolution equations of this molecular system. This approach provide us with the equation of motion reduced to a nonlinear Schrodinger equation with a saturable nonlinearity. This equation under certain restrictions in the parametric space, support traveling periodic triangular, bell, bubble and kink like solutions.

91

**Rong Chen**, Australian National University, Research School of Biology, Australia

**Derong Lu**, University of Queensland, , Australia

**Zili Xie**, Wuhan University, , China

**Jing Feng**, Wuhan University, , China

**Zhongfan Jia**, University of Queensland, , Australia

**Junming Ho**, Australian National University, , Australia

**Michelle Coote**, Australian National University, , Australia

**Yingliang Wu**, Wuhan University, , China

**Michael Monteiro**, The University of Queensland, Australian Institute for Bioengineering and Nanotechnology (AIBN), Australia

**Shin-Ho Chung**, Australian National University, , Australia

**Abstract:**Four end-functionalized star polymers that could attenuate the flow of ionic currents across biological ion channels were first de novo designed computationally, then synthesized and tested experimentally on mammalian K+ channels. The 4-arm ethylene glycol conjugate star polymers with lysine or a tripeptide attached to the end of each arm were specifically designed to mimic the action of scorpion toxins on K+ channels. Molecular dynamics simulations showed that the lysine side chain of the polymers physically occludes the pore of Kv1.3, a target for immuno-suppression therapy. Two of the compounds tested were potent inhibitors of Kv1.3. The dissociation constants of these two compounds were computed to be 0.1 µM and 0.7 µM, respectively, within 3-fold to the values derived from subsequent experiments. These results demonstrate the power of computational methods in molecular design and the potential of star polymers as a new infinitely modifiable platform for ion channel drug discovery.

**Acknowledgements:**Supported by the National Health and Medical Research Council, the National Computational Infrastructure (NCI), and The Medical Advances Without Animals Trust (MAWA).

92

**Evgeny Zharikov**, Mendeleev University of Chemical Technology of Russia, Crystals Chemistry and Technology, Russian Federation

**Abstract:**Physical and mechanical properties of ceramic-matrix composites on the basis of Al2O3, reinforced by carbon nanotubes, essentially depend on the porosity of the composite. Mathematical model of spark plasma sintering based on the balance equation of the number of pores, to calculate the distribution function of the pore size in time of the process. Two stages of the process: heating and temperature exposure are considering. The functions for shrinking rate of pores in these two stages, depending on the current diameter of the pores, the heating rate of composite, the current temperature and the volume fraction of carbon nanotubes have been found out. The equation for the change in pore size distribution function is: df/dt - dfη(t,l)/dl = 0 , where f (t, l) - pore size distribution function; t - time of the process, l - pore diameter, η - shrinking rate of pores. To solve this equation in partial derivatives of the first order we developed the numerical scheme with the second approximation on time and coordinate (l), which appeared to be absolutely stable. Getting the absolute stable implicit difference scheme with second-order approximation in two variables is a novel result. From comparison of the calculated and experimental data on the composite porosity the parameters of mathematical model were determined. Based on computational experiment the optimum conditions of sintering of composite, namely, sintering temperature 1600 °C, heating rate 383 °C/min, and heating time 3 min have been found. Using the optimal sintering mode the nanocomposites containing up to 50 vol. % of carbon nanotubes with zero porosity and flexural strength in the range of (580-640 MPa) were fabricated.

**Acknowledgements:**This work was supported by Grant of the Russian Scientific Foundation № 14-19-00522.

93

**Aicha Bareche**, Research Unit LaMOS, University of Bejaia, Department of Technology, Algeria

**Abstract:**In this paper, we provide an approximate analysis of an M/M/s queue using the operator method (strong stability method). Indeed, we use this approach to study the stability of the $M/M/\infty$ system (ideal system), when it is subject to a small perturbation in its structure (M/M/s is the resulting perturbed system). In other words, we are interested in the approximation of the characteristics of an M/M/s system by those of an $M/M/\infty$ one. For this purpose, we first determine the approximation conditions of the characteristics of the perturbed system, and under these conditions we obtain the stability inequalities for the stationary distribution of the queue size. To evaluate the performance of the proposed method, we develop an algorithm which allows us to compute the various obtained theoretical results and which is executed on the considered systems in order to compare its output results with those of simulation.

94

**Amit Tribedi**, Susil Kar College, University of Calcutta, Physics, India

**Abstract:**Genuine Quantumness present in Quantum Systems is the resource for implementing Quantum Information and Computation Protocols which can outperform the classical counterparts. These Quantumness measures encompass non-local ones known as quantum entanglement (QE) and quantum information theoretic (QIT) ones, eg. quantum Discord (QD). In this paper, I have studied two well-known measures of QE and QD in two naturally available molecular magnetic systems, one is a trimeric complex and the other is a wheel-like cluster compound, where the dominant interaction is the spin-spin exchange interaction. I have used exact analytic methods. Some counter-intuitive non-trivial features, like enhancement of quantum correlations with temperature, non-vanishing quantum-ness at high temperatures etc. indicated by the behaviour of the correlation and the QIT measures have been found. The measures, being operational ones, can be used to realize the resource of Quantumness in experiments.

**Acknowledgements:**University Grants Commission, Government of India

95

**Narek Martirosyan**, Yerevan Physics Institute(YerPhi), Computational Physics and IT Department, Armenia

**Abstract:**Pseudo-random number generators (PRNG) are crucial in science and industry. Bad PRNGs may lead to wrong results, erroneous explanations, technical expenditures, security fails etc. Hence it is necessary to distinguish good versus bad PRNGs. This task is usually carried out via statistical tests. Here we present a statistical test based on the multidimensional random walk. Both the theoretical support and simulations of the test are described and discussed. We implement the test for various PRNGs available on the market.

96

**Alper Selver**, Dokuz Eylül University, Electrical and Electronics Engineering, Turkey

**Abstract:**Multi-dimensional transfer functions (MDTF) are occasionally designed as two step approaches. At the first step, the constructed domain is modelled coarsely using global volume statistics and an initial TF is designed. Then, a finer classification is performed using local information and TF design is refined. In this study, both a new TF domain and a novel two-step MDTF strategy are proposed for visualization of abdominal organs. The proposed domain is generated by aligning the histograms of the slices, which are reconstructed based on user aligned majority axis/regions through an interactive Multi-Planar Reconstruction interface. It is shown that these user aligned histogram stacks (UAHS) exploit more a priori information by providing tissue specific inter-slice spatial domain knowledge. For initial TF design, UAHS is approximated using a multi-scale hierarchical Gaussian mixture model, which is designed to work in quasi real time. Then, a finer classification step is carried out for refinement of the initial result. Application to several MRI data sets acquired with various sequences show accurate visualization of abdomen.

**Acknowledgements:**This study is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant number EEEAG 112E032.

97

Evaluation of Waveform Structure Features on Time Domain Target Recognition under Cross Polarization

**Alper Selver**, Dokuz Eylül University, Electrical and Electronics Engineering, Turkey

**Abstract:**Classification of aircraft targets from scattered electromagnetic waves is a challenging application, which suffers from aspect angle dependency. In order to eliminate the adverse effects of aspect angle, various strategies were developed including the techniques that rely on extraction of several features and design of suitable classification systems to process them. Recently, a hierarchical method, which uses features that take advantage of waveform structure of the scattered signals, is introduced and shown to have effective results. However, this approach has been applied to the special cases that consider only a single planar component of electric field and cause no-cross polarization at the observation point. In this study, two small scale aircraft models, Boeing-747 and DC-10, are selected as the targets and various polarizations are used to analyse the cross-polarization effects on system performance of the aforementioned method. The results reveal the advantages and the shortcomings of using waveform structures in time-domain target identification.

98

**Sergey Gladkov**, Moscow aviation institute (national research university) (MAI), Mathematical modelling , Russian Federation

**anatolii vestyak**, Moscow aviation institute (national research university) (MAI), , Russian Federation

**Abstract:**. It has been proved that the solution of the quasi-classical kinetic equation for Bose and Fermi statistics can be represented in the general form, using the relaxation time approximation. The general solution found for the distribution function helps calculate any non – equilibrium characteristics of metals, magnets, and dielectrics in any order of the perturbation theory according to the relaxation time .

99

**Sarmila Sahoo**, Heritage Institute of Technology, Kolkata, Department of Civil Engineering, India

**Abstract:**Composite shell structures are extensively used in aerospace, civil, marine and other engineering applications. In practical civil engineering applications, the necessity of covering large column free open areas is often an issue and hyperbolic paraboloid shells are used as roofing units. Quite often, to save weight and also to provide a facility for inspection, cutouts are provided in shell panels. The paper considers free vibration characteristics of stiffened composite hyperbolic paraboloid shell panel with cutout in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element. The size of the cutouts and their positions with respect to the shell centre are varied for different edge conditions of cross-ply and angle-ply laminated shells. The effects of these parametric variations on the fundamental frequencies and mode shapes are considered in details to conclude a set of inferences of practical engineering significances.

100

**Rustem Sakhapov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Marat Makhmutov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Muhammat Gatiyatullin**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Regina Nikolaeva**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Abstract:**The article presents the results of a study of road safety indicators that influence the development and operation of the transport system. Road safety is considered as a continuous process of risk management. Authors constructed a model that relates the social risks of a major road safety indicator - the level of motorization. The model gives a fairly accurate assessment of the level of social risk for any given level of motorization. Authors calculated the dependence of the level of socio-economic costs of accidents and injured people in them. The applicability of the concept of socio-economic damage is caused by the presence of a linear relationship between the natural (loss of life, loss of property) and economic (monetary) indicators damage from accidents. The optimization of social risk is reduced to finding the extremum of the objective function that characterizes the economic effect of the implementation of measures to improve safety. The calculations make it possible to maximize the net present value, depending on the costs of improving road safety, taking into account socio-economic damage caused by accidents. The proposed econometric models make it possible to quantify the efficiency of the transportation system, allow to simulate the change in road safety indicators, evaluate them and take effective decisions on the development of the transport system.

101

**Rustem Sakhapov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Marat Makhmutov**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Muhammat Gatiyatullin**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Regina Nikolaeva**, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

**Abstract:**The article presents the results of a study of the transfer functions of a construction machine as a complex dynamic system. Authors constructed a dynamic model of a construction machine. The paper formulates and solves a system of nonlinear differential equations of motion of the chassis system of a construction machine on the basis of the d'Alembert-Lagrange equation. The numerical values of the transfer function coefficients for the construction machines were determined from the experimentally obtained curves of acceleration, processed by area method. Authors determined the experimental curves of the transition process of chassis system of a construction machine. The results of the study show that the difference of source curves ordinates and calculation of transients is less than 4% on average, which indicates a fairly accurate description of the process. The resulting expressions of transfer system functions of the chassis with sufficient precision can be used for practical purposes in the design and development of new construction machines.

102

**Nikolay Bukhman**, Samara State University of Architecture and Civil Engineering, Department of Physics, Russian Federation

**Abstract:**The article deals with one-dimensional problem of rise-time distortion signal without carrying signal, that appears in the starting point intermittently, that is signal distortion at front edge or one of its derivative. The authors show that front edge of signal isn’t distorted in case of propagation in unrestricted (including absorbing) area (amplitude of starting signal step or of one of its derivatives doesn’t change) and move with the accuracy of vacuum light speed. The paper proves that it is the time interval shortage that causes signal loss with the route extension, but not the reduction of its starting amplitude, during which front edge of signal retains its starting value. The research presents new values for this time interval.

103

**Mohamed Reda Oudih**, University of Sciences and technology, Houari Boumediene, Algiers, Algeria

**Abstract:**Nanomaterials are a mesoscopic intermediate state between the atom and the bulk system. The transition from macroscale to the nanoscale leads to a passage from a band structure to a discrete energy spectrum which results in a substantial quantum effect. In such systems the quantum fluctuations become important when the gap between the quantum levels of the grain becomes of the same order of magnitude as the superconducting gap. The thermal behavior of these systems also displays several features not present in the bulk limit. Most of studies carried out to date on isolated superconducting nanomaterials are based, for reasons of simplicity on the grand canonical BCS approach. However, the conventional BCS approach fails to provide a good description of thermal properties essentially because of the particle-number fluctuations. Since the electron number in the grain is fixed, an accurate description of the nanoscale superconductors should involve a canonical ensemble treatment. The latter can be related to the grand-canonical ensemble by particle-number projection. However, an exact particle-number projection leads to complicated equations and therefore not easy to use in practice. In this contribution, we introduce an approximate particle-number projection method that allows the treatment of nanoscale superconductivity at finite temperature keeping the simplicity provided by the grand canonical ensemble. Starting from an exact projection method, it is shown that the effect of the particle-number fluctuation can be eliminated by a simple renormalization of the pairing-strength in the grand canonical BCS equations. Quantities such as condensation energy, pairing gap, entropy and heat capacity are considered. The test of the method versus the picket fence model, for which an exact solution of the pairing problem is available, has shown that our results are valid for any temperature and with any mean-level spacing. It is shown in particular that the second-order superfluid-normal phase transition is completely washed out.

104

**Manuel De La Sen**, UPV, Department of Electricity, Spain

**Abstract:**Relevant attention is being paid in the last two decades to the study of mathematical epidemic models which are modelled by integro- differential equations and/ or difference equations. Those models describe the evolution of the various subpopulations considered as the disease under study progresses. Typically, the models have three essential subpopulations (namely, susceptible, infected and recovered by immunity) whose dynamics are mutually coupled. There different degrees of complexity in the statement of the models. The simplest ones have only “susceptible” (S) and “infected” (I) subpopulations and are referred to as SI- models. A second degree of complexity adds a third one said to be the “recovered by immunity” subpopulation and those models are said to be SIR- models. A further complexity degree splits the infected into two subpopulations (or compartments), namely, the so-called “infected” or “ exposed” (E) ( those having the disease but do not present yet external symptoms) and the “infectious” or “infective” (those having external symptoms). The generic acronym used for this last category of models is SEIR, being referred to as SEIR epidemic models. General description of epidemic models and some mathematical analysis on them is given in some classical books. See, for instance, [1-3]. More sophisticated models have been described and analyzed in the literature. See, for instance, [8-12] and references therein. On the other hand, it turns out due to medical experience that there are individuals who are infected but do not have significant external symptoms, the so-called the “asymptomatic” (A) subpopulation, [7]. This occurs even in the common known influenza disease. If such an asymptomatic subpopulation is considered in the model then it turns out that the exposed have different transitions to the infective and to the asymptomatic so that a part of the exposed become asymptomatic later one while others become infective. Finally, it is well -known that in the ebola disease, the lying dead corpses are infective [4-6] what causes serious sanitary problems in third world tropical countries with low or scarce sanitary means when an ebola disease spreads thoroughly specially when it is transmitted from rural areas to high populated urban ones. In particular, it is pointed out in [4] that the simultaneous presence of asymptomatic infective population with dead-infective corpses is compatible in the ebola disease propagation. The dead corpses can be considered in the model as a new subpopulation “D”. References [1] D. Mollison Ed., Epidemic Models: Their Structure and Relation to Data, Publications of the Newton Institute, Cambridge University Press, 1995, Denis Mollison Editor (transferred to digital printing 2003). [2] M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton and Oxford, 2008. [3] D.J. Daley and J. Gani, Epidemic Modelling. An Introduction, Cambridge Studies in Mathematical Biology: 15, Cambridge University Press, New York, 2005. [4] S.E. Bellan, J.R.C. Pulliam, J. Dushoff and L.A. Meyers, “Ebola control: effect of asymptomatic infection and acquired immunity”, The Lancet, Vol. 384, No. 9953, pp. 1499-1500, 2014. [5] E. Santermans, E. Robesyn, T. Ganiani. B. Sudre, C, Faes , C. Quinten, W. Van Bortel, T. Haber, T. Kovac, F. Van Reeth, M. Testa, N. Hens and D. Plachouras, “ Spatiotemporal evolution of ebola disease at sub-national level Turing the 2014 west Africa epidemic: model scrutinity and data meagreness”, Plos One, Vol. 11, No. 1, 2016 , doi:101371/journal.pone.0147172. [6] I. Al-Darabsah and Y. Yuan, “A time-delayed epidemic model for ebola disease transmission”, Applied Mathematics and Computation (in press). [7] A. Ebrahimi, M. Sharifi and M. Shahrokhi, “Nonlinear adaptive control of influenza epidemic in the presence of model uncertainties” (submitted). [8] H. Khan, R.N. Mohapatra, K. Varajvelu and S, J. Liao, “The explicit series solution of SIR and SIS epidemic models”, Applied Mathematics and Computation, Vol. 215, No. 2, pp. 653-669, 2009. [9] X. Y. Song, Y. Jiang and H.M. Wei, “Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays”, Applied Mathematics and Computation, Vol. 214, No. 2 , pp. 381-390, 2009. [10] M. De la Sen,R. P. Agarwal, A. Ibeas and S. Alonso-Quesada, “On the existence of equilibrium points, boundedness, oscillating behaviour and positivity of a SVEIRS epidemic model under constant and impulsive vaccination”, Advances in Difference Equations, Vol. 2011, Article ID 748608, Vol. 2011, doi:10.1155/2011/748608. [11] M. De la Sen, R. P. Agarwal, A. Ibeas and S. Alonso-Quesada, “On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination”, Advances in Difference Equations, Vol. 2010, Article ID 281612, doi:10.1155/20101/281612. [12] M. De la Sen and S. Alonso-Quesada, “Vaccination strategies based on feedback control techniques for a SEIR- epidemic model”, Applied Mathematics and Computation, Vol. 218, No. 7, pp. 3888-3904, 2011.

105

**Kashi Saha**, Jadavpur University, Mechanical Engineering , India

**Abstract:**The post-elastic analyses of thermo-mechanically loaded non-uniform bars are important for designing mechanical, aerospace and civil structures. The solution of thermal stress problem available in textbook are valid for uniform cross-section bars under uniform temperature field only. In general the solution fails because the assumption of equality of thermal and mechanical strains at every point within the domain is not true. However, an overall equilibrium of the bar system is achieved by balancing forces coming from the strain differentials, existing within the domain. Hence a detail analysis of the generalized system yields a different strain field, and subsequently a different stress field, which are often much more critical. The simple analytical method also fails when the induced thermal stress is in post-elastic region due to insufficiency in capturing the physics of material behaviour. The prediction of the elasto-plastic behaviour of solid slender bars of various types of geometry as well as loading is an interesting area of work for the designers. This paper attempts to address the post-elastic behaviour of thermo-mechanically loaded non-unifom bars by using a numerical method based on variational principle. A solution algorithm using von-Mises yield criterion has been developed to obtain an approximate solution of the unknown displacement field from the governing equation in an iterative manner. The present paper employs an energy approach to get the appropriate governing equations for the non-uniform bars in elasto-plastic state. The formulation is displacement based and the unknown displacement field is approximated by finite linear combination of admissible orthogonal functions. The analysis is carried out based on the assumptions that material properties are independent of temperature variation and plane cross-sections remain plane maintaining axisymmetry. Present analysis is based on bi-linear material model, but the method is generalized enough to include any other non-linear material behaviour, as well. Moreover, it is assumed that the bar geometry is stub enough to exclude buckling failure from the scope of analysis. The term 'bar' used in this paper is in generic sense and hence the formulation is applicable for all one dimensional elements, e.g., rods, pipes, truss members, etc.

106

**ARUNABHA CHANDA**, JADAVPUR UNIVERSITY, Mechanical Engineering, India

**Abstract:**Boiling in micro channels is a very efficient mode of heat transfer in which very high heat and mass transfer coefficients can be achieved. Pumping power required for two-phase flows is lesser than single-phase liquid flows to achieve a given heat removal. Applications include heat pumps, automotive air conditioners etc. Although experimental investigations have been carried out on the topic there is a severe scarcity of literature attempting mathematical modelling. A numerical study of two phase flow through the micro channel has been carried out in this study. The objective of the study is to understand the effects of different fluid inlet velocities and fluid inlet temperature. The computational fluid dynamics (CFD) model equations are solved using commercial software ANSYS fluent 13.0 to understand the hydrodynamic and thermal behavior of the two phase flows through microchannels. The numerical model is validated against available literature . İt is found that the incipient heat flux is influenced by both the inlet velocity as well as the fluid inlet temperature independently, to a great deal. Also as the mass flux is increased (by increasing Reynolds number), the region of single phase flow increases. The heat transfer coefficient at the inlet is high and it falls sharply along the flow direction. But once the boiling process starts , the temperature at the heated wall starts fluctuating which causes fluctuation in the heat transfer coefficient as well. Both convective and nucleate boiling components are present in the range of simulation operation ( i.e.. Re =200 to 550 and constant temperature and heat flux.)

107

**Prasanta Sahoo**, Jadavpur University, Department of Mechanical Engineering, India

**Abstract:**The present work considers analysis of adhesive friction of rough surfaces using n-point asperity concept for statistical definition of surface roughness features, and accurate finite element analysis of elastic-plastic deformation of single asperity contact. In conventional models the asperities are defined as peaks having some regular form at the tip. Also all such asperities on the surface are assumed to have identical tip radius with only variation in peak heights. This peak height concept of asperity means that it is a three point asperity. Though the models based on such asperity concept yield results in good agreement with experimental ones, fact remains that such definition of surface roughness features is far away from reality. The n-point asperity concept introduced by Hariri, Zu, and Ben Mrad [1] uses such assumptions to define surface roughness features that it gives close to realistic picture of asperities. In the name ‘n-point asperity’, ‘n’ stands for number of height ordinates of which an asperity is comprised. Models with n-point asperities assume that at particular level of separation between an interfering plane and a rough surface, there exist asperities of different sizes (i.e. different radii of curvatures and different heights). Also each asperity doesn’t exist as a separate entity throughout the progression of contact but the earlier asperity gets merged into a new asperity with contact progression. As compared to conventional three point asperities, the statistical definition for existence of n-point asperities is much more complex. This is because the existence of each n-point asperity is governed by the joint probability density function of ‘n’ number of height ordinates for variation in their heights and an auto correlation function for variation in spacing of height ordinates. Contact between two rough surfaces is simplified as the contact between a rigid flat and an equivalent rough surface by using well established earlier theories. First the contact behavior of single n-point asperity is modeled and then by incorporating this into statistical multi asperity contact model, the total effect of contact phenomenon is quantified for the whole surface. The whole range of deformation of an n-point asperity viz. from fully elastic, through elastic-plastic, to fully plastic is considered. Well defined adhesion index and plasticity index are used to study the prospective situations arising out of variation in load, material properties, and surface roughness. To model the elastic-plastic adhesive friction in n-point asperity frame-work, the applied load and tangential force in fully elastic and plastic zones of deformation are modelled by following Roy Chowdhury and Ghosh (RG) [2] theory incorporating contribution from intermediate elastic-plastic transition regime and uing Chang, Etsion and Bogy’s (CEB) [3] analytical model and Kogut and Etsion’s (KE) [4] finite element results. The general trend of behavior observed is that the friction force is almost proportional to applied load. Plots with higher plasticity index (elastic deformation) and lower adhesion index (rough surface) values show non linearity. From the present results it is possible to locate the combinations of adhesion index and plasticity index that may yield very low coefficient of friction. Thus suitable choice of surface and material parameters for the contact of two rough surfaces can be made in order to minimize friction typically at low load and micro scale roughness situations. References [1] A. Hariri, J. W. Zu, and R. Ben Mrad (2006). n-Point asperity model for contact between nominally flat surfaces. ASME Journal of Tribology, 128, 505-514. [2] S. K. Roy Chowdhury and P. Ghosh (1994). Adhesion and adhesional friction at the contact between solids. Wear, 174, 9-19. [3] W. R. Chang, I. Etsion, and D. B. Bogy (1987). An elastic-plastic model for the contact of rough surfaces. ASME Journal of Tribology, 109, 257-263. [4] L. Kogut and I. Etsion (2003). A finite element based elastic-plastic model for the contact of rough surfaces. Tribological Transactions, 46(3), 383–390.

108

**Goutam Pohit**, Jadavpur University, Kolkata, India., Department of Mechanical Engineering, India

**Abstract:**The present work accounts centrifugal stiffening effect on the nonlinear vibration response of a FGM Timoshenko beam. Analysis is carried out for a cantilever beam fixed with a rotating hub. Material is assumed to have a gradation relation along the depth of the beam. Centrifugal force and axial displacement raised due to the rotating hub is incorporated in the strain energy equations. Subsequent to this, an iterative technique is employed to obtain amplitude dependent vibration response of a rotating Timoshenko beam while material follows a gradation relation along the beam depth. Main objective of the work is to obtain the effects of rotational speeds, hub radius and different gradation relations on the linear as well as nonlinear frequencies and mode shapes.

109

**Nicholas Protonotarios**, Academy of Athens, Research Center of Mathematics, Greece

**George Spyrou**, Biomedical Research Foundation of the Academy of Athens, Center for Systems Biology, Greece

**George Kastis**, Academy of Athens, Research Center of Mathematics, Greece

**Abstract:**The issue of edge determination of a single object in reconstructed nuclear medicine images has been examined thoroughly in the past, nevertheless most of the investigation has focused on the concepts of either numerical sinogram differentiation or segmentation. This work aims to develop an automated method for determining the contour of a single convex object in PET and SPECT reconstructed images, which can be used for computing body edges for attenuation correction, as well as for eliminating streak artifacts outside the specific object. This was accomplished by implementing a modified cumulative sums (CUSUM) scheme in the sinogram. Our method can automatically detect the object’s boundary in the reconstructed image. This approach has been tested in simulated as well as real phantoms and it performed efficiently for all convex objects. We were able to detect the contour of a single object in the image space, which in turn enabled us to eliminate streak artifacts outside and thus to obtain body edges necessary for attenuation correction.

110

**Nicholas Protonotarios**, Academy of Athens, Research Center of Mathematics, Greece

**Athanasios Fokas**, University of Cambridge, Department of Applied Mathematics and Theoretical Physics, United Kingdom

**George Kastis**, Academy of Athens, Research Center of Mathematics, Greece

**Abstract:**The analytical approach to single photon emission computed tomography (SPECT) requires the inversion of a certain generalization of the two-dimensional Radon transform, which is called attenuated Radon transform. Both Radon and attenuated Radon transforms are line integrals. Here we present a modification of the explicit formula for this inversion which was derived in 2006 by one of the authors, following the pioneering work of Novikov. We also present a numerical implementation of this Inverse Attenuated Radon Transform (IART), which we call the attenuated Spline Reconstruction Technique (aSRT). For this numerical implementation we utilize both the attenuated sinogram obtained from SPECT and the reconstructed attenuation coefficient obtained from CT. These data can be provided by a SPECT/CT scanner. Our analytic formula of the IART involves the calculation of the Hilbert transform of the linear attenuation correction coefficient and the Hilbert transform of two sinusoidal functions of the attenuated sinogram. For the aSRT we have employed custom-made cubic splines, i.e. interpolation through piecewise-continuous third degree polynomials. The purpose of this work is to present the mathematical formulation of aSRT and to evaluate it via the reconstruction of various simulated phantoms, including an image-quality (IQ) phantom under Poisson noise.

111

**Sojeong Park**, Chosun University, Department of Physics, Korea, Republic Of

**Wooseop Kwak**, Chosun University, Department of Physics, Korea, Republic of

**Abstract:**We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume-Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.

112

**Evgeny Popko**, Ural Federal University, NANOTECH Centre, Russian Federation

**Ilya Weinstein**, Ural Federal University, NANOTECH Centre, Russian Federation

**Abstract:**Genetic Algorithms (GA) have proven to be good optimization methods to solve various technical problems. Previously, we have demonstrated that the evolutionary approach for modeling the thermoluminescence processes (TL) in wide-band-gap dosimetric materials is high efficient. The Genetic Algorithms use both bit and floating-point representations of chromosomes. The former translates a parameter value into a binary code, the latter stores the parameter value as real. Researchers compared the efficiency of these two types of GA and arrived at different conclusions. For some problems (for example, the use of the Rosenbrock function, a multi-extremal test function), the binary-coded algorithms show the best results. For other problems, (for example, some dynamic control problems), the real GAs are more advantageous. As a rule, priority is given to the type that provides the most accurate and/or a quick search for the desired values of main parameters in the problem at hand. The case study compares the effectiveness of the two types of GA, real and binary-coded, to calculate kinetic models of the TL process in crystals. As a primary efficiency criterion, the paper employs the quality of the approximation of the experimental data within the model chosen for the same computational costs. Earlier, we carried out work on the choice of the GA structure consisting of evolutionary mechanisms with the most optimal speed settings. For different types of encoding, we used architecture with modified parameters of the tournament selection, a multipoint linear crossover and adaptive mutation. Within the model utilized, we built comparable algorithms with different encoding types. In calculating, the population size was 200 individuals, the number of iterations was 200 generations. To evaluate the effectiveness of GA, as experimental peaks, we generated curves using pre-assigned parameters. We applied two widespread TL-schemes: “one trap-one recombination center” (OTOR) and the non-interactive multi-trap system (NMTS). Also, we showed that, in most cases, the real-coded GA provides more accurate results when searching for optimal solutions. In this case, the approximation quality criterion runs through values from 0.01% to 1.22%. At the same time, the binary encoding places the calculated objective function values into the range from 0.3% to 3.36%. Thus, the real-coded algorithm is a preferred choice to implement evolutionary calculations of the TL processes in wide-band-gap materials.

**Acknowledgements:**This work was supported by contract № 02.A03.21.0006, Act 211 Government of the Russian Federation.

113

**Alexey Sukhinin**, Southern Methodist University, Mathematics, United States

**Edward Downes**, Southern Methodist University, Mathematics, United States

**Alejandro Aceves**, Southern Methodist University, Mathematics, United States

**Jean-Claude Diels**, University of New Mexico, Electrical and Computer Engineering, United States

**Ladan Arissian**, University of New Mexico, Electrical and Computer Engineering, United States

**Abstract:**We present numerical simulations of co-propagation of a nanosecond UV pulse and femtosecond IR pulse. The model proposed assumes the long UV pulse to act as a guide. We explore the effect of such guiding in suppressing known IR spatio-temporal instabilities.

**Acknowledgements:**This work was supported by ARO MURI Light Filamentation Science, contract No W911NF1110297 and partly by US Department of Energy grant, contract No DE-SC0011446.

114

**Sergey Gladkov**, Moscow aviation institute (national research university) (MAI), Mathematical modelling , Russian Federation

**Sophie Bogdanova**, Moscow Aviation Institution (National Research University) (MAI), mathematic simulation, Russian Federation

**Abstract:**There has been found the analytical solution to the problem set by J. Bernoulli on brachistochrone curve considering friction forces (internal friction force, friction force proportional to velocity, and dry friction force). It is shown that the solution to the problem can only be presented as quadratures, and different figures of optimal trajectories under dissipation are shown as a result of numerical computations. It is proved that, in absence of friction forces, any motion along the curved gutter under only gravity is always reduced to the problem of brachistochrone curve that can be solved using just general principles of dynamics of curvilinear motion without methods of calculus of variations and optimal control. There is found a point of ‘geometrical phase transition’ corresponding to the qualitative transition of brachistochrone curves from the one class of trajectories to another class. The behaviour of trajectories in close vicinity to the points of ‘geometrical phase transition’ is numerically described. Analytically and numerically, it is proved that when the system comes to steady conditions, the trajectory will look like a usual parabola with periodical pendulum-like motion along it.

115

**Gordana Jovanovic Dolecek**, Institute INAOE, Department of Electronics, Mexico

**Abstract:**Minimum-phase (MP) filters have all zeros inside and/or unit circle. As a consequence, the group delay of an MP system is always less than that of non-minimum phase systems, having the equal magnitude responses. Minimum-phase (MP) filters find applications where it is necessary to have a low group delay, like in communications, speech processing, and predictive coding, among others. This paper presents a novel simple method for the direct design of low-pass minimum-phase (MP) filters. Method is based on design of two compensated combs, using a multiplier-less minimum-phase compensator, and sharpening technique. The first comb defines the pass band of the MP filter, while the second comb decreases side lobes of the first comb, thus increasing attenuation of the resulting MP filter. Knowing that all zeros of comb filter are on the unit circle, the compensated comb is also a MP filter. Similarly, using the special condition, the sharpening of multiplier-less compensated comb is also a MP multiplier-less filter. The benefit of the proposed method is illustrated in the provided design examples.

**Acknowledgements:**This work is supported by the CONACYT grant No. 179587.

116

**Aleksandr Strelkov**, Samara State University of Architecture and Civil Engineering, Department of Water Supply and Wastewater Disposal, Russian Federation

**Svetlana Teplykh**, Samara State University of Architecture and Civil Engineering, Department of Water Supply and Wastewater Disposal, Russian Federation

**Nikolay Bukhman**, Samara State University of Architecture and Civil Engineering, Department of Physics, Russian Federation

**Abstract:**Railway bed gravel foundation has a constant permanent impact on urban ecology and ground surface. It is only natural that larger objects, such as railway stations, make broader impact. Surface run-off waters polluted by harmful substances existing in railroad track body (ballast section) flow along railroad tracks and within macadam, go down into subterranean ground flow and then enter neighboring rivers and water basins. This paper presents analytic calculations and characteristics of surface run-off liquid filtration which flows through gravel multiple layers (railroad track ballast section). The authors analyse liquids with various density and viscosity flowing in multi-layer porous medium. The paper also describes liquid stationary and non-stationary weepage into gravel foundation of railroad tracks.

117

**Emil Gazazyan**, Institute for Physical Research, Theoretical Physics, Armenia

**Abstract:**Coherent interaction of resonant laser radiation with single atoms and atomic environments have received wide practical application in such fields of study as laser cooling of atoms, new precision magnetometry techniques, coherent control of chemical reactions and others[1-2]. Construction of the set of coherent superposition states of atoms in a macroscopic volume is one of the key problems of quantum information [3-4]. Another significant problem is the quantum information storage and subsequent restoration of optical and quantum information [5-6]. The excitation of atoms from the ground state to the Rydberg states attracts attention of researchers in recent years in the field of quantum and nonlinear optics because of their characteristic strong interaction and the so-called "dipole blockade" [7]. Although multilevel atomic and atomlike systems do not provide new physical principles in addition to quantum interference and the principle of superposition, they widen essentially the possibilities of experimental realizations and practical applications. In this work we have studied in detailed the necessary conditions for the formation of a dark state in five level system similar to the dark state in a three-level system. The adiabatic pulse propagation in resonant medium consisting of such atoms is investigated analytically and numerically. We showed optical and quantum information double storage and retrieval, controllable population transfer and Rydberg state excitation in the whole volume of the medium and analyzed the influence of the self-phase modulation on this processes. 1. K. Bergmann, H. Theuer, B.W. Shore. Rev. Mod. Phys., 70,1003 (1998). 2. P. Kral, I. Thanopulos, M. Shapiro. Rev. Mod. Phys., 79, 53 (2007). 3. H. Kimble. Nature (London), 453, 1023 (2008). 4. L. Li, Y.O. Dudin, A. Kuzmich. Nature (London), 498, 466 (2013). 5. M.D. Lukin. Rev. Mod. Phys., 75, 457 (2003). 6. I. Novikova, R.L. Walsworth, Y. Xiao. Laser Photonics Rev., 6, 333 (2012). 7. A.V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl. Phys. Rev. Lett. 107, 133602 (2011).

**Acknowledgements:**The work was supported by the Ministry of Education and Science of Armenia, State Committee of Science (15 T-1S066) and IRMAS project.

118

**Evgeny Popko**, Ural Federal University, NANOTECH Centre, Russian Federation

**Ilya Weinstein**, Ural Federal University, NANOTECH Centre, Russian Federation

**Abstract:**Fuzzy logic is actively used in many technological problems related to the pattern recognition. In particular, great attention is paid to accurate identification of handwritten characters in classification and analysis of documents, automatic serial number recording, and vehicle identification. One of the promising trends is the employment of artificial convolutional neural networks to imitate biological nervous systems with learning ability. Convolutional neural networks are the extension of a multi-layer perceptron, optimized for two-dimensional pattern recognition (a character identification task), face detection, and so on. The goal of this work is to recognize handwritten digits and improve the classification results by way of a newly devised version of convolutional neural network through integrating a logical correction module into their structure. In this work, as a prototype, we have used the network architecture with four layers. The input layer receives images of recognizable characters. This is followed by a layer of six convolutional feature maps of size 13 * 13. Each map element is connected to the receptive field of 5 * 5 on an input image. Further, there is an additional convolutional layer consisting of 50 maps of size 5 * 5. The next layer is fully-connected and contains 100 neurons. The fifth layer contains neurons corresponding to the digits from 0 to 9. As shown by preliminary tests, the major difficulty of CNNs is to identify gaps in specific areas of characters and individual structural elements, for the classification. The network errors mentioned above appear due to the omission of these features. For example, in the case when the character “2” was incorrectly identified as “7”, the neural network was not able to determine clearly whether the bottom element as a line corresponds to two or seven. We have introduced a fuzzy logic module into the system. Its main intention is to ascertain the existence of certain structural elements of recognizable characters and to yield an appropriate correction penalty for the neural network outputs. The logical module includes a rule database for producing correction values. Each fuzzy rule can be represented as a vector model: P =

**Acknowledgements:**This work was supported by contract № 02.A03.21.0006, Act 211 Government of the Russian Federation.

119

**Rachid FERMOUS**, University of Djilali Bounaama Kemis-Miliana, Faculty of Sciences and Technology, Algeria

**Abstract:**Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of dense plasma. The weakly relativistic electrons are produced by ultra-intense laser pulses while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

120

**Yehuda Roth**, Oranim college, physics, Israel

**Abstract:**The following will introduce the A.I.E.S model, in which nonlinear maps determine the evolution of an inanimate substance to form an organic substance (Biopoiesis). We will demonstrate that when relating this model to a window of coherence that appears in the chaotic bifurcation diagram, biological characteristics of warm-blood animate systems appears. Our model provides a mathematical platform in understanding Biopoiesis, that is, the process by which living organisms develop from inanimate matter.

121

**Eugen Anitas**, Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Russian Federation

**Abstract:**The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: “convex/concave” - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power-law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.

122

**Petr Bour**, Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University in Prague, Department of Mathematics , Czech Republic

**Vaclav Kus**, Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University in Prague, Department of Mathematics , Czech Republic

**Jiri Franc**, Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University in Prague, Department of Mathematics, Czech Republic

**Abstract:**Binary decision trees are widely used tool for unsupervised classification of high-dimensional data, for example among particle physicists. We present our proposal of the supervised binary divergence decision tree with nested separation method based on the generalized linear models or on the kernel density estimation procedure. A key insight we provide is the clustering driven only by a few selected physical variables. The proper selection consists of the variables achieving the maximal divergence measure between two different classes. Further we apply our method to Monte Carlo data set simulating measured observations from the ttbar lepton+jets decay channel at DZERO experiment in Fermilab. The efficiency of our algorithm achieves 90 % AUC. We also introduce the modification of statistical tests applicable to weighted data sets in order to test homogeneity of the Monte Carlo simulation and real data. We provide a justification of powers of these modified tests by presenting their p-values for weighted Monte Carlo samples .

**Acknowledgements:**This work was supported by the grant SGS15/214/OHK4/3T/14 and INGO II - LG15047.

123

**Orestis George Ziogos**, National Technical University of Athens, School of Chemical Engineering, Greece

**Grigorios Megariotis**, National Technical University of Athens, Chemical Engineering, Greece

**Doros N. Theodorou**, National Technical University of Athens, , Greece

**Abstract:**This study concerns atomistic and coarse-grained molecular dynamics simulations of pristine Hexabenzocoronene (HBC) molecular crystals. HBC falls in the category of polyaromatic hydrocarbons that find numerous applications in the field of organic electronics. The HBC molecule is initially simulated in an all-atom representation by employing the well-known AMBER force field. The atomistic model reproduces fairly well the structural experimental properties of this system and thus can be used as a reliable starting point for the development of a coarse-grained model in a bottom-up coarse-graining approach. All simulations were conducted at a temperature of 300K, where the system is found in the crystalline phase. In particular, the system consists of molecules that self-organize into well aligned molecular stacks which in turn create a perfect monoclinic molecular crystal. The coarse-grained model is developed by applying Iterative Boltzmann Inversion, a systematic coarse-graining method which reproduces a set of target (atomistic) radial distribution functions and intramolecular distributions at the coarser level of description. This model allows the simulation of HBC crystals over longer time and length scales. In particular, upon coarse-graining, the integration time step of the equations of motion increases from 1fs to 12fs, while the number of interaction sites per molecule is reduced from 60 to 6. The polyaromatic core of HBC at the coarse-grained level is replaced by six superatoms of the same type lying in the same plane. The crystalline phase is analyzed in terms of the Saupe tensor and its eigenvalues.

**Acknowledgements:**This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Programme ‘Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF) – Research Funding Programme: THALIS. Investing in knowledge society through the European social fund [grant number MIS 379436] and by the IKY Fellowships of Excellence for Postgraduate Studies in Greece – Siemens Programme [award number 11126/13a]. Grigorios Megariotis and Doros N. Theodorou also thank the Limmat Foundation.

124

**Sabit Bekov**, Eurasian National University, General and Theoretical Physics, Kazakhstan

**Kairat Myrzakulov**, Eurasian National University, General and Theoretical Physics, Kazakhstan

**Ratbay Myrzakulov**, Eurasian National University, General and Theoretical Physics, Kazakhstan

**Abstract:**In the present work we considered cosmological model of the universe in the frame of F(R) gravity with f-essence for homogenous and isotropic FRW space-time. We obtained field equations for the given model. There was used Noether symmetry approach for defining unknown F, h and K functions.

125

**Jorge Linares**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Salim Guerroudj**, Université de Versailles-St. Quentin en Yvelines, Département de Sciences Physique, France

**Kamel Boukheddaden**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Abstract:**There has been a growing in a recent years, of the interest to design spin crossover (SCO) nanoparticles [1], with controlled shape and environment, due to their potential applications as sensors, bistable and reversible memories or nano-actuators. The experimental studies confirmed the role of the surface effects leading to unusual and non-trivial size dependence of their bistable character. In particular in some cases, the SCO nanoparticles may show a cooperative switching accompanied with a thermal hysteresis at small sizes while they exhibit gradual conversions (no phase transitions) at bigger sizes. This goes against common sense of usual thermodynamics. Even thought, in some special cases, re-entrant phase transitions are obtained with size. The mechanisms of these intriguing behaviors remain however still misunderstood and so their modeling becomes necessary. In this contribution we investigate, the above cited effects on SCO materials, by means of an Ising-like Hamiltonian [2, 3] including short and long-range interactions as well as the interaction of the edge molecules of the system with their local environment. The Hamiltonian is solved in the frame of Monte Carlo Metropolis procedure for 2D (N_x×N_y) rectangular-shaped and 3D parallelepiped rectangle (N_x×N_y×N_z) SCO nanoparticles. The thermal dependence of the high-spin fraction is then derived for different particle sizes and the results are discussed with the help of analytical predictions allowing to evaluate the size dependence of the transition temperature and the conditions of occurrence of the re-entrant phase transition. In practice, the latter emerged from the MC simulations below some critical nanoparticle size and for well identified conditions on the model parameter values. References. [1] Thibault C., Molnar G., Salmon L., Bousseksou A., Vieu C., Langmuir 2010, 26, 1557-1560 [2] Bousseksou A., Nasser J., Linares J., Boukheddaden K., Varret F., Journal de Physique I, 1992, 2, 1381-1403 [3] Linares J., Jureschi C., Boukheddaden K., Magnetochemistry, in press

**Acknowledgements:**CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.

126

**Ioannis ZOIS**, Public Power Corporation, Testing, Research & Standards Centre, Greece

**Abstract:**The motivation for this work came from an attempt to give an alternative definition for the meter, the SI unit for measuring length. As a starting point towards this goal we present the underlying theory behind our approach which uses ideas from quantum field theory and non-commutative geometry, in particular the notion of an odd K-cycle which is based on the Dirac operator (and its inverse, the Dirac propagator). Using physics terminology, the key point in our strategy is this: instead of measuring ordinary length in space-time we measure the “algebraic (or spectral) length” in the space of quantum states of some fermion acted upon by the Dirac propagator.

127

**Pablo Martin**, Universidad de Antofagasta, Physics, Chile

**Jorge Olivares-Funes**, Universidad de Antofagasta, Mathematics, Chile

**Luis Cortes-Vega**, Antofagasta University, Mathematics Department, Chile

**Adrian Sotomayor**, Antofagasta University, Department of Mathematics, Chile

**Abstract:**The computation of Bessel functions is very important in several areas of Physics [3], Mathematics [5] and Chemistry [7], though the radius of convergence of the power series is infinite, however the number of terms required to calculate the functions in big values are many. There are several approximations to this functions [2-5], however the accuracy is not enough for some applications or the range of approximation is narrow. Here via a Multipoints Quasirational Approximations (MPQA Technique) [6] which have better accuracy than previous ones and the degrees of the polynomials in the approximation are only second order. Each approximation can be used with good accuracy for any positive value of the variable. The simplest approximation is obtained with one rational function, quotient of two polynomials combined with some auxiliar functions, and the most accurate approximations are obtained using two rational functions.

128

**William Yamashita**, Universidade Federal de Juiz de Fora, , Brazil

**Lucy Takahashi**, Universidade Federal de Juiz de Fora, Mathematics, Brazil

**Grigori Chapiro**, Universidade Federal de Juiz de Fora, Mathematics, Brazil

**Abstract:**The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations [1,2]. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration [3]. Obtained solutions are validated through direct numerical simulations using finite difference schemes. [1] I. Freire, M. Torrisi, Symmetry methods in mathematical modeling of Aedes aegypti dispersal dynamics, Nonlinear Anal.-Real 14 (3) (2013) 1300 – 1307. [2] L. Takahashi, N. Maidana, W. Ferreira Jr., P. Pulino, H. Yang, Mathematical models for the aedes aegypti dispersal dynamics: travelling waves by wing and wind, B. Math. Biol. 67 (3) (2005) 509–528. [3] W. M. S. Yamashita, L. T. Takahashi, G. Chapiro, Traveling wave solutions for the dispersive models describing population dynamics of Aedes Aegypti. Submitted, 2016

**Acknowledgements:**This work was supported, in part, by FAPEMIG

129

**Boris Kryzhanovsky**, Scientific Research Institute for System Analysis RAS, Center for Optical Neural Technologies, Russian Federation

**Leonid Litinskii**, Scientific Research Institute for System Analysis RAS, Center of Optical Neural Technologies, Russian Federation

**Abstract:**In [1] we proposed the n-vicinity method suitable for approximate calculations of the partition function of a spin system with an arbitrary connection matrix. The method is based on approximation of the state energies from the n-vicinity of the initial configuration with the aid of the Gaussian distribution. The method was illustrated by the calculation of the critical temperatures of the 2D, 3D and 4D Ising models since in these cases the connection matrices are fairly simple. In the present work, in the most general form we obtained the state equation whose coefficients are expressed in terms of the parameters of the connection matrix. One of the parameters is the effective coordination number q that is the average value of the interconnection per spin. Depending on the value of q, the system goes through the phase transition of the second kind or the transition is preceded by the jump of the magnetization. For the three-dimensional Ising model and different values of the parameter q the free energy is plotted and analyzed; the influence of the homogeneous magnetic field is studied. The physical systems with the rapidly decreasing long-interactions are examined. [1] Journal of Physics: Conference Series, vol. 574(2015) 012017. doi:10.1088/17426596/574/1/012017. http://iopscience.iop.org/1742-6596/574/1/012017/pdf/1742-6596_574_1_012017.pdf

130

**Grigorios Megariotis**, National Technical University of Athens, Chemical Engineering, Greece

**Georgios G. Vogiatzis**, National Technical University of Athens, School of Chemical Engineering, Greece

**Ludwig Schneider**, Georg-August-Universität, , Germany

**Marcus Müller**, Georg-August-Universität, , Germany

**Doros N. Theodorou**, National Technical University of Athens, , Greece

**Abstract:**A new methodology and the corresponding C++ code for mesoscopic simulations of elastomers are presented. The test system, crosslinked cis-1,4-polyisoprene, is simulated with a Brownian Dynamics/kinetic Monte Carlo algorithm as an assemblage of beads, each consisting of 5-10 Kuhn segments. Three kinds of beads (nodal points) are considered: end-points, internal beads, and crosslinks. Polymer networks are created from linear melts by either random crosslinking or end-grafting. From a thermodynamic point of view, the system is described by a Helmholtz free-energy containing contributions from entropic springs between successive beads along a chain, slip-springs representing entanglements between beads on different chains, and non-bonded interactions. All beads execute Brownian motion in the high friction limit. The free-energy density of non-bonded interactions is derived from the Sanchez-Lacombe equation of state and the isothermal compressibility of the polymer network is predicted correctly. The ends of each slip-spring hop between adjacent beads along the chains it connects. These thermally activated hops are tracked by a microscopically reversible Kinetic Monte Carlo scheme. Moreover, slip-spring creation/destruction takes place at dangling chain ends in the polymer network. The methodology is employed for the calculation of the stress relaxation function from simulations of several microseconds at equilibrium, as well as for the prediction of stress-strain curves of crosslinked polymer networks under deformation.

**Acknowledgements:**The major part of this work was funded by Volkswagen Foundation in the context of the project Mesoscopic Simulations of Viscoelastic Properties of Networks. In addition, it was funded by the European Union through the projects COMPNANOCOMP and COMPNANOCOMP-DPI under grant number 295355 and Limmat Foundation. Grigorios Megariotis and Doros N. Theodorou also thank the Limmat Foundation for giving them the opportunity to continue this research on polymer networks. Georgios G. Vogiatzis thanks the Alexander S. Onassis Public Benefit Foundation for a doctoral scholarship.

131

**Ju Chunhua**, Harbin Institute of Technology, Department of Materials Science, China

**Abstract:**GRP pipes for its excellent performance has been widely used for oil and gas gathering pipe. Because CO2 is used as displacing agent, causing corrosion problems CO2 FRP pipe, so the research GFRP pipe corrosion mechanism and performance in CO2 media evolution is important. Based on material corrosion theory summary FRP pipe used in CO2 environment, we analyze the main form and the specific process material corrosion, the use of aromatic amine curing and acid anhydride curing two fiberglass pipe as a test tube, analog GFRP pipe containing crude oil, the next CO2 and water medium corrosion test, by surface morphology material, the glass transition temperature changes, and performance to evaluate physical corrosion mechanism of FRP in CO2 in; the test results show that CO2 environment, glass and steel addition to the visible Exterior changes, its glass transition temperature, Pap hardness, ring stiffness, density, and curing of the resin content showed a downward trend.

132

**Ju Chunhua**, Harbin Institute of Technology, Department of Materials Science, China

**Abstract:**GRP pipes for its excellent performance has been widely used for oil and gas gathering pipe. Because CO2 is used as displacing agent, causing corrosion problems CO2 FRP pipe, so the research GFRP pipe corrosion mechanism and performance in CO2 media evolution is important. Based on material corrosion theory summary FRP pipe used in CO2 environment, we analyze the main form and the specific process material corrosion, the use of aromatic amine curing and acid anhydride curing two fiberglass pipe as a test tube, analog GFRP pipe containing crude oil, the next CO2 and water medium corrosion test, by surface morphology material, the glass transition temperature changes, and performance to evaluate physical corrosion mechanism of FRP in CO2 in; the test results show that CO2 environment, glass and steel addition to the visible Exterior changes, its glass transition temperature, Pap hardness, ring stiffness, density, and curing of the resin content showed a downward trend.

133

**Ju Chunhua**, Harbin Institute of Technology, Department of Materials Science, China

**Abstract:**GRP pipes for its excellent performance has been widely used for oil and gas gathering pipe. Because CO2 is used as displacing agent, causing corrosion problems CO2 FRP pipe, so the research GFRP pipe corrosion mechanism and performance in CO2 media evolution is important. Based on material corrosion theory summary FRP pipe used in CO2 environment, we analyze the main form and the specific process material corrosion, the use of aromatic amine curing and acid anhydride curing two fiberglass pipe as a test tube, analog GFRP pipe containing crude oil, the next CO2 and water medium corrosion test, by surface morphology material, the glass transition temperature changes, and performance to evaluate physical corrosion mechanism of FRP in CO2 in; the test results show that CO2 environment, glass and steel addition to the visible Exterior changes, its glass transition temperature, Pap hardness, ring stiffness, density, and curing of the resin content showed a downward trend.

134

**Pantea Davoudifar**, Research Institute for Astronomy and Astrophysics of Maragha , Astroparticle Physics , Iran (Islamic Republic of)

**Keihanak Rowshan Tabari**, Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Astroparticle physics Group, Iran (Islamic Republic of)

**Abstract:**A model of turbulent galactic magnetic fields was developed, in which the type of magnetic fields were considered to be Kolmogorov. We tested the effect of this model on an isotropically distributed flux of ultra high energy cosmic ray in the extragalactic space. To do this, a giant halo of Galaxy was considered. Regular and random components of the Galactic Magnetic Fields were considered to have the mean observed relevant values and also satisfy a Kolmogorov field type. The deviation from isotropy then were calculated using this model and the results were discussed to show how isotropic is the flux of ultra high energy cosmic rays in the extragalactic space.

**Acknowledgements:**This work has been supported financially by research Institute for Astronomy and Astrophysics of Maragha (RIAAM)-Maragha, under research project No. 1/4165-23

135

**Pantea Davoudifar**, Research Institute for Astronomy and Astrophysics of Maragha , Astroparticle Physics , Iran (Islamic Republic of)

**Keihanak Rowshan Tabari**, Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Astroparticle physics Group, Iran (Islamic Republic of)

**Abstract:**Using a Galactic magnetic field model in combination with an extragalactic model of magnetic fields and considering the observed flux of ultra high energy cosmic rays; an anisotropic flux of these particles were estimated in the intergalactic space. To do this, we have considered the ultra high energy events were all originated from extragalactic sources in the distances not more than 75 mega parsecs. Then using our results, the origin of ultra high energy cosmic rays in the energies ranged from 10^18 up to the highest energies were discussed for the possible extragalactic point sources.

**Acknowledgements:**This work has been supported financially by research Institute for Astronomy and Astrophysics of Maragha (RIAAM)-Maragha, under research project No. 1/4165-27

136

**Ayse Humeyra Bilge**, Kadir Has University, Faculty of Engineering and Natural Sciences, Turkey

**Abstract:**The Istanbul Straight (Bosphorus) is a 31 km long narrow channel in the north-south direction joining the Black Sea and the Sea of Marmara basins. The high salinity Mediterranean water flows at the bottom layer from south to north while the low salinity Black Sea water flows at the top layer in the reverse direction. Increased river fluxes to the Black Sea during the spring and strong southward/northward wind systems influence and disturb the stratified flow in the Istanbul straight, causing blockages and current reversals under extreme conditions. The south and north exits of the straight are marked by sills at depths 33 and 61 meter respectively, forming hydrological control points. There is a third control point 10 km north of the southern entrance, caused by a contraction. Salinity profiles show that the flow along this 10 km part of the straight is a nearly horizontal stratified flow [Ozsoy, Iorio, Gregg, Backhaus, J. Marine Systems 31 (2001) 99-135]. There is about 30 cm difference between the sea levels at the north and south entrance, causing a net southward flux throughout the year. Excessive river runoffs to the Black Sea, that are more effective in summer, cause variations in the fluxes of both layers but the effects of atmospheric forcing on flux variations is less accentuated [Jarozs, Teage, Book, Besiktepe, Geophys. Res. Lett. 38 (2011) L21608]. In this work we study the variations in the upper layer due to wind effects under the assumption of uniform flow with constant flux, as a toy model at least for the region between the two south control points of the Bosphorus. Such effects have been analysed in an experimental study [Plate and Goodwin, Proceedings Santa Barbara Speciality Conference (1965)] where it is shown that sufficiently prolonged strong winds lead to increased velocities and decreased height in open channel flows. We use an analytical model to describe the steady-state water velocity profile induced by wind effects and use the constant flux assumption to compute the steady state layer height by determining the boundaries of the flux integral. The results agree with the available data for the water and wind speeds at observed blocakge and current reversal events.

137

**Vladimir Kahsurnikov**, National Research Nuclear University (Moscow Engineering Physics Institute), Physics of the Solid State and Nanosystems, Russian Federation

**Anastasiya Maksimova**, National Research Nuclear University (Moscow Engineering Physics Institute), Physics of the Solid State and Nanosystems, Russian Federation

**Igor Rudnev**, National Research Nuclear University (Moscow Engineering Physics Institute), Physics of the Solid State and Nanosystems, Russian Federation

**Dmitry Odintsov**, National Research Nuclear University (Moscow Engineering Physics Institute), Physics of the Solid State and Nanosystems, Russian Federation

**Abstract:**The Monte Carlo simulations have been used to study the dynamics of three-dimensional vortex system in layered high-temperature superconductors with internal nanosized ferromagnetic defects. The magnetization processes in the array of ferromagnetic defects under the field of Abrikosov vortices have been taken into account. The current-voltage characteristics under applying of external dc magnetic field have been obtained. It has been shown that S-type nonlinearity of E(J) curve which had previously been obtained for two-dimensional vortex system also appears in more realistic anisotropic three-dimensional case. The effect of vortex-vortex inter-layer coupling on the S-nonlinearity has been analyzed. The wave of defects magnetization in three-dimensional case arising for the vortex flow has been shown.

**Acknowledgements:**Research was done with the financial support of RSF under grant № 14-22-00098

138

**Alexander Zuevsky**, Academy of Science of the Czech Republic, Mathematics, Czech Republic

**Abstract:**We give a conformal block description for the Zhu reduction formulae for vertex operator algebras with formal parameters associated to local coordinate on a genus two Riemann surface formed by sewing two initial tori in a geometric procedure. An example of Heisenberg vertex operator algebra is given.

139

**Humberto Híjar**, La Salle University Mexico, Engineering School, Mexico

**Abstract:**We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations. We also present an irreversible thermodynamics approach for the study of this system.

**Acknowledgements:**Authors acknowledges La Salle University Mexico for support under grant NEC-04/15

140

**Pierre Dahoo**, Université de Versailles-St. Quentin en Yvelines, LATMOS, France

**Jorge Linares**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Daniel Chiruta**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Christian Chong**, LISV, Université de Versailles St. Quentin en Yvelines, 78035 Versailles, France, , France

**Philippe Pougnet**, VALEO, 14 avenue des Béguines - BP 68532 Cergy, 95892 Cergy Pontoise Cedex, France, , France

**Constantin Meis**, CEA-Saclay , National Institute for Nuclear Science and Technology, France

**Abdelkhalak El Hami**, INSA ROUEN Laboratoire de Mécanique, Pôle Technologique du Madrillet Avenue de l'Université, BP 8-76801 Saint Etienne du Rouvray, , France

**Abstract:**A Monte Carlo (MC) simulation of a 2D microscopic Ising model is developed to study the effect of thermal cycling on the lead free interconnect alloy of a mechatronics device. In order to understand the physical degradation processes of this alloy leading to failure, the impact of of temperature cycling on the growth and crack propagation [1] is studied. This work focuses on specific mechatronics systems in which die attach reliability needs to be improved. To determine the physical processes leading to failure, an ABV model [2] (Metals A and B and void V) is developed. A Monte Carlo (MC) simulation of this 2D microscopic Ising model is used to study the evolution of a homogeneous structure of a binary alloy containing voids at a particular temperature. In this approach a three states Ising Hamiltonian is used which depends on 3 parameters K,J and U and a fictitious spin σ value which can be set to -1, 0, 1. K, J and U are parameters function of the interaction energy parameters between the metal atoms A, B and void V. In order to model the observed diffusion of intermetallics in interconnexion materials, the interaction parameters EAA, EBB and EAB are adjusted and the time evolution of this material pseudo-spin configuration is calculated. The results are discussed in terms of intensity of these parameters and void percentage. 1: Pierre Richard Dahoo, Nadim Alayli, Armelle Girard, Philippe Pougnet, Ky-Lim Tan and Jean-Michel Morelle, Reliability in Mechatronic Systems from TEM, SEM and SE Material Analysis, in Reliability and Materials Issues of Semiconductor Optical and Electrical Devices and Materials, edited by O. Ueda, M. Fukuda, S. Pearton, E. Piner, P. Montanegro, Mater. Res. Soc. Symp. Proc. Warrendale, PA, 1195, B07-04.R1 (2010). 2: Yaldram, K. and Binder, K., Monte-Carlo simulation of phase-separation and clustering in the ABVmodel. Journal of Statistical Physics, 62, 161, 1991

**Acknowledgements:**CHAIR MSE UVSQ

141

**Pierre Dahoo**, Université de Versailles-St. Quentin en Yvelines, LATMOS, France

**Raphael Puig**, CHAIR Materials Simulation and Engineering UVSQ, Université Paris Saclay, 78035 Versailles Cedex, France, , France

**Azzedine Azzedine Lakhlifi**, Institut UTINAM-UMR 6213 CNRS- Université de Franche-Comté, Observatoire de Besançon, 25010 Besançon Cedex, France, , France

**Constantin Meis**, CEA-Saclay , National Institute for Nuclear Science and Technology, France

**Abstract:**: Clathrates are characterized by a compact assembly of low temperature nano-cages that naturally contain an atom or molecule that stabilizes their formation as cubic sI and sII or hexagonal sH structures. Infrared vibrational frequencies of triatomic carbon dioxide CO2 trapped in the nano cages are shifted (less than 0.5% of the observed gas phase frequencies as a result of a slight perturbation of the intramolecular electronic potential of the CO2 trapped molecule) from those of gas phase and the spectra are simpler because the rotational and translational degrees of freedom are cage-hindered. The energy levels (eigen states of the Hamiltonian operator) of the different degrees of freedom of CO2 are calculated within the frame of the Born Oppenheimer approximation [1][2]. The potential energy hypersurface experienced by the molecule in its nanocage of type n can then be written in terms of the minimum of the potential energy (the equilibrium configuration); the vibrational dependence in the normal vibrational coordinates {Q}; the orientational dependence in Euler angles(Omega=(phi, theta, khi),khi=0 for a linear molecule);the vibration-orientation coupling term, which induce the relaxation channels and n characterize the site (n=1 for small and n=2 for or large cage). The the displacement vectors (centre of mass) of of water molecules of the clathrate and the trapped molecule are calculated from the Green functions of the perfect crystal. In an attempt to simulate the relaxation of absorbed infrared energy in a clathrate, the different channels through which energy can spread inside, after CO2 absorbs infrared radiation are depicted. The results of these calculations are to be connected to the effects of global warming on the stability of clathrates. Depending on the competition between radiative and non-radiative relaxation, a limited temperature rise warming effect of the clathrate may occur as in low temperature matrices because of stimulated emission. This depends on how isolated CO2 is inside the nanocages of a clathrate. Results are compared from the point of view of the trapping site effect, the shifts observed for the different fundamental vibrational modes and the effect of coupling on the relaxation constants of intramolecular energy levels. [1] A. Lakhlifi, P.R. Dahoo, E. Dartois, E. Chassefière et O. Mousis, Modeling IR spectra of CO2 isotopologues and trapped In type I clathrate EPOV 2012: From Planets to Life - Colloquium of the CNRS Interdisciplinary Initiative "Planetary Environments and Origins of Life", Paris, France, November 29-30, 2012, février, vol 2, 03008, EDP Sciences, BIO Web of Conferences, M. Ollivier et M.-C. Maurel, eds., ISBN: 978-2-7598-1180-9, [2]P.R Dahoo., A. Lakhlifi, S. Picaud, C. Thomas, E. Dartois and E. Chassefière, Spectroscopy of CO2 modelled in Clathrates, 56th ICASS, U. Alberta, Edmonton, Canada, 15-18 August 2010.

**Acknowledgements:**CHAIR MSE UVSQ

142

**Natalya Shipulya**, Peter the Great St.Petersburg Polytechnic University, , Russian Federation

**Stepan Konakov**, Peter the Great St.Petersburg Polytechnic University, , Russian Federation

**Valeria Krzhizhanovskaya**, University of Amsterdam, The Netherlands; ITMO University and St. Petersburg Polytechnic University, , Russian Federation

**Abstract:**In this work we present the results of analytical modeling and 3D computer simulation of microfluidic Wheatstone bridge, which is used for high accuracy measurements or precision systems. A geometrical configuration of microchannels was selected based on analytical estimations. The detailed 3D model is based on Navier-Stokes equations for a laminar flow of liquid in microchannels with low Reynolds number. We proposed and simulated a new method of a bridge balancing process by changing the microchannel geometry. This process is based on the “etching in microchannel” technology we developed earlier. Our method implements a precise control of flow rate and flow direction in the ‘‘bridge’’ microchannel. An advantage of our approach is ability to work without any control valves and other active electronic systems, which are usually used for bridge balancing. Using an analytical model and results of 3D computer simulation we investigated the behavior of the Wheatstone bridge with different model parameters. We found a relation between the channel resistance and flow rate through the bridge, and calculated a pressure drop across the system under different total flow rates and viscosities. Some ideas about application of described Wheatstone bridge in accuracy measurements and complex precision microfluidic systems were suggested for future work.

143

**Irina Knyazeva**, Pulkovo observatory, sector of mathematical modeling in geophysics, Russian Federation

**Irina Makarenko**, Newcastle University, UK, , United Kingdom

**Alina Vdovina**, Newcastle University, UK, , United Kingdom

**Nikolay Makarenko**, Pulkovo observatory, , Russian Federation

**Fedor Urtiev**, Pulkovo observatory, , Russian Federation

**Abstract:**Analysing dynamics of the photospheric magnetic field of the Sun is one of the most important problems in Solar Physics. Different estimates of the complexity of magnetograms of the Sun Active Regions (AR) are used to predict the time and the strength of the solar flares. Complexity of random fields (including magnetic fields) is described by the structure and behavior of their critical points. A magnetogram is a highly variable discrete image with very large number of local extrema. We use an idea of extraction of stable critical points within a framework of the scale-space proposed in [Steve Gu et al, 2010]. The convolution of the image with a Gaussian kernel and the difference between the received images allow to get a stable estimation of the Laplacian. A critical graph is constructed using maxima and minima of the Laplacian. This graph is not a Morse graph since it does not have saddle points. In the process of evolution of an AR the number and the values of local extrema are changing. Therefore the structure of a critical network is also changing. So the dynamics of critical graphs can be used for diagnosis of dynamical regimes of ARs. As a numerical descriptor we propose to use the so-called spectral gap. It is the difference between the two largest eigenvalues of the discrete Laplacian of the graph constructed for critical networks. Here we provide results for several ARs.

144

**Chehung Wei**, Tatung University, Mechanical Engineering, Taiwan

**Li-Chung Chang**, Tatung Univerisity, Mechanical Engineering, Taiwan, Province Of China

**Abstract:**The effect of substrate roughness on the film hardness is often modeled by a periodic roughness distribution to simplify the analysis. However, in real world application the roughness is random rather than periodic. Therefore, it is essential to assess the discrepancy between simplified and real world modeling. To address this problem, the hardness is evaluated by a nanoindentation finite element analysis using diamond-like carbon (DLC) film on a rough silicon substrate. Arithmetic average roughness Ra is chosen to represent the substrate roughness. Two types of roughness distributions, periodic and random distributions are used to represent the simplified and real world problem, respectively. The comparison is based on fact that the average roughness magnitude in random distribution is the same as that in periodic distribution. Six roughness magnitudes 5 nm, 20 nm, 35 nm, 50 nm, 200 nm, 350 nm and 500 nm are utilized to investigate the effect of roughness distribution. The results show the hardness is affected by the substrate roughness variation. For periodic roughness distribution, the hardness exhibits a synchronized pattern irrespective of the roughness magnitude. For random roughness, the randomness in hardness variation is not significant when Ra is less than 50 nm. When Ra is above 200 nm, the hardness variation becomes larger and exhibits no specific pattern. The local hardness in low Ra might be larger than that in high Ra. This indicates for random roughness, Ra alone can not predicate the overall hardness behavior. Another finding is, the average hardness in periodic roughness is larger than that in random roughness for same average Ra. This implies roughness modeling by periodic roughness tends to overestimate the hardness. In conclusion, the type of roughness distribution has an effect in local and overall hardness. The local roughness might affect the hardness measurement.

145

**Vladimir Kashurnikov**, National Research Nuclear University MEPhI, , Russian Federation

**Andrey Krasavin**, National Research Nuclear University MEPhI, Physical and Technical Problems of Metrology, Russian Federation

**Yaroslav Zhumagulov**, National Research Nuclear University MEPhI, , Russian Federation

**Abstract:**The momentum distribution of charge carriers in two-dimentional FeAs-clusters modeling iron-based superconductors was calculated within the limits of the two-orbital model. The calculation was implemented by use of quantum world-line Monte Carlo algorithm. Matsubara Green's function was calculated for clusters with sizes up to 10x10 FeAs-cells. Profiles of the distributions are presented for the entire Brillouin zone. The data indicate the presence of a jump near the Fermi level, which is the evidence of the Fermi-type distribution. The influence on the momentum distribution of the value of the interaction parameter, cluster size and temperature is discussed.

146

**Andrei Lebed**, University of Arizona, Department of Physics, United States

**Abstract:**We determine active gravitational mass operator of the simplest composite quantum body - a hydrogen atom - within the semiclassical approach to the Einstein equation for a gravitational field. We show that the expectation value of the mass is equivalent to energy for stationary quantum states, as expected. On the other hand, it occurs that, for superpositions of stationary quantum states with constant expectation values of energy, the expectation values of the gravitational mass exhibit time-dependent oscillations. This breaks the equivalence between active gravitational mass and energy and can be observed as a macroscopic effect for a macroscopic ensemble of coherent quantum states of the atoms. We discuss experimental aspects of the above-mentioned breakdown and stress that the corresponding experiment could be the first direct observation of quantum effects in General Relativity.

**Acknowledgements:**This work was partially supported by the NSF under Grant DMR-1104512.

147

**Ayse Humeyra Bilge**, Kadir Has University, Faculty of Engineering and Natural Sciences, Turkey

**Abstract:**Let y(t) be a sigmoidal function, i.e, a monotone increasing curve with horizontal asymptotes and such that all derivatives vanish at infinity. Let t_n be the point where the n'th derivative of y(t) reach its global extremum. Under fairly general assumptions on the Fourier and Hilbert transforms of y(t), we prove that the sequence {t_n} is convergent and call it "the critical point of the sigmoidal curve". In the context of phase transitions, the limit point is interpreted as a junction point of two different regimes where all derivatives undergo their higest rate of change. The existence of a critical point implies in particular a preferred choice of the origin of the time axis and an intrinsic definition of the even and odd components of a sigmoidal function. The location of the critical point agrees qualitatively with the location of the gel point in the sol-gel transition as discussed in previous work.

148

**Pedro Alberto**, University of Coimbra, Department of Physics, Portugal

**Manuel Malheiro**, Instituto Tecnológico de Aeronáutica, DCTA, 12228-900 São José dos Campos, , Brazil

**Tobias Frederico**, Instituto Tecnológico de Aeronáutica, DCTA, 12228-900 São José dos Campos, , Brazil

**Antonio Castro**, Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratinguetá, , Brazil

**Abstract:**A generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg, is proposed. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2- and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.

**Acknowledgements:**Universidade Estadual Paulista, Guaratinguetá Campus, FAPESP thematic project 2015/26258-4 and CNPq.

149

**Julio Espinoza-Ortiz**, Federal University of Goias, Physics Department , Brazil

**F. C. Bauke**, Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin, Brazil

**R. E. Lagos**, Universidade Estadual Paulista, Departamento de Física, IGCE, Brazil

**Abstract:**We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.

**Acknowledgements:**JSEO would like to thank the support of the Goiás Research Foundation - FAPEG

150

**Won-Kwang Park**, Kookmin University, Mathematics, Korea, Republic of

**Abstract:**Throughout various works, it has been confirmed that only a small number of directions of incident fields is needed for applying topological derivative. In this contribution, we consider topological derivative based technique with a small number of such directions for imaging of thin, curve-like dielectric inhomogeneities embedded in a homogeneous domain and explore a suitable condition via various results of numerical simulations.

151

**Hossein Ghaffarnejad**, Semnan University, Physics, Iran (Islamic Republic of)

**Abstract:**Two dimensional analogue of vacuum sector of the Brans Dicke gravity [1] is studied to obtain dynamics of anisotropic spherically symmetric perfect fluid. Solutions of dynamical field equations are obtained in terms of time and radial coordinates. In static regime the obtained solutions describe dark matter fluid regime with state equation $\gamma=\frac{p(\rho)}{\varrho}=-0.25.$ For non-static regime the fluid can be treat as regular matter with positive barotropic index $\gamma>0.$ Evaluation of total mass of the fluid leads to choose particular values on the Brans Dick parameter as $\omega>\frac{2}{3};\omega<-1$. Positions of the horizons (event and apparent) of the collapsing fluid are obtained in its static regime. In case $\omega>0$ the apparent horizon is covered by event horizon where the cosmic censorship hypothesis is still valid. \\ In second part of the paper we obtain de Broglie pilot wave of our fluid model. It can be describe particles ensemble which are distinguished from each other via different values $\omega.$ Incident current density of particles ensemble is evaluated on the event and apparent horizons describing which can be called as the `Hawking radiation`. The quantum potential is calculated on the event (apparent) horizon which is independent (dependent) to values of the Brans Dicke parameter $\omega.$

152

**BOUSSAHEL MOUNIR**, M'sila University, Physics, Algeria

**Abstract:**The construction of the (331) model was successfully performed within a framework of the graded Lie algebra NCG. In input, the Dirac representation can be the most general, by adopting the condition of Wulkenhaar, the (331) gauge models are obtained with new physical properties in addition to classical models, if not mathematical model building in the case of NCG itself is the source of a new physics especially concerning the Higgs.

153

**Reza Abazari**, Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran, Department of Mathematics, Iran (Islamic Republic of)

**Abstract:**In this paper, the (G'/G)-expansion method is proposed to construct the exact traveling solutions of a second order wave equation of KdV type: u_t-u_{xxx}+\frac{1}{8}u_x^3-u_x(p\,e^u+q\,e^{-u})=0, where pq=/= 0. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. The method appears to be easier and faster by means of a symbolic computation system.

154

**Ioannis ZOIS**, Public Power Corporation, Testing, Research & Standards Centre, Greece

**Abstract:**We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.

155

**Spyridon Vossos**, NKUA, Chemistry, Greece

**Elias Vossos**, NKUA, Physics, Greece

**Abstract:**Relativity Theory (RT) and the corresponding Relativistic Quantum Mechanics (RQMs) are the fundamental theories of physics. Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs), through Linear Spacetime Transformation (LSTT) of linear spacetime. Classic Relativity (CR) uses real spacetime endowed with Lorentz metric and two frames of RIOs with parallel spatial axes are related through Lorentz Boost (LB). This cancels the transitive attribute in parallelism, when three RIOs are related, because LB is not closed transformation, causing Thomas Rotation. In this presentation, we consider a closed LSTT of Complex Spacetimes (CSTs), so there is no necessity for spatial axes rotation and all the frames are chosen having parallel spatial axes. The solution is expressed by a 4x4 matrix with elements containing components of the complex velocity of one RIO (βx, βy, βz) wrt another RIO and two functions of its norm (h, λ). Moreover, it emerges an equation (condition) relating the above parameters. So, it emerges a class of metrics which are in accordance with the condition. Choosing one of the acceptable metrics or an invariant quantity (isometry), the problem is totally solved. Sometimes the elements of the 4x4 matrix are complex numbers and the corresponding spacetime is necessarily complex and sometimes not. Thus, we have infinite number of closed LSTTs, each one with the corresponding special relativity theory. The first solution is Galileo Transformation (GT) endowed with Euclidean metric of real space and the invariant time, in which any other closed LSTT is reduced, if one RIO has small velocity wrt another RIO. A second solution is Vossos transformation (VT) endowed with Lorentz metric of complex spacetime and invariant spacetime interval (or equivalently invariant speed of light in vacuum – c), which produce the theory of Euclidean Complex Relativistic Mechanics (ECRMs). Some other closed LSTTs endowed with their acceptable metric of spacetime and their invariant quantity, are presented. In case that we relate observers with different metric of spacetime, we have the case of General Relativity (GR). The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any complex or real spaces of dimension four endowed with the same or different metric, whose elements (four-vectors) have spatial part (vector) with Euclidean metric.

156

**Shabnam Jamshidzadeh**, Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran, Mathematics, Iran (Islamic Republic of)

**Abstract:**In this paper, we applied the (G'/G)-expansion method to construct more general exact solutions of three special types of Boussinesq equation: namely Boussinesq equation, improved Boussinesq equation and variant Boussinesq equation, where the French scientist \textit{Joseph Valentin Boussinesq} (1842–-1929) described in the 1870’s model equations for the propagation of long waves on the surface of water with a small amplitude. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.

157

**Bartek Wierzba**, Rzeszow University of Technology, Materials Science, Poland

**Abstract:**The complete understanding of the phenomenological process related to the evolution of the ternary multiphase systems is still lacking. In this paper the ternary interdiffusion process in multiphase system is discussed by means of numerical modeling. The entropy production principle is proposed to chose the proper diffusion path during the process (e.g. internal oxidation). The simulations present the local entropy production curve that determines the diffusion path in Ni-Al-Ti ternary diffusion couple.

158

**Marcin Lawnik**, Silesian University of Technology, Faculty of Applied Mathematics, Poland

**Abstract:**The logistic map is commonly used in, for example, chaos based cryptography. However, its properties do not render a safe construction of encryption algorithms. Thus, the scope of the paper is a proposal of the generalization of a logistic map by means of a well-recognized family of chaotic transformations. In the next step, an analysis of Lyapunov exponent and the distribution of a iterative variable are studied. The obtained results confirm that the analyzed model can safely and effectively replace a classic logistic map for applications involving chaotic cryptography.

159

**Liang Zhang**, Jiangsu Normal University, School of Mechanical and Electrical Engineering, China

**Zhi-quan Liu**, Chinese Academy of Sciences, , China

**Liang Zhang**, Jiangsu Normal University, School of Mechanical and Electrical Engineering, China

**Yu-tong Ji**, Jiangsu Vocational Institute of Architectural Technology, , China

**Abstract:**Anand constitutive relation of SnAgCu and SnAgCu-nano Al solders were studied under uniaxial tension, and the constitutive model was used in the finite element simulation to analyze the stress-strain response of lead-free solder joints in 3D IC devices. The results showed that the nine parameters of the Anand model can be determined from separated constitutive relations and experimental results. Based on Anand model, the finite element method was selected to calculate the stress-strain response of lead-free solder joints, it was found that in the 3D IC device the maximum stress-strain concentrated in the concern solder joints, the stress-strain of SnAgCu-nano Al solder joints was lower than that of SnAgCu solder joints, which represented that the addition of nano Al particles can enhance the reliability of lead-free solder joints in 3D IC devices.

160

**Jorge Linares**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Abstract:**C. Jureschi, J. Linares, P. R. Dahoo, Yasser Alayli ABSTRACT Monte Carlo methods are one of the most utilized methods by researches in order to model probabilistic or stochastic systems whose analytical solutions are too complicated or impossible to obtain. In this paper we present the Monte Carlo entropic sampling [1] applied to an Ising-like model for 2D and 3D system in order to show the interaction influence of the edge molecules of system with their local environment. To take into account the interaction between the edge molecules with the environment, we use the Hamiltonian system proposed in a previous work [2]: We show that, as for the 1D [2], 2D [3] spin crossover (SCO) systems, the origin of multi steps transition in 3D SCO is the effect of the edge interaction molecules with local environment. Another important result worth noting is the co-existence of step transition with hysteresis and without hysteresis and that by increasing the value of the edge interaction, L, the transition is shifted to the lower temperatures: it means that the role of edge interaction is equivalent to a applied negative pressure. We analyze also, in this contribution, the role of the short- and long-range interaction, J respectively G, with respect to the environment interaction, L in equation (1). 1. Linares, J.; Enachescu, C.; Boukheddaden, K.; Varret, F., Monte Carlo entropic sampling applied to spin crossover solids: the squareness of the thermal hysteresis loop. Polyhedron 2003, 22, (14-17), 2453-2456. 2. Chiruta, D.; Jureschi, C.-M.; Linares, J.; Dahoo, P.; Garcia, Y.; Rotaru, A., On the origin of multi-step spin transition behaviour in 1D nanoparticles. The European Physical Journal B 2015, 88, (9), 1-5. 3. Jureschi, C.-M.; Pottier, B.-L.; Linares, J.; Dahoo, P.R.; Alayli, Y.; Rotaru, A., Simulation of multi-steps thermal transition in 2D spin-crossover nanoparticles. Physica B: Condensed Matter,

**Acknowledgements:**CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay, 78035 Versailles Cedex, France.

161

**Alessandra Magno**, Universidade Federal de Juiz de Fora, Departamento de Ciência da Computação, Brazil

**Itamar De Oliveira**, Universidade Federal de Juiz de Fora, Departamento de Ciência da Computação, Brazil

**João Vitor De Sá Hauck**, Instituto Federal do Rio de Janeiro, Campus Engenheiro Paulo de Frontin, Brazil

**Abstract:**The main goal of this work is to add and analyse an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Goldbeter (2011). The cell division occurs when the cyclinB/Cdk1 complex is totally degraded and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cytoplasmic content of the mother cell. The equations of our base model are only valid if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation principle for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were accomplished: deterministic and stochastic. In the stochastic simulation, the volume affects every model's parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation an stability analysis was performed. This elucidates how the growth factor impacts the stability of the model's limit cycles. In order to find the approximated solution of the deterministic model, the fourth order Runge Kutta method was implemented. As for the stochastic model, the Gillespie's Direct Method was used. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the cell volume variation.

162

**Pavel Tonkaev**, Peter the Great St.Petersburg Polytechnic University, Institute of physics, nanotechnology and telecommunications, Russian Federation

**Alexey Kondikov**, Peter the Great St. Petersburg Polytechnic University, Institute of physics, nanotechnology and telecommunications, Russian Federation

**Vladimir Chaldyshev**, Peter the Great St. Petersburg Polytechnic University, , Russian Federation

**Abstract:**Measurements of the optical reflection spectra from periodic structures with two quantum wells in the elementary cell have been done. The dependencies of the light reflection on the angle of the light incidence, polarization and temperature were studied. An analysis of the experimental data showed that the pattern with 60 cells is a good Bragg reflector with reflectivity more than 90% in the maximum of the spectral band.

163

**Alexey Kondikov**, Peter the Great St. Petersburg Polytechnic University, Institute of physics, nanotechnology and telecommunications, Russian Federation

**Vladimir Chaldyshev**, Peter the Great St. Petersburg Polytechnic University, , Russian Federation

**Pavel Tonkaev**, Peter the Great St.Petersburg Polytechnic University, Institute of physics, nanotechnology and telecommunications, Russian Federation

**Abstract:**Software was developed for quick numerical calculations and graphic display of the absorption, reflection and transmittance spectra of two-dimensional systems of small conductive particles, which allowed us to make instant comparison with experimental data. A lattice-gas model was used to simulate nearly distributed particles, and the coherent-potential approximation is applied to obtain a solution to the problem of interacting particles. The Delphi programming environment was used.

164

**Tomasz Blachowicz**, Silesian University of Technology, Institute of Physics, Poland

**Andrea Ehrmann**, Bielefeld University of Applied Sciences, Department of Engineering Sciences and Mathematics, Germany

**Abstract:**Magnetic nano-structures can be used in various applications. Due to their possible utilization in data storage media, examinations of nano-structured systems often aim at decreasing the pattern size, in order to enhance the possible information density in a given area. Since this scaling process is limited by the resolution of the lithography process which is used to produce the nano-particles, it is important to determine the influence of erroneous shape modifications on the magnetic properties, such as magnetization reversal processes and coercive fields. For this, a square nano-wire system from permalloy has been simulated using Magpar. In a former work, changes of the wire diameter have been shown to result in different magnetization reversal mechanisms and significantly altered coercive fields. In a new project, the intersections of the wires – which are most susceptible to undesired shape modifications – have been changed by adding or subtracting parts. Additionally, the wire intersections have been separated step by step, resulting in a qualitatively changed angular dependence of the coercive fields. Similar experiments have been performed for nano-squares with walls of rectangular cross-section. This study allows for estimation of the reliability of magnetic properties of nano-structures with respect to undesired shape modifications in the lithography process.

165

**Tomasz Blachowicz**, Silesian University of Technology, Institute of Physics, Poland

**Andrea Ehrmann**, Bielefeld University of Applied Sciences, Department of Engineering Sciences and Mathematics, Germany

**Abstract:**While the properties of conductive fibers and coatings on textiles can easily be measured and calculated, magnetic coatings of fibers, yarns and fabrics still lack descriptions of their physical properties. Since magnetic textiles can be used for a variety of applications, from magnetic filters to invisible water-marks to magnetic coils and sensors, simulations would be supportive to understand and utilize their properties. The articles gives an overview of different coatings on textile fibers, varying the magnetic materials as well as the fiber composition, giving rise to the interactions between neighboring coated fibers. In this way, it is possible to understand the strong shape anisotropy which must be taken into account when the magnetic properties of textiles are to be tailored. Additionally, the differences between several possible magnetic coating materials become visible. This study can help adjusting the magnetic properties of textile fabrics to a desired application.

166

**Jaqueline Da Silva**, UFVJM, , Brazil

**Abstract:**We present a computational model for the tree growth process in flooded areas of the Amazon Forest that contemplates seed dispersion processes and influence of light in the model. These processes, strongly influenced by the annual food, occur early in the plant's life cycle and affect the distribution, structure and dynamics of tree populations. The study of these processes is very important to understand the dynamics of the flooded ecosystems and their sustainable management. To study the spatial distribution of seeds in a region and the growth of germinated seeds, we define an influence region for a mature tree in the growth of the seeds, the growth neighborhood of young trees and the probability of a seed to fall at any point of this neighborhood. We make the hypothesis that every year each mature tree produces affixed number of seeds. The seeds are distributed in accordance with a probability that varies with the distance from a mature tree. Seed-germination and the growth process depend on access to the solar light. In particular, since the canopies of mature-trees in a neighborhood of a young-tree contain sufficient dense leaves and twigs structure, the light shall vary and influence the growth of surrounding trees. Indeed, for most species, the nearer a young-tree is from a mature-tree, smaller will be its possibility to survive. In some cases it may occur the death of these individuals by shading.

167

**Vladimir Zeitlin**, Ecole Normale Supérieure, Laboratory of Dynamical Meteorology, France

**Abstract:**Thermodynamics of the moist air is very complicated so, for the purposes of weather and climate modeling, various simplifications and parameterzations are being used in general circulation models of the atmosphere. Dynamics of atmospheric jets and vortices which, together with inertia-gravity waves, constitute the principal dynamical entities of large-scale atmospheric motions, is well-represented in the framework of one- or multi-layer rotating shallow water models, which are obtained by vertically averaging of full "primitive" equations. We show that by adding a simple relaxational parameterization of precipitations and coupling the precipitation with convective fluxes with the help of moist enthalpy conservation results in moist-convective rotating shallow water model ( Bouchut, Lambaerts, Lapeyre and Zeitlin, 2009, Phys. Fluids, v. 21, 116604; Lambaerts, Lapeyre, Zeitlin and Bouchut, 2011, Phys Fluids, v. 23, 046603) which provides an optimal compromise between simplicity and fidelity of reproducing the moist-precipitating dynamics. Numerical simulations with a well-balanced shock-resolving finite-volume numerical scheme (Bouchut and Zeitlin, 2010, Disc. Cont. Dyn. Sys. B, v.13, 739) capture surprisingly well the life-cycle of the moist baroclinic instability (Lambaerts, Lapeyre and Zeitlin, J. Atmos. Sci. 2012, v. 69, 1405). The life-cycle of tropical cyclones is also well-reproduced within the model (N. Lahaye and V. Zeitlin, 2016, J. Atmos. Sci. , to appear). We will give further examples of the applications of the model.

168

**Rubén BOURDON GARCÍA**, Saint Matthew Fundation for the High Education, Technology Development Center - CDTEC, Colombia

**Javier BURGOS SALCEDO**, Ciinas Corporation, Research and Development, Colombia

**Abstract:**Actually, there is a huge necessity to generate novel strategies to social-ecological systems analyses for resolving global sustainability problems. This dissertation has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Angel Maya, who without doubt, was one of the most important environmental philosophers in South America; Angel Maya proposed and established that Ecosystem - Culture relations, instead Human - Nature ones, is determinant in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept - super- concept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne - Guigues base), were determined for the ecosystem - culture relations.

169

**Leonid Son**, Ural Federal University, Physical - technical institute, Russian Federation

**Dmitry Shulgin**, Ural Federal University, Physical - technical institute, Russian Federation

**Olga Ogluzdina**, Ural Federal University, Physical - technical institute, Russian Federation

**Abstract:**A wide variety of systems may be described by specific dependence, which is known as logistic curve, or S-curve, between the internal characteristic and the external parameter. Linear feedback between these two values may be suggested for a wide set of systems also. In present paper, we suggest a bifurcation behavior for systems with both features, and discuss it for two cases, which are the Ising magnet in external field, and the development of innovative enterprise.

**Acknowledgements:**The work was supported by Russian Ministry of Science and Education (Government job 2014/392 projects 2391 and 1177), and by Goverment of the Russian Federation, act 211 contract № 02.A03.21.0006.

170

**Marco Zoli**, University of Camerino, School of Science and Technology, Italy

**Abstract:**Many experiments have demonstrated that DNA exhibits sequence-dependent bending and torsional flexibility which influence the DNA-protein interplay and are relevant for biological processes like transcription and replication in living cells. DNA flexibility is tested by a path integral method [1-4] which analyses the propensity of short DNA sequences to convert to the circular form. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the model potential, mostly to the non-linear stacking parameters. We find that the J -factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent data provided by fluorescence resonance energy transfer assays. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales. I also discuss some preliminary results regarding the single molecule stretching under the effect of an external force which samples the DNA mechanical properties at the nano-metric scale. [1] M. Zoli, The Journal of Chemical Physics 141, 174112 (2014). [2] M. Zoli, Soft Matter 10, 4304-4311 (2014). [3] M. Zoli, Journal of Physics: Conference Series 574, 012094 (2015). [4] M. Zoli, Europhysics Letters 110, 18001 (2015).

171

**Ju Chunhua**, Harbin Institute of Technology, Department of Materials Science, China

**Abstract:**GRP pipes for its excellent performance has been widely used for oil and gas gathering pipe. Because CO2 is used as displacing agent, causing corrosion problems CO2 FRP pipe, so the research GFRP pipe corrosion mechanism and performance in CO2 media evolution is important. Based on material corrosion theory summary FRP pipe used in CO2 environment, we analyze the main form and the specific process material corrosion, the use of aromatic amine curing and acid anhydride curing two fiberglass pipe as a test tube, analog GFRP pipe containing crude oil, the next CO2 and water medium corrosion test, by surface morphology material, the glass transition temperature changes, and performance to evaluate physical corrosion mechanism of FRP in CO2 in; the test results show that CO2 environment, glass and steel addition to the visible Exterior changes, its glass transition temperature, Pap hardness, ring stiffness, density, and curing of the resin content showed a downward trend.

172

**Jorge Linares**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Catalin Jureschi**, Université de Versailles-St. Quentin en Yvelines, LISV, France

**Daniel Chiruta**, Université de Versailles-St. Quentin en Yvelines, GEMaC, France

**Yasser Alayli**, Université de Versailles-St. Quentin en Yvelines, LISV, France

**Corneliu Turcu**, University of Suceava, Electrical Engineering and Computer Science, Romania

**Pierre Dahoo**, Université de Versailles-St. Quentin en Yvelines, LATMOS CNRS-UMR 8190, France

**Abstract:**Spin crossover (SCO) [1] is a symbolic example of molecular bistability, in which a diamagnetic low-spin (LS) and a paramagnetic high spin (HS) states are switchable by different physical causes such as magnetic field, pressure, light, and temperature or electrical filed [1]. The SCO materials are formed by 3d transition metal ions (3d4 - 3d7) in an octahedral coordination environment, which display a spin transition between the two states. In recent years, the SCO phenomenon has drawn an increasing attention from physics and chemist points of view, because of potential applications in future devices as sensor, display or data storage devices. In this paper we use a recent model called atom-phonon coupling model [2,3] to explain and illustrate the behavior of a linear chain of molecules. It is well known that besides the thermodynamic parameters which influence the hysteretic behavior of SCO compounds, the system’s architecture state configuration also plays a determinant role. The analysis of the system’s behavior has been studied using Free Energy method, and Monte Carlo Metropolis (MC) method which take into account the phonon contribution. In particular we compare the MC algorithm and the dynamic-matrix method and we determine how the thermal behavior of a 1D SCO system varies as a function of different factors. Furthermore we have blocked the edge atoms of the chain in high spin state to study the system’s behavior. The variation of entropy and heat capacity are analyzed in the ferro-like case for both architectures.

**Acknowledgements:**CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged

173

**Oleg Shkolik**, Ural Federal University, Graduate School of Economics and Management, Russian Federation

**Larisa Chirkova**, Ural Federal University, Institute of Physics and Technology, Russian Federation

**Polina Chirkova**, Ural Federal University, Graduate School of Economics and Management, Russian Federation

**Abstract:**Developing (underdeveloped) countries are territories of slow economic growth (catch-up growth). Perspectives of their economic growth largely depend on developing and introducing financial and technological innovations in the sphere of the financial markets. The level and quality of those innovations should enable provision of faster growth of the financial sector of the national economy by rising stability and effectiveness of the financial institutions. Powerful and stable financial sector is the basic element for attracting investments and upsurge of liquidity in the economic system of a developing country that aims to have developed economy. Intellectual capital is the most important of the fundamental factors of production in the financial sphere. It is a catalytic element of the process of the economic development. From this position, the researchers’ collective develops and presents a mathematical model which characterizes the connection between the intellectual capital and financial results of the commercial activity of financial institutions. The model is applied in the analysis of the activity of financial institutions that are part of the EEU.

174

**Xianwei Kang**, University of Murcia, Department of Physics, Spain

**Abstract:**Standard Model (SM) has becomes a fundamental theory in particle physics, but the efforts for searching for the New Physics (NP) phenomenon beyond SM never desists. The baryon-violating process that is prohibited by SM is one of the main directions, which is also related to the more basic question of understanding the baryon asymmetry in the universe. We notice that the standard DDbar mixing technique can be extended to the Lambda baryon sector, if the Lambda and antiLambda oscillation exists. In BES experiment, huge of Jpsi data can be accumulated. We then discuss the possibility of searching for Lambda-antiLambdar oscillation in the decay Jpsi->\Lambda \bar\Lambda. With one-year luminosity, we can put a constraint that the Lambda-antiLambda oscillation mass is smaller than 10^(-15) MeV at 90% confidence level, corresponding to the oscillation time of 10^(-6) second around. These measurments should be an extremely valuable information besides the neutron oscillation experiment, and also would be the first-time access by experiment.

**Acknowledgements:**I am very grateful for Prof. Hai-Bo Li in IHEP, Beijing, who imparts lots of knowledge. With whom, this work can be realized.

175

**ANA CARIUS**, Instituto Federal do Rio de Janeiro, Campus Duque de Caxias, Brazil

**Ricardo Júnior**, Instituto Federal do Rio de Janeiro, Campus Duque de Caxias, Brazil

**Willian Leal**, Instituto Federal do Rio de Janeiro, Campus Duque de Caxias, Brazil

**Beatriz Cavalcante**, Instituto Federal do Rio de Janeiro, Campus Duque de Caxias, Brazil

**Abstract:**The course of Differential and Integral Calculus for functions of one variable is present in several undergraduate courses in Brazilian universities, such as engineering, chemistry, physics and mathematics. However, despite being a basic and very important discipline in the training of students that begin their studies in an undergraduate course, it is a source of many failures and evasion, by students . Several studies about this theme were developed over the past few years. We may highlight, as a common characteristic in some of them, the necessity for contextualization of the contents developed in the course of Differential and Integral Calculus, with the goal of providing the student a broad view of the insertion of mathematics in the daily life, particularly in his undergraduate course. In this sense, the role of mathematical modeling is crucial: through the use of themes inherent in undergraduate chemistry course, the Differential and Integral Calculus is developed. Therefore, this paper aims to present the results of an experiment carried out in an undergraduate degree in chemistry, developed during the course of Differential and Integral Calculus, that used mathematical modeling as a tool for the contextualization of the Differential and Integral Calculus in chemical problems.

**Acknowledgements:**CNPq for supporting the authors.

176

**Ayman Iskakova**, L.N. Gumilyov Eurasian National University , Fundamental Mathematic, Kazakhstan

**Abstract:**In this work the new multivariate discrete probability model of distribution of processes distortion of radiation from remote sensing data is proposed and studied. Research was performed on a full cycle adopted in mathematical statistics, namely, the model was constructed and investigated, various methods for estimating the parameters was proposed and test of hypothesis that the model adequacy observations, was considered.

177

**Sergei Chernov**, Far Eastern Federal University, School of natural science, Russian Federation

**Igor Prokhorov**, Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, , Russian Federation

**Andrei Sushchenko**, Far Eastern Federal University, Informatics, Mathematic and Computer Modeling, Russian Federation

**Abstract:**In this paper was researched the theoretical aspects of the formation of sonar images in fluctuating ocean under conditions when a significant effect on the measured signal is the scattering properties of the marine environment. In the framework of the theory of radiation transfer was researched the inverse problem consisting in determination of the seafloor scattering coefficient. In the approximation of single scattering obtained explicit solution of the inverse problem, and presents the results of theoretical and numerical analysis of the influence of dimensional scattering on the quality of sonar images. At paper [3] was researched acoustic waves in a fluctuating ocean which based on radiation transfer equation. The solution of this equation gives an explicit solution of the inverse problem in the approximation of single scattering and narrow beam receiving antenna. The equation consist of two components. The first term is useful signal. The second term is interpreted as adjustment in the determining seafloor scattering coefficient, which caused by a dimensional scattering in the ocean. Numerical experiments were made with fragments of “scan lines” sonar image which obtained from side-scan sonar device on board of the autonomous underwater vehicle. ”Scanlines” are physical sample of reflected signals envelope. Thus, the authors proposed a digital signal processing algorithm which includes the volume scattering in a medium. The algorithm is allowed to recover the scattering coefficient of the bottom. Authors developed software the data using different filters. In the issue numerical experiments with model and real data were performed. The result of the side-scan sonar is a file containing a data unit and the information obtained during the monitoring of the seabed. In order to visually see the results, you need to format the resulting converted into image format. The algorithm is implemented by means of parallel technologies.

**Acknowledgements:**The work was supported by the Russian Science Foundation (Project № 14-11-00079)

178

**Evgenii Kovalenko**, Far Eastern Federal University, School of Natural Science, Russian Federation

**Igor Prokhorov**, Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, , Russian Federation

**Andrei Sushchenko**, Far Eastern Federal University, Informatics, Mathematic and Computer Modeling, Russian Federation

**Abstract:**Nowadays the problem of seabed imaging by underwater unmanned vehicles (UUV) is relevant. A side-scan sonar (SSS), based on UUV, is a highly effective device for processing of object-reflective signal. SSS data is used for seabed map construction, monitoring of underwater object, mineral exploration, etc. SSS signal is distorted, whereupon echograms include visible defects. Some of them are caused by volume scattering in the ocean. Properties of it are studied in approximation of narrow directivity pattern of SSS’ receiving antenna [1,2]. The problem of signal modeling in randomly inhomogeneous plane environment with plane inhomogeneous boundary (ocean floor) is reviewed. The process of propagation of acoustic waves is described by the radiative transfer equation. The source and receiver move with constant speed along a straight line. The source have a narrow radiation pattern of receiving antenna and finite interval f the emission pulse. In this paper is solved the direct problem which determines a source signal with the above restrictions. It was received an explicit of the direct problem. In previous works the authors researched a similar problem but with point source [3] . One of the objectives of this work is the definition of the error of approximation. In this work it was produced a numerical analysis of the influence of the final pulse of the range emission on receiver signal.

**Acknowledgements:**The work was supported by the Russian Science Foundation (Project № 14-11-00079)

179

**Hamid E Limodehi**, Institut National de la Recherché Scientifique (INRS), Énergie, matériaux et télécommunications (EMT), Canada

**Abstract:**In this work, using simulation, we proposed a side-polished micro-structured optical fiber sensor based on surface plasmon resonance (SPR) showing good capabilities for refractometry and thermometry. Surface Plasmons, propagating at a metal–dielectric interface, are extremely sensitive to the changes in the refractive index (RI) of the dielectric. This feature constitutes the core of many surface plasmon resonance sensors. Because of remote sensing capabilities, optical fiber-based SPR sensors have been introduced in which surface plasmons of a deposited metal layer are excited by interacting with the evanescence fields of the core guided modes inside the optical fiber. In order to boost the evanescence fields in a typical fiber optic SPR sensor, it is necessary to polish out the fiber. The main issue for these conventional fiber optic sensors is their restrictions in detection range of analyte’s refractive index and as well as operating wavelength. To overcome these restrictions, we employ micro-structured optical fibers (MOF) because they enable us to establish required conditions for SPR at a desired wavelength and refractive index of the analyte, a privilege which is not possible for the case of conventional fiber optic [7, 8]. Our proposed structure in this work is a hybrid structure that includes the benefits of both traditional side-polished and MOF-based SPR sensors; that is a side-polished MOF-based SPR sensor. References: A. Hassani, M. Skorobogatiy, “Design of the microstructured optical ﬁber-based surface plasmon resonance sensors with enhanced microﬂuidics” , Opt. Express 14, (2006) 616–621. 8. Hamid Esmaeilzadeh, Ezatollah Arzi, François Légaré, Alireza Hassani,“ Boundary Integral Method to Calculate the Sensitivity Temperature Error of Microstructured Fiber Plasmonic Sensors”. J. Phys. D: Appl. Phys. 46 (2013) 325103 (8pp).

180

**Jin Lee**, American University of Sharjah, Department of Mechanical Engineering, United Arab Emirates

**Abstract:**A biomimetic miniature underwater acoustic sensor is modelled and analysed for the measurement of directivity of underwater sound propagation. Unlike a hydrophone array, which detects propagation direction by the arrival time of sound waves, this novel sensor is based on a mechanically coupled mechanism, which amplifies the time delay of the arriving sound wave. A mathematical model related to mechanical sensitivity is developed as a function of material properties and geometry of the sensor, with which evaluates and compares the parametric analyses of five degrees-of freedom based lumped parameter model as well as two degrees-of-freedom based model. Effects of the fluid-structure interaction are examined through simulation of the sensor model. In order to consider the damping effect due to the fluid-structure interaction, the damping term is modelled as Rayleigh damping based on the finite element analysis. A challenge in such study is that, two degree-of-freedom based lumped parameter model is not complicated enough to capture the characteristics of the sensor well enough compared to the reduced order model. The result of this study will later be used to help to design the sensor in a systematic way which leads to design optimization. The main contribution of the study is to use the simple but complicated enough five degrees-of-freedom model to design a sensor via parametric study. Finally, the performance of the sensor is compared with a result from finite element analysis. The results show that the sensor model can be used to accurately predict the performance of the sensor in the sensor development.

181

**Vladimir Kan**, Far Eastern Federal University, Department of Information Science, Mathematical and Computer Modeling, Russian Federation

**Igor Prokhorov**, Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, , Russian Federation

**Andrei Sushchenko**, Far Eastern Federal University, Informatics, Mathematic and Computer Modeling, Russian Federation

**Abstract:**At the present time the problem of mapping the ocean floor using the side scan-sonars set on the board of an autonomous unmanned submersible is very topical and perspective. The functioning of the sonar is based on periodic emission of the pulsed sound signals and detection of the echo signals reflected from the distant segments of sea bottom. When the sonar's antenna is moving, an acoustic image is formed on both sides of the submersible. Specificity of this work is that we consider case when volume scattering have a significant influence on the probing process in a fluctuating medium [1, 2]. Mathematical description of this physical process is possible with engaging a kinetic model based on the non-stationary integro-differential transfer equation with the appropriate initial and boundary value conditions [1-3]. In this paper, we continue research of recent article [1]. In [1] for the kinetic model framework, an inverse problem is formulated and studied for reconstructing a function describing small deviation of the bottom level from a horizontal plane. In the single-scattering approximation and under certain constrains on the directional diagram of the receiving antenna an explicit formula is obtained for determinging the sought function. In this paper there is numerical analysis derived in [1] formulae depending on width of diagram directivity and distance sounding. [1] I. V. Prokhorov, A. A. Sushchenko, V. A. Kan, On a Problem of Reconstructing the Bottom Topography of a Fluctuating Ocean // Journal of Applied and Industrial Mathematics, 2015, Vol. 9. P. 37–48. [2] Prokhorov I.V., Sushchenko A.A., Imaging Based on Signal from Side-Scan Sonar // Applied Mechanics and Materials, 2015. Vol. 756. P. 678-682. [3] Bal G., Kinetics of scalar wave fields in random media // Wave Motion, 2005. Vol. 43. P. 132-157.

**Acknowledgements:**The authors were supported by the Russian Foundation for Basic Research (project no. 14–11– 00079).

182

**Mauricio Pato**, Universidade de Sao Paulo, Instituto de Fisica, Brazil

**Gabriel Marinello**, Universidade de São Paulo, Física Matemática, Brazil

**Abstract:**Tight binding models appear in many applications in condensed matter physics. For a one dimensional system, they are described by sparse matrices for which the only non-zero elements are beside the diagonal ones the off-diagonals which describe interactions between nearest neighbors of relevance to the problem at hand [1]. In the early 2000s, tridiagonal matrix models were used to provide an extension of certain classical cases of random matrix theory, which became known as the β-ensembles [2]. This was the starting point of recent efforts to provide models whose matrices verify the pseudo-Hermitian condition [3, 4, 5], satisfied by the non-Hermitian Hamiltonians of PT-symmetry [6, 7]. In the present work, we report results on the properties of these non- Hermitian models. By utilizing the tight-binding interpretation of the Hamiltonian matrix, we compare the behaviors of the open and the closed chains. References [1] A. Altland and B. Simons. Cambridge University Press, 2006. [2] P. J. Forrester. Princeton University Press, 2010. [3] O. Bohigas and M. P. Pato. In: AIP Advances 3.3 (2013), p. 032130. [4] G. Marinello and M. Pato. In: Physica A: Statistical Mechanics and its Applications 444 (2016), pp. 1049–1061. [5] G. Marinello and M. Pato. In: Proceedings of the 15th Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics (to appear) (2016). [6] C. M. Bender. In: Rep. Prog. Phys. 70.6 (2007), pp. 947–1018. [7] A. Mostafazadeh. In: International Journal of Geometric Methods in Mod- ern Physics 07.07 (2010), pp. 1191–1306.

183

**Sumbul Sehar**, Government college university Lahore, Physics Department, Pakistan

**Abstract:**In many physical situations such as space or laboratory plasmas a hot low-density electron populations can be generated superimposed on the bulk cold population, resulting in a particle distribution function consisting of a dense cold part and hot superthermal tail. Space observations show that electron distributions are often observed with flat top at low energies and high energy tails. The appropriate distribution to model such non-Maxwellian features is the generalized (r,q) distribution function which in limiting forms can be reduced to kappa and Maxwellian distribution functions. In this study, Kinetic model is employed to study the electron-acoustic and ion-ion acoustic instabilities in four component plasma with generalized (r,q) distribution function for both magnetized and unmagnetized plasmas. Departure of plasma from Maxwellian distributions significantly alters the growth rates as compared to the Maxwellian plasma. Significant growth observed for highly non-Maxwellian distributions as well as plasmas with higher dense and hot electron population. Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian. These results may be applied in both experimental and space physics regimes.

184

**roger nakad**, Notre Dame University Louaizé, Department of Mathematics and Statistics, Lebanon

**Abstract:**We extend the Friedrich inequality for the eigenvalues of the Dirac operator on Spinc manifolds with boundary under four different boundary conditions. Limiting cases are then studied and many examples and applications in physics are given.

185

**Rodrigo Signoreti**, Unicamp, , Brazil

**Rafael Camargo**, Unicamp, , Brazil

**Laura Canno**, Unicamp, , Brazil

**Marta Pires**, Unicamp, , Brazil

**Lubienska Cristina Lucas Jaquiê Ribeiro**, Unicamp, Saneamento, Brazil

**Abstract:**Challenged with the high rate of leakage from water supply systems, these managers are committed to identify control mechanisms. In order to standardize and control the pressure Pressure Reducing Valves (VRP) are installed in the supply network, shown to be more effective and provide a faster return for the actual loss control measures. It is known that the control pressure is while controlling the occurrence of leakage. Usually the network is sectored in areas defined by pressure levels according to its topography, once inserted the VRP in the same system will limit the downstream pressure. This work aims to show the importance of VRP as loss reduction for tool.

186

**Karen Akiyama**, Unicamp, , Brazil

**Caroline Bressan**, Unicamp, , Brazil

**Marta Pires**, Unicamp, , Brazil

**Laura Canno**, Unicamp, , Brazil

**Lubienska Cristina Lucas Jaquiê Ribeiro**, Unicamp, Saneamento, Brazil

**Abstract:**The issue of water pollution has worsened in recent times due to releases, intentional or not, of pollutants in natural water bodies. This causes several studies about the distribution of pollutants are carried out. The water quality models have been developed and widely used today as a preventative tool, ie to try to predict what will be the concentration distribution of constituent along a body of water in spatial and temporal scale. To understand and use such models, it is necessary to know some concepts of hydraulic high on their application, including the longitudinal dispersion coefficient. This study aims to conduct a theoretical and experimental study of the channel dispersion coefficient, yielding more information about their direct determination in the literature.

187

**Wesley Oliveira**, Unicamp, , Brazil

**Marta Pires**, Unicamp, , Brazil

**Laura Canno**, Unicamp, , Brazil

**Lubienska Cristina Lucas Jaquiê Ribeiro**, Unicamp, Saneamento, Brazil

**Abstract:**The Computational Fluid Dynamics (CFD) is a tool used to numerically simulate fluid flow behavior, and all the laws that govern the study of fluids is the mass transfer and energy, chemical reactions, hydraulic behaviors, among others applications. This tool mathematical equations solves the problem in a specific manner over a region of interest, with predetermined boundary conditions on this region. This work is to study the flow channel through the CFD technique.

188

**Valery Rudyak**, Novosibirsk State University of Architecture and Civil Engineering, Theoretical mechanics, Russian Federation

**Evgeny Lezhnev**, Novosibirsk State Technical Univercity, Applied Mathamtucs, Russian Federation

**Abstract:**In this paper, we propose an algorithm for computation of the transport coefficients of rarefied gas, which is based on stochastic modeling of phase trajectories considered molecular system. The hard spheres potential is used. The number of operations is proportional to the number of used molecules. Naturally in this algorithm the conservation laws are performed. The efficiency of the algorithm is demonstrated by the example of the viscosity and diffusion coefficient of several gases (argon, neon, xemom, kripton). It was shown that the accuracy of the order of 1-2% can be obtained by using a relatively small number of molecules. The accuracy dependence on the number of used molecules, statistics and calculation time was analyzed.

**Acknowledgements:**This work was supported by the Russian Science Foundation (grant No. 14-19-00312).

189

**Jorge Bellorin**, Simón Bolívar University, Physics Department, Venezuela

**Alvaro Restuccia**, Antofagasta University, Physics Department, Chile

**Adrian Sotomayor**, Antofagasta University, Department of Mathematics, Chile

**Abstract:**We study static spherically symmetric solutions of the nonprojectable Horava theory with and without cosmological constant. The solutions we find are two side wormholes and (single side) naked singularities. Interestingly, in the case of negative cosmological constant we find that at one asymptotic side the wormhole acquires a scaling between space and time analog to the scaling of the Lifshitz solution, which was previously found to be a full vacuum solution of the theory and is not spherically symmetric. This result leads us to pose the question whether in the case of negative cosmological constant the asymptotic anisotropic Lifshitz scaling is a generic feature of the vacuum field equations rather than the asymptotic AdS-like scaling.

190

**Astghik Kuzanyan**, Institute for Physical Research NAS of Armenia, Material sciense, Armenia

**Vahan Nikoghosyan**, Institute for Physical Research NAS of Armenia, Material Science, Armenia

**Astghik Kuzanyan**, Institute for Physical Research NAS of Armenia, Material Science, Armenia

**Armen Kuzanyan**, Institute for Physical Research NAS of Armenia, Material Science, Armenia

**Abstract:**The thermoelectric single-photon detector (TSPD) is one of the real competitors to superconducting detectors for single photon detection in a wide range of the electromagnetic spectrum [1, 2]. Single-photon detectors are required in research in different areas of modern science, particularly in space astronomy, high energy physics, quantum computing and quantum cryptography. The TSPD can also serve as a basis for the development of a new generation of measuring systems for applications in medicine, homeland security, elemental microanalysis, analysis of defects in microchips, etc. The TSPD operation principle is based on photon absorption by absorber as a result of which a temperature gradient is generated on the edges of the sensor [3]. Photon detection becomes possible by measuring the potentials’ difference, emerging between the two absorbers. The results of computer simulation of processes of heat distribution in the multi-layer sensor of thermoelectric detector after UV single photon absorption are presented. The multi-layer sensor consists of a photon absorber (tungsten), which is deposited on the thermoelectric layer (thermoelectric with high figure of merit at helium temperatures) and the latter is deposited on the electrically conductive layer of heat sink. This ''sandwich'' is located on a dielectric substrate, on which are also set electrical contacts to count the potential difference ΔU, generated between the absorber and the heat sink by the absorbed photon. The calculations were carried out by the matrix method for differential equations [4], using parameters for the tungsten absorber and thermoelectric thin film layer made of (La, Ce)B6 or CeB6 hexaboridesc. Changing the thickness of absorber and thermoelectric layer we can modified the parameters of sensor such as count rate and energetic resolution. According to the results of computer modeling presented in this paper it can be stated that detection of single photons of 4eV – 100 eV energy and the possibility to define their energy with accuracy no less than 1% is realistic. The count rate exceeding 400 GHz can be achieved. Reference [1] G. G. Fritz, K. S. Wood, D. Van Vechten, A. L.Gyulamiryan, A. S. Kuzanyan, N. J. Giordano, T. M.Jacobs, H.-D. Wu, J. S. Horwitz, A.M. Gulian, Proceedings of SPIE Vol. 4140, pp. 459-469 2000. [2] A. Gulian, K. Wood, D. van Vechten, G. Fritz, J. Mod. Optic, 51 pp. 9-10, 2004 [3] A.A.Kuzanyan, A.S. Kuzanyan. Proc. SPIE 8773, Photon Counting Applications IV: Quantum Optics and Quantum Information Transfer and Processing, 87730L (May 6, 2013). [4] A. Kuzanyan, V. Nikoghosyan, A.Kuzanyan, Proc. of SPIE, 9504, 95040O 2015.

**Acknowledgements:**This work was supported by the RA MES State Committee of Science and Russian Foundation for Basic Research (RF) in the frames of the joint research projects SCS 15RF-018 and RFBR 15-53-05047 accordingly.

191

**Teruaki Ohnishi**, Institute of Science and Technology for Society, Urayasu Branch, Japan

**Abstract:**Among the people moving in crowd there appear social and psychological forces together with physical force as friction and resistance. With the definition that the field of crowd is the region of those forces continuously extending with variable strength, together with the pre-requisite that the spatial distribution of crowd, that is the distribution of the field, varies according to the hydro-dynamical rule, a methodology was proposed to describe the behavior of crowd as the movement of compressible, turbulent fluid. The internal and external pressures were treated as the cause of motion of a compressible turbulent fluid regardless of the crowd density. Representing the crowd with many agent particles, their dynamic states were calculated by solving the Navier-Stokes equation at each position of the particles. A discrete method was introduced in numerical calculation so as to smoothly shift from the turbulent equation to the ordinary equation of motion with the decrease of the crowd density. As for the feasibility study for such a method, a numerical calculation was exemplified for the dynamic behavior and spatial distribution of crowds during movements when there appears a conflict between groups with different characters, imaging for instance the medieval battle of Breitenfeld.

192

**Elena Savelova**, Dubna State University, Applied Mathemetics, Russian Federation

**Abstract:**We consider the spacetime foam picture in which vacuum is filled with virtual wormholes. In the presence of external fields the distribution of wormholes changes. We consider an anisotropic distribution of wormholes and analyze its relation to the speed of light. We explicitly demonstrate that in this case the speed of light acquires an anisotropic character and save the normal dispersion vacuum state may possess also an anomalous dispersion, i.e., when the velocity of light exceeds that in the absence of the external field.

193

**Xianwei Kang**, University of Murcia, Department of Physics, Spain

**Abstract:**The CP violation in the beauty and strange quark sector have well been determined. They can be successfully described by the Cabibbo–Kobayashi–Maskawa (CKM) matrix, which has been an indispensible ingredient in the Standard Model. However, as for the charm quark, mainly for the D meson decays, the CP violation has still not been confirmed by experiment. This problem lasts yet. In our present work, we will construct some new observables that can be detected by experiment. In the process of D decaying to vector meson pairs, the polarizations of the vector mesons can provide rich information, and our observables are just constructed out of the combinations of these polarization vectors. Specifically, we will focus on two channels: psi(3770)->DDbar-> (VV)(VV) and D->VV, where V denotes a vector meson. In the former, the quantum correlation is exploited while in the latter T-violating (and of course, CP violating assuming CPT invariance) signal are elaborated. Both of these can be measured by Charm factory, e.g., by the BES collaboration and the high-energy LHCb. As a first step forward, we also estimate the statistical sensitivity on these experiments. These proposals are very promising since any clear signal would be an indication of New Physics.

**Acknowledgements:**I thank my collaborators S. Descotes Genon (Orsay, LPT), J.Charles (Marseille CPT), Hai-Bo Li (IHEP, Beijing), and A. Datta (Mississippi Uni, USA) for many beneficial discussions. Most of the work presented here are based on the paper collaborating with them.

194

**Alexandr Kirillov**, Dubna State University, Theoretical physics, Russian Federation

**Abstract:**The problem of free-particle scattering on virtual wormholes is considered. It is shown that, for all types of relativistic fields, this scattering leads to the appearance of additional very heavy particles, which play the role of auxiliary fields in the invariant scheme of Pauli--Villars regularization. A nonlinear correction to the effective action that describes the back reaction of particles onto the vacuum distribution of virtual wormholes is obtained. We also discuss the problem of the creation of a coherent vacuum distribution of virtual wormholes by applying specific configurations of external fields.

195

**Antonino Amoddeo**, Università 'Mediterranea', DICEAM, Italy

**Abstract:**Applying appropriate electric pulses to a nematic liquid crystal confined between plates, the bulk order reconstruction can occur, a mechanism allowing the switching between topologically different nematic textures without any director rotation. Using a moving mesh finite element method we describe the order tensor dynamics for a nematic inside an asymmetric π-cell, putting in evidence as textural distortions induced by strong asymmetries can be relaxed via both bulk and surface order reconstruction, occurring close to a confining plate with different time duration.

196

**Jean-pierre Magnot**, académie de clermont-ferrand, lycée jeanne d'arc, France

**Abstract:**We describe a smooth structure, called Fr\"olicher space, on CW complexes and spaces of triangulations. This structure enables differential methods for e.g. minimization of functionnals. As an application, we exhibit how an optimized triangulation can be obtained in order to get an optimized $H^1$ approximation in a prescribed a class of triangulations.

197

**Warda Nasir**, Forman Christian College (A Charted University), Department of Physics, Pakistan

**Abstract:**Whistler waves are right handed circularly polarized waves and are frequently observed in space plasmas. The Low frequency branch of the Whistler waves having frequencies nearly around 100 Hz, known as Lion roars, are frequently observed in magnetosheath. Another feature of the magnetosheath is the observations of flat top electron distributions with single as well as two electron populations. In the past, lion roars were studied by employing kinetic model using classical bi-Maxwellian distribution function, however, could not be justified both on quantitatively as well as qualitatively grounds. We studied Whistler waves by employing kinetic model using non-Maxwellian distribution function such as the generalized (r,q) distribution function which is the generalized form of kappa and Maxwellian distribution functions by employing kinetic theory with single or two electron populations. We compare our results with the Cluster observations and found good quantitative and qualitative agreement between them. At times when lion roars are observed (not observed) in the data and bi-Maxwellian could not provide the sufficient growth (damping) rates, we showed that when generalized (r,q) distribution function is employed, the resulted growth (damping) rates exactly match the observations.

198

**Yuichi Tamura**, Konan University, Dept. Information and Informatics, Japan

**Abstract:**The purpose of this study is to extract key frames from 360 degree videos. Recent advances of small image sensors make cameras smaller and cheaper. Moreover 360 degree cameras, which can record around users at a time, have been proposed. These types of cameras are utilized not only in general use, but also for training task, scientific research and so on. For using this camera in research fields, it is necessary to extract phenomena changing points from the video precisely. These points are known as key frames. It is difficult to extract key frames from the video manually. Therefore, we propose an extraction method of 360 degree videos using singular spectrum transformation (SST). SST is originally used in geophysics for detecting changing point. We apply this method for finding key frames on 360 degree videos. Moreover, we propose a synchronization method movie and sound using SST.

199

**KAUSHIK GHOSH**, VIVEKANANDA COLLEGE, UNIVERSITY OF CALCUTTA, INDIA, PHYSICS, India

**Abstract:**In this article, we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Schwarzschild black hole background using the brick wall model of t' Hooft. In the original article, the scalar field was taken to be vanishing at a radial distance, known as the brick wall cut-off, away from the horizon. The Wentzel-Kramers-Brillouin approximation was used to find the modes that are globally stationary. In a series of previously published articles, we have improved the method of calculations and obtained new results. In this brief note we will consider the entropy of a thin shell of matter field of a given thickness surrounding the black hole horizon. The thickness is chosen to be large compared with the Planck length and is of the order of the atomic scale. We will discuss the corresponding boundary conditions and the appropriateness of the WKB approximation using the Regge\textendash Wheeler tortoise coordinates. When expressed in terms of a covariant cut-off parameter, known as the proper brick wall cut-off, the entropy of a thin shell of matter field of a given thickness and surrounding the horizon in the Schwarzschild black hole background is given by an expression proportional to the area of the black hole horizon. The leading order divergent term in the cut-off parameter is logarithmically divergent. The logarithmic divergence is expected from the nature of the near-horizon redshift factor. However, unlike the previous calculations, we find that the proper brick wall almost coincides with the horizon if the scalar field entropy is chosen to be of the order of the black hole entropy itself. The proper brick wall cut-off is orders of magnitude less than the Planck length. This indicate a bulk to the inner boundary correlation for the degrees of freedom of a scalar field confined in the near horizon region. This is familiar, although the exact nature of the correlation obtained in this article is more compelling. We will find that these discussions are significant in the context of the continuation to the Euclidean sector and the corresponding regularization schemes used to evaluate the thermodynamical properties of matter fields in curved spaces. These are related with to geometric aspects of curved spaces.

200

**Nor Azni Shahari**, Universiti Teknologi MARA, Mathematics, Malaysia

**Nurizzah Jamil**, Universiti Teknologi MARA, Statistics, Malaysia

**Khairul Rasmani**, Universiti Teknologi MARA, Mathematics, Malaysia

**Abstract:**A single phase heat and mass model has always been used to represent the moisture and temperature distribution during the drying of food. Several effects of the drying process, such as physical and structural changes, have been considered in order to increase understanding of the movement of water and temperature. However, the comparison between the heat and mass equation with and without structural change (in terms of shrinkage), which can affect the accuracy of the prediction model, has been little investigated. In this paper, two mathematical models to describe the heat and mass transfer in food, with and without the assumption of structural change, were analysed. The equations were solved using the finite difference method. The converted coordinate system was introduced within the numerical computations for the shrinkage model. The result shows that the temperature with shrinkage predicts a higher temperature at a specific time compared to that of the non-shrinkage model. Furthermore, the predicted moisture content decreased faster at a specific time when the shrinkage effect was included in the model.

**Acknowledgements:**This work was supported by Ministry of Higher Education, Malaysia under Grant No 600-RMI/RAGS 5/3 (147/2014) and Universiti Teknologi MARA, Malaysia

201

**Bivudutta Mishra**, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Mathematics, India

**Abstract:**The problem of diagonal Bianchi type III space-time is investigated in scale invariant theory with dark energy. The matter field is considered in the form of perfect fluid. The field equations for scale invariant theory has been solved by applying a variation law for generalized Hubble’s parameter. The gauge function depends on time coordinate only (Dirac gauge). The cosmological model is constructed and it was observed that the dark energy model in scale invariant theory is consistent with the recent claim of accelerated expansion of the ubniverse. The EoS parameters and skewness parameter turn out to be functions of cosmic time t. This study is significant, because dark energy is the best candidate to explain the cosmic acceleration in the general and alternative theories of gravitation.

202

**Ali Al-JANABI**, Hacettepe University, Physics Engineering , Turkey

**Abstract:**Abstract High-temperature superconductor compound Tl2Ba2Can−1CunO2n+4+δ (n = 2, 3, 4) was prepared by solid-state reaction evacuated sealed tube method. The research was carried out to investigate the effect of parameter (n) on the superconductor behavior of the compound Tl2Ba2Can−1CunO2n+4+δ. The structural phase of prepared samples was analyzed by X-ray diffraction (XRD) patterns, and the results showed the demand phase depend on the parameter (n). The resistivity measurement by four-probe technique used to investigate the critical temperature. The parameter (n) has major effect on definition of critical temperature for superconductor compound. The results showed that the sample prepared with n = 2 has a critical temperature Tc = 102 K; meanwhile, the sample prepared with n = 4 has a critical temperature Tc = 99 K; however, the sample which was prepared with n = 3 has a maximum critical temperature Tc = 121 K. There is a match between the result of magnetic susceptibility and the resistivity measurements at n = 3.

**Acknowledgements:**We are very grateful to La Rochelle University, France. Many thanks directed to Prof. B.Elouadi at La Rochelle University, France, Nami Nakamori, La Rochelle University, Ola, Prof. Emad Al-Shakarchi for his collaboration and advising in the analysis and measurements that were done.

203

**Mohammad Mohsen Hatami**, Khaje Nasir Toosi University of Technology, Physics, Iran, Islamic Republic Of

**Abstract:**Using two-fluid model and hydrodynamic equation, dynamic behavior of a pulsed plasma sheath consisting of equilibrium electron density distribution and collisional ion is simulated. Assuming a rectangular cross –section groove over the flat cathode, effect of ion-neutral collision on the temporal evolution of kinetic energy of incident ions over the groove surfaces is simulated by numerical method.

204

**Gerard Berginc**, THALES, R&T, France

**Abstract:**In this paper, we consider the coherent component of the electromagnetic wave field inside random media composed of dielectric or metallic nanoscale particles. The subject of our interest concerns a random medium with rough boundaries, consisting of a statistical ensemble of different scattering species and artificial material structures developed on base of dielectric or metallic resonant particles. The starting point of our theory is the multiple scattering theory, the averaged electric field satisfies a Dyson equation with a mass operator related to the effective dielectric permittivity of the homogenized structure. Quantum multiple scattering theory has been transposed in this electromagnetic case. We give a formal solution for the mass operator by introducing the T-matrix formalism. We show that the T-matrix satisfies a Lippman-Schwinger equation. Then, we introduce the Quasi-Crystalline Coherent Potential Approximation (QC-CPA), which takes into account the correlation between the particles with a pair-distribution function.The mass operator includes geometric effects, caused by resonant behavior due to the shape and size of particles, cluster effects because of correlations between particles. Significant modifications of particle scattering properties can be observed. The first intent of this paper is to establish new formulas for the effective dielectric constant which characterizes the coherent part of an electromagnetic wave propagating inside a random medium with randomly rough surfaces. In the high frequency limit the expression includes the vectorial case generalization of the result obtained by Keller, which has been derived, using a scalar theory. The equations are identical to equations obtained previously by Keller under conditions that the dyadic Green’s function is replaced by the scalar Green’s function. We obtained an important tensorial generalization of the notion of effective permittivity. Another aim of this paper is to discuss the contribution of light interaction with high-index dielectric nanoparticles supporting optically induced electric and magnetic Mie resonance. These nanoparticles are randomly distributed inside the film with rough boundaries. Near plasmon resonance frequencies, non-Rayleigh light scattering with unusual scattering diagrams can be observed. Attention is paid also to cooperative phenomena in this ensemble of randomly dispersed nanoparticles. We can demonstrate that dielectric structures allow to control both magnetic and electric components of light in a desirable way.

205

**Seiki Saito**, National Institute of Technology, Kushiro College, Electrical Engineering, Japan

**Abstract:**Tungsten material attracts many researchers because it is planned to employ for divertor plates of nuclear fusion device. The material is also expected for the engineering use, because it is discovered that fibrous structure is generated when tungsten irradiated by helium plasma under specific condition. Moreover, it is known that bubble structure is formed as a precursor of the fibrous structure under helium plasma irradiation. The existence of the bubbles may affect the plasma-material interaction. In this study, therefore, binary-collision-approximation-based (BCA) simulation is performed for the investigation of the effects of the existence of helium bubbles on the retention process of incident hydrogen atoms.

206

**Arman Kussainov**, al-Farabi Kazakh National University, Physics and Technology, Kazakhstan

**Natalya Pya**, Nazarbayev University, Department of Mathematics, School of Science and Technology , Kazakhstan

**Abstract:**We have assessed the potential application of the neutron monitor hardware as a random number generator for the normal distribution. The data from acquisition channels with no apparent changes in the signal level, besides the diurnal and other variations typical for this type of data, were chosen as the retrospective model. Variational Monte Carlo method for the quantum harmonic oscillator was used to test the targeted quality of our data. The data delivery rate is of importance and if the conventional minute based neutron counts' averages are insufficient we could always settle for an efficient seed generator to feed into the faster algorithmic random number generator. Scaling our data to the zero mean and variance of one was sufficient to obtain a stable standard normal random variate. Distributions under consideration are passable under all available normality tests. Inverse transform sampling is suggested to use as a source of the uniform random numbers.

**Acknowledgements:**This research was supported by grant №3824/ГФ4 provided by the Science Committee at the Ministry of Science and Education of Republic of Kazakhstan to the principal investigator at the National Nanotechnology Laboratory of Open Type, Physics and Technology Department, al-Farabi Kazakh National University.

207

**Leonid Afremov**, Far Eastern Federal University (FEFU), Department of Theoretical and Experimental Physics, Russian Federation

**Aleksandr Petrov**, Far Eastern Federal University, School of Natural Sciences, Russian Federation

**Abstract:**The aim of this work is to modelling the dependence of the magnetic phase transition’s critical temperature on the NPs’ size and concentration of the “magnetic atoms”. The study was based on “average spin” method developed earlier [1] and it main principles are given below: 1) N “magnetic atoms” are distributed uniformly over M sites of cubic-shaped NP with L size with concentration p=N⁄M ; 2) fields of interaction h between atom’s spin magnetic moments are distributed randomly and there is direct exchange interaction between nearest neighbors only. Atom’s spin magnetic moments are oriented along axis oz (in the approximation of the Ising model). The calculation results provide a completely natural results: a) reducing of the NP’s size leads to a drop phase transition’s temperature as well as reducing of the ultrathin films’ thickness [2]; b) the critical temperature decreases with concentration of the “magnetic atoms” due to decreasing of the number of the interacting atoms. Moreover, at a certain critical concentration Curie temperature drops to zero - the system moves from an ordered to a disordered (paramagnetic) state. [1] Y. Kirienko, L. Afremov. Advanced Materials Research 472-475, 1827-1830 (2012). [2] T. Ambrose, C.L. Chien. Physical review letters 76(10), 1743-1746 (1996).

208

**Xuesong Yuan**, University of Electronic Science and Technology of China, School of Physical Electronics, China

**Abstract:**In order to develop microwave and millimetre wave vacuum electron radiation source devices based on carbon nanotube field emission cold cathode, simulation model of carbon nanotube field emission cold cathode is investigated in this paper. Field emission current curve of a carbon nanotube cold cathode is firstly obtained according to experimental test. Using a numerical fitting method based on the curve, approximate Fowler-Nordheim constants A and B are calculated. Then, A and B are used in a 3D particle in cell simulation software and simulation model of carbon nanotube will be established. Carbon nanotube vacuum electron devices can be designed by using this model.

209

**Eva Oliveira**, Unicamp, , Brazil

**Mayara Maia**, Unicamp, , Brazil

**José Nunhez**, Unicamp, , Brazil

**Lubienska Cristina Lucas Jaquiê Ribeiro**, Unicamp, Saneamento, Brazil

**Abstract:**The Computational Fluid Dynamics (CFD) is used to numerically simulate the behavior of fluid flow, and all the laws that rule the study of fluids, both the energy and mass transfer, chemical reactions, hydraulic behavior, and other applications. Among these innumerable applications, the local behavior of a mixing tank can be estimated using the CFD techniques. In order to follow-up studies in the literature giving them increased credibility, this project aimed to determine whether both the scheduling Potency/Volume and Torque/Volume maintain the necessary level of agitation in the mix tank to extrapolate the volume 10 times and 100 times, using an axial impeller blades inclined at 45 degrees type (PBT 45), and a radial impeller (Rushton turbine) with the use of the CFD. With the results, was analyzed if a criterion is superior to the other in terms of maintaining the level of agitation in scheduling. The case study made it possible to achieve the main objective, deepen studies in Computational Fluid Dynamics. Therefore, managed to the largest domain in tools offered by CFX-ANSYS 14.0 software, allowing future work to be conducted.

210

**Muddassir Ali**, Laurentian University, Bharti School of Engineering, Canada

**Redhouane Henda**, Laurentian University, Bharti School of Engineering, Canada

**Abstract:**Pulsed electron beam ablation (PEBA) has proven to be a promising and powerful technique for the growth of high quality thin films. Pulsed electron beam film deposition consists of many physical processes including target material heating, target ablation, plasma plume expansion, and film growth on a substrate. Plasma plume expansion into a vacuum or an ambient gas is a fundamental issue in PEBA as the quality of thin films deposited onto the substrate depends on the composition, energy and density of particles ejected from the target. In the present study, gas-dynamics equations are solved to investigate plasma expansion induced by interaction of a nanosecond electron beam pulse (~100 ns) with a graphite target in an argon atmosphere at reduced pressure. The effect of the electron beam efficiency and power density on plume expansion is assessed. The temperature, pressure, velocity and density profiles of the plasma plume are numerically simulated as a function of spatial dimension. The model is validated by comparing some of the obtained simulation results with experimental data available in the literature.

211

**Ana Pereira Baccon**, Universidade Estadual de Ponta Grossa, Departamento de Matemática de Estatística, Brazil

**Jose Lunardi**, University of Glasgow, School of Physics and Astronomy, United Kingdom

**Abstract:**The characterization of the statistical distributions of observed weather data is of crucial importance for both constructing and validating weather models, such as the so-called Weather Generators. In such models the distribution for a given variable (such as daily precipitation or daily temperature, for instance) is often assumed to have a given shape, whose parameters for a given locality are then estimated from the aggregate historical data. For example, some models in the literature assume that data in the time series of daily temperatures in a given location are normally distributed within a month, whose mean and variance are estimated by pooling together several years of daily observations corresponding to that month. However, if there were changes in these parameters along the years then such a procedure would result in an inaccurate estimate for that distribution; what is worse, even if the variable were normally distributed in each month of the entire period such a change in the parameters along the years would cause a deviation from the normal shape in the aggregate distribution, and thus the shapes of the observed and the predicted distribution would not match. So, it is of crucial importance to test whether a given shape --and eventually the same parameters-- is in fact shared by all distributions of a weather variable within a given month and in several levels of aggregation (as, for instance, in the aggregate of all years of observation, or all months of a given year, or all weather stations). This is not a trivial task due to the fact that the time series for a single month is very short, and the usual statistical tools to test the distribution shapes for data in a single time series would not be suitable in this case. In this work we will address this issue by using a test procedure former introduced to investigate the shape of distributions of growth rates data (with a few time records) of business firms in large aggregates, and will apply such a procedure to test some alternative distribution shapes for balanced panels of weather data sets available in the software Wolfram Mathematica®.

**Acknowledgements:**JTL thanks CNPq/Brazil for partial support.

212

**Nikolaos Dimakis**, Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Chile

**Abstract:**In reparametrization invariant systems, such as mini-superspace Lagrangians, the existence of constraints can lead to the emergence of additional non-local integrals of motion in phase space. In the case of an FLRW flat/non-flat space-time minimally coupled to an arbitrary scalar field, we manage to use such conserved quantities to completely integrate the system of equations of motion. This is achieved without constraining the potential in any way. Thus, obtaining the most general solution that encompasses all possible cosmological scenarios which can be based on the existence of a scalar field.

**Acknowledgements:**The author acknowledges financial support by FONDECYT postdoctoral grant no. 3150016.

213

**Tetsuya Takaishi**, Hiroshima University of Economics, Faculty of Economics, Japan

**Abstract:**We study the stock market instability by cross correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross correlations the correlation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high we apply the principal components analysis and measure the cumulative risk fraction (CRF) which is the system variance associated with the first few principal components. From the CRF we detected three volatile market stages corresponding to the bankruptcy of Lehman Brothers, Tohoku Region Pacific Coast Earthquake and FRB QE3 reduction observation in the period we studied. We further apply the random matrix theory for the risk analysis and found that the first eigenvector is more equally delocalized when the market is volatile.

214

**Halina Grushevskaya**, Belarusian State University, Physics Department, Belarus

**Nina Krylova**, Belarusian State University, Physics Department, Belarus

**Ihor Lipnevich**, Belarusian State University, Physics Department, Belarus

**Abstract:**In this paper electrocapillary effects at an interphase boundary are subject to modeling by means of Finsler-Lagrange structures which have been proposed in [1-4]. We have shown that such effects are the dependency of system behavior on velocity and the non-conservation of particle mass. A developed simulation technique has been applied to describe the formation of the Langmuir--Blodgett monomolecular layer (monolayer) of amphiphilic molecules on the air / water subphase interface. Experimental data for compressibility of the monolayer in first-order phase transition state are well-approximated by obtained results of the mathematical modelling. [1] V. Balan, H.V. Grushevskaya, N.G. Krylova, M. Neagu, A. Oana. On the Berwald-Lagrange scalar curvature in the structuring process of the LB-monolayer. Applied Sciences. Vol. 15, 30-42 (2013). [2] H.V. Grushevskaya, N.G. Krylova. Effects of Finsler geometry in physics surface phenomena: case of monolayer systems. Hypercomplex Numbers in Geometry and Physics. Vol. 8, 128-146 (2011). [3] M. Neagu, N.G. Krylova, H.V. Grushevskaya. Jet theoretical Yang-Mills energy in the geometric dynamics of 2D-monolayer. J. Math. Phys. Vol. 54, 031508 (2013). [4] V. Balan, H. Grushevskaya, N. Krylova. Finsler geometry approach to thermodynamics of first order phase transitions in monolayers. Differential Geometry - Dynamical Systems. Vol. 17, 24-31 (2015).

215

**Marcin Schroeder**, Akita International University, , Japan

**Abstract:**Neither Ralph Landauer’s declaration that “Information Is Physical”, nor John A. Wheeler’s slogan “It from Bit” or extensive research that followed made information authentically physical. Similarly, attempts to naturalize computation did not make it a natural process. Information and computation became associated with physical phenomena and processes, but nothing would be lost from our understanding of physics, if we drop the terms “information” or "computation" and stay within standard conceptual framework of the discipline using orthodox terms, such as “entropy”. In the case of information, the reason was the lack of a clearly defined concept of information with ontological status of entity independent from underlying physical entities. In the case of computation, it was the lack of autonomy of computation from some forms of human intervention and the lack of recognition that natural processes occur through interactions, not goal oriented actions. In the earlier publications the author provided a conceptual framework for information and computation free from these deficiencies together with an appropriate mathematical formalism and a slightly generalized version of a Turing machine based on interaction (s-machine, which becomes Turing’s a-machine when we consider a special case of one-way actions). This generalization makes it possible to consider evolution of the machine in terms of dynamical changes of both the tape and the head through mutual interaction. The present paper presents more detailed study of the dynamics of information involved in interactions of information systems together with issues related to the invariance with respect to transformations (symmetry). The latter is of special importance, as it is only invariance with respect to reference frame that can give the status of an (objective) physical entity.

216

**Georgiy Nujdov**, Institute of ionic, plazma and laser technology, laboratory of physics of multiphase systems, Uzbekistan

**Valeriy Krivorotov**, Institute of ionic, plazma and laser technology, laboratory of physics of multiphase systems, Uzbekistan

**Sirojiddin Mirzaev**, Institute of ionic, plazma and laser technology, laboratory of physics of multiphase systems, Uzbekistan

**Abstract:**The article presents the results of quantum-chemical calculations of the potential energy of the lattice during a motion of fluoride ions in different areas of the lattice of the rare earth trifluoride LnF3 both dielectric and superionic phases. The profiles of potential energy of the lattice during such a movement are presented and compared. Also shown, that the efficiency of ion transport in the surface layer of the crystal lattice is significantly higher than in the bulk.

217

**Tatyana Gnitetskaya**, Far Eastern Federal University, School of Natural Sciences , Russian Federation

**Abstract:**In this paper the information model of intradisciplinary connections and semantic structures method are described. The information parameters, which we use in information model, are introduced. The question we would like to answer in this paper is – how to optimize the Physics Course’ content. As an example, the differences between entropy values in the contents of physics lecture with one topic but different logics of explanation are showed.

218

**Elias Vagenas**, Kuwait University, Department of Physics, Kuwait

**Abstract:**It had been shown earlier that the Generalized Uncertainty Principle (GUP), motivated from theories of quantum gravity, suggests quantization of measured lengths, areas and volumes at the fundamental level in flat spacetimes. In this work, we generalize this to curved spacetimes, by adding a weak gravitational field to the GUP modified Schrodinger, Klein-Gordon, and Dirac equations, and show that the discreteness results continue to hold. However, the nature of this new quantization is quite complex, although under proper limits, it reduces to cases without gravity. This supports the universal nature of quantum gravity effects.

219

**Inna Belashova**, Kazan Federal University , radiophysics, Russian Federation

**Vladimir Bochkarev**, Kazan federal university, Radiophysics, Russian Federation

**Abstract:**In this paper, nonlinear filtering algorithms for time series are tested using statistical modeling. The goal is to find a representation of the time sequence in a form of a wavelet series with a small number of non-zero coefficients (in other words to substantially reduce the dimensionality of the data). Thus, only statistically significant data remain in the filtered series. There are well-known efficient algorithms for nonlinear wavelet filtering for the case when the values of the time series have a normal distribution. In the case when distribution is not normal, good results can be obtained using the maximum likelihood estimation. We describe filtering using the criterion of maximum likelihood on the example of Poisson time series. This case is of great interest because such series are common for various problems of science and technology (for example, ranks of word usage frequency, number of sunspots, network traffic). We use different stochastic (genetic algorithms, simulated annealing) and deterministic optimization algorithms for direct optimization of the likelihood function. The algorithm was tested on model series, as well as on empirical data (ranks of rare words frequencies and number of sunspots were used). The conducted statistical modeling has shown that filtering using the maximum likelihood method can be significantly more efficient compared to the known algorithms for the case of Poisson series. The most promising methods of optimization were also selected for a given task.

220

**Pierre MILLET**, Université Paris-Sud, Chemistry, France

**Abstract:**The purpose of this communication is to present recent developments in gas-phase impedance spectroscopies and to outline their ability to provide accurate and detailed information on solid-gas reaction mechanisms. The discussion will focus on solid-hydrogen interactions, with a special emphasis on hydriding and permeation reactions. Basic principles of pneumato-chemical impedance spectroscopy (PIS) were introduced in 2005 [1]. PIS can be viewed as the direct transposition of electrochemical impedance spectroscopy (EIS) to solid-gas reactions. In PIS analysis, an analogy is made between pressure and electrical potential on one hand, gas flow and electric current on the other hand, and pneumato-chemical transfer functions are derived from gas phase measurements. Potentially, this spectroscopy can be used to analyze the dynamics of any solid-gas system including adsorption (surface) and absorption (bulk) phenomena, gas (H2) permeation across metallic membranes and electrocatalysis in gaseous fuel cells. Experiments can be performed using simple and conventional Sievert’s-type gas distribution apparatus. Measurements are well adapted to systems showing significant hysteresis. When applied to hydrogen absorption by intermetallic compounds [2] (a process of great practical interest for hydrogen storage applications) or to hydrogen permeation across metallic membranes [3], surface and bulk rate constants can be measured separately, opening the way to detailed kinetics analysis at microscopic levels and to system optimization. State-of-art as well as recent advances in the field will be presented and some perspectives will be discussed. references [1] P. Millet, Pneumato-chemical impedance spectroscopy : (I) principles, J. Phys. Chem., 109 (2005) 24016 – 24024 [2] P. Millet, Pneumato-chemical impedance spectroscopy : (II) dynamics of hydrogen sorption by metals, J. Phys. Chem., 109 (2005) 24025-24030 [3] C. Decaux, R. Ngameni, A. Ranjbari, S. Grigoriev, P. Millet, Dynamics of hydrogen permeation across metallic membranes, Int. J. Hydrogen Energy, 38 (2013) 8584–8589

221

**Daniele Pires Magalhães**, UNIVERSIDADE FEDERAL DE JUIZ DE FORA, PÓS GRADUAÇÃO EM MODELAGEM COMPUTACIONAL, Brazil

**Abstract:**The Calcium induced Calcium release (CICR) is mediated by the ryanodine receptor (RyR) on the sarcoplasmic reticulum (SR) and contributes to the global intracellular Calcium transient that drives cardiomyocyte contraction . In various disease settings, spontaneous Calcium release (SCR) from the SR gives rise to arrhythmic ectopic activity. SCR occurs in the form of waves of self propagating CICR. These waves result in Calcium dependent depolarizing currents generated by the electrogenic Na/Ca exchanger activity on the cell membrane giving rise to delayed afterdepolarizations (DADs) and consequently to triggered arrhythmias and Spontaneous Action Potential(SAPs). Our study is to improve the model Bondarenko to play DADs, SCR and SAPs. The main goal now is to replace or improve chain Markov Ryanodina to deliver results in accordance with existing experimental data.

**Acknowledgements:**UFJF, Capes e Fapemig.

222

**Dérek Bomfim Prates**, UFVJM, ICET, Brazil

**Caio Jardim**, Federal University of the Valleys of Jequitinhonha and Mucuri, Institute of Science and Technology, Brazil

**Letícia Figueiredo**, UFVJM, , Brazil

**Jaqueline Da Silva**, UFVJM, , Brazil

**Maurício Kritz**, LNCC, , Brazil

**Abstract:**Several mathematical models can be found in the literature for describing and analyzing epidemics. Some of these models allow the vaccination study of a determined population in an epidemic scenario. This work will address and compare two important vaccination strategies in a modified SIR model: a constant vaccination, where a certain parcel of the population is immediately and always vaccinated after its birth, and a vaccination in pulses, where in each time interval the vaccine is applied on a parcel of the population. Furthermore, an analysis of the epidemic behavior of different populations submitted to the same vaccination strategy, but whose vaccinated parcels are different, is performed. The analysis and results are performed through numerical solutions of the model and a conditional function that models the pulse vaccination periodicity is proposed.

**Acknowledgements:**We thank CNPQ for the scientiﬁc scholarship given to the undergraduate student who participates in this work.

223

**Rebecca Melkerson**, Washington and Lee University, Physics and Engineering, United States

**Gillenhaal Beck**, Washington and Lee University, Physics and Engineering, United States

**Carlos M. da Fonseca**, Kuwait University, Mathematics, Kuwait

**Irina Mazilu**, Washington and Lee University, Physics and Engineering, United States

**Dan Mazilu**, Washington and Lee University, Physics and Engineering, United States

**Abstract:**We discuss the general methodology of finding exact solutions for two state systems using matrix theory. We analyze specific tridiagonal matrices with known spectra and propose new ones with eigenvalues that can be calculated exactly. We analyze the associated intractable eigenvectors numerically and present exact solutions for a specific experimental application, the ionic self assembly of nanoparticles. We also explore other applications of these tridiagonal matrices for a variety of other physical systems, such as epidemics, voter models, and traffic patterns.

224

**Gillenhaal Beck**, Washington and Lee University, Physics and Engineering, United States

**Mohammad Abudayyeh**, Washington and Lee University, Physics and Engineering, United States

**Rebecca Melkerson**, Washington and Lee University, Physics and Engineering, United States

**Dan Mazilu**, Washington and Lee University, Physics and Engineering, United States

**Irina Mazilu**, Washington and Lee University, Physics and Engineering, United States

**Abstract:**We present experimental data and theoretical analysis which sheds new light on the rate and behavior of polymer/nanoparticle self-assembly. We study the adsorption of anionic silica nanoparticles in a colloidal suspension to cationic poly(diallyldimethylammonium chloride) (PDDA) polymer on glass and report on the time scale at which the surface coverage of the substrate reaches a steady-state when no further adsorption occurs. Our novel experimental method allows us to study particle self-assembly at time scales down to a few hundredths of a second, three orders of magnitude smaller than previously reported in literature. We compare our data with existing stochastic models in an analysis which both confirms the models’ prediction of pre-steady-state adsorption rates and allows us to incorporate real time into what was previously a theoretical calculation with arbitrary time units.

225

**Halina Grushevskaya**, Belarusian State University, Physics Department, Belarus

**George Krylov**, Belarusian State University, Physics Department, Belarus

**Abstract:**Based on earlier developed quasi-relativistic self-consistent Dirac - Hartree - Fock field approximation for graphene [1,2], we perform simulations of charge transport properties of monolayer graphene both in optical case and near zero-frequency limit with accounting of spatial dispersion. Contributions of different nature to conductivity have been considered. Problem of monolayer graphene minimal conductivity is discussed in detail. [1] H.V. Grushevskaya and G.G. Krylov. Graphene: Beyond the Massless Dirac's Fermion Approach // In: Nanotechnology in the Security Systems, NATO Science for Peace and Security Series C: Environmental Security, J. Bonča and S. Kruchinin (eds.). (Springer, 2015). P. 21-31 [2] H.V. Grushevskaya, G. Krylov. Quantum Field Theory of Graphene with Dynamical Partial Symmetry Breaking // J. of Modern Phys. Vol. 5, Р. 984-994 (2014) [3] H.V. Grushevskaya, G. Krylov. Partially Breaking Pseudo-Dirac Band Symmetry in Graphene // J. Nonlin. Phen. in Complex Sys. Vol. 17, Р.86-96 ( 2014)

226

**Abdeen Omer**, Energy Research Institute (ERI), Department of Renewable Energy, United Kingdom

**Abstract:**Globally buildings are responsible for approximately 40% of the total world annual energy consumption. Most of this energy is for the provision of lighting, heating, cooling and air conditioning. An increase in awareness of the environmental impact of CO2, NOx and CFCs emissions triggered a renewed interest in environmentally friendly cooling and heating technologies. Under the 1997 Montreal Protocol, governments agreed to phase out chemicals used as refrigerants that have the potential to destroy stratospheric ozone. It was therefore considered desirable to reduce energy consumption in order to decrease the rate of depletion of world energy reserves as well as the pollution to the environment. One way of reducing building energy consumption is to design buildings, which are more efficient in their use of energy for heating, lighting, cooling and ventilation. Passive measures, particularly natural or hybrid ventilation rather than air-conditioning, can dramatically reduce primary energy consumption. Therefore, promoting innovative renewable energy applications including the ground source energy may contribute to preservation of the ecosystem by reducing emissions at local and global levels. This will also contribute to the amelioration of environmental conditions by replacing conventional fuels with renewable energies that produce no air pollution or the greenhouse gases (GHGs). An approach is needed to integrate renewable energies in a way to achieve high building performance standards. However, because renewable energy sources are stochastic and geographically diffuse, their ability to match demand is determined by the adoption of one of the following two approaches: the utilisation of a capture area greater than that occupied by the community to be supplied, or the reduction of the community’s energy demands to a level commensurate with the locally available renewable resources. Ground source heat pump (GSHP) systems (also referred to as geothermal heat pump systems, earth-energy systems and GeoExchange systems) have received considerable attention in recent decades as an alternative energy source for residential and commercial space heating and cooling applications. The GSHP applications are one of three categories of geothermal energy resources as defined by ASHRAE and include high-temperature (>150°C) for electric power production, intermediate temperature (<150°C) for direct-use applications and GSHP applications (generally (<32°C). The GSHP applications are distinguished from the others by the fact that they operate at relatively low temperatures.

227

**Hafida CHEMOURI**, preparing school in sciences and technics tlemcen, chemistry, Algeria

**Abstract:**The hetero Diels Alder reaction (HAD) of 1-aza-1,3-butadiene with dimethylvinylamine is an efficient method for the synthesis of nitrogen heterocycles that constitute good intermediates for the preparation of complicated heterocycles and pharmacological systems. Experimentally, it has been found that the cycloaddition of 1-aza-1,3-butadiene derivatives (R = H, (CH3)CO, (CH3)CO–BH3) with dimethylvinylamine gives preferentially the ortho regioisomers17. Our aim in this work is to put in evidence the regioselectivity of these HDA reactions using four theoretical models based on the use of reactivity indices. The quantum chemical calculations were performed using the B3LYP/6-31G(d) implemented in Gaussian 09 suite of programs.

228

**Meriem MERAD - BENAROU**, university of Tlemcen , chemistry, Algeria

**Abstract:**The knowledge of the enzymes is capital, because it is catalyze the majority of the chemical reactions of the living organisms. The deterioration of the enzymes by specific inhibiters makes it possible to block the biochemical ways, only a particular site of enzymatic protein comes into contact with its substrate: it is the active site, At the active site, the behavior of atoms is quite different in the approach of the enzyme and substrate. In this approach, there are enzyme substrate interactions that govern the stability of an ES complex to produce the commodity according to the specificity of the enzyme. It is here that lies the difficulty of understanding the interactions between enzyme and substrate, starting from this idea we propose to elucidate the mechanism by molecular modeling. Our research objective is to study the inhibition of the phosphathase Cdc25 through the molecular modeling methods.

229

Use of two families species of Brassica and Solanaceae source in the fight against Alzheimer disease

**ABDELLI Imane**, a: Preparatory School in Science and Technology- Tlemecen-Algeria. b: University Abou-BakrBelkaid-Faculty of Science- Department of Chemistry- Laboratory of Natural Substances and Bioactive(LASNABIO)-Tlemcen-Algeria., Chemistry, Algeria

**Abstract:**Since always, the medicinal herbs were used to prevent or to look after various diseases and the current drugs have, for the majority of them, a natural origin. Research on natural substances has been a carrying topic for a few years and the pharmaceutical laboratories, always in search new compounds active, turn more and more to the identification and the characterization of molecules resulting from natural matrices, and, take as a starting point their molecular structure to imagine new drugs. The flavonoids are natural compounds, which can be met in a broad fruit variety and vegetables consumed daily by the human being. Besides their role in the plants pigmentation, some of these compounds present interests biological activities, such as anti-radicalizing and antioxidant actions. Their large structure varieties (9000 identified compounds) biological activities (antioxydant, anti-allergic, antiviral, anti-inflammatory and drug inhibiting) flavonoids make a particularly complex study object. Studies suggested that the oxidative stress has a critical role in the Alzheimer's disease (MA) is responsible with the β-amyloid neurotoxicity. Attenuation oxidative stress by the anti oxidant molecules is proposed as a potential treatment therapeutic in MA. This disease is characterized by the presence of β-amyloid deposits in the cerebral blood-vessels. The flavonoids can act in various ways in the processes of the stress oxidizing regulation, are known primarily for the protection of the cellular walls and of the blood-vessels they are regarded as good β-secretase inhibitors. Our item consists to study the inhibition of the β-secretase, enzyme implied in the Alzheimer's disease with a Brassica and Solanaceae family by molecular modeling methods. The purpose of this study is to decrease the formation of β-Amyloïd and consequently to delay its progression.

230

**Guang Choi**, Soon Chun Hyang University, Department of Pharmaceutical Engineering, Korea, Republic Of

**Abstract:**In situ monitoring techniques are essential for the control and optimization of the co-crystallization process. In our previous study, we successfully monitored indomethacin−saccharin (IMC−SAC) co-crystallization by anti-solvent addition using a method based on near-infrared principal component analysis (NIR−PCA). In this study, a calibration model was developed to predict the solute concentration of the two components. Several samples withdrawn from five sets of experiments were used to develop the calibration model. The actual concentrations of the two components were determined using UV−vis spectroscopy and high performance liquid chromatography (HPLC). The amount of solid-phase material in suspension was calculated from these solute concentration data. Correlations between NIR spectra and solid concentrations were evaluated using partial least-squares (PLS) regression analyses. Reasonably good calibration models with determination coefficients (R2) higher than 0.979 were obtained. Process monitoring was performed using in situ NIR and Raman spectroscopies to predict the concentrations of both IMC and SAC in solution and to identify the solid-phase materials, respectively. The calibration models were deemed suitable, with reasonable accuracy and precision, for in situ concentration monitoring of the anti-solvent crystallization of IMC−SAC co-crystals. This combination of NIR and Raman spectroscopies was able to detect the formation and phase transition of the resulting co-crystal. In this poster presentation, we’d like to show you the detailed modelling procedure and resulting data for a comprehensive discussion.

231

**Valery Kot**, NASci of Belarus, A. V. Luikov Heat and Mass Transfer Institute, Belarus

**Abstract:**The main challenge of solving nonlinear Stefan-type boundary-value problems is due to the fact that moving boundaries form variable regions and that the positions of these boundaries are unknown; they should be determined in the process of solving a problem. In the present work, approximate solutions of Stefan-type boundary-value problems were obtained with the use of the integral method of boundary characteristics (BChIM) that proposes to represent the desired temperature (concentration) profile u(x,t) in the form of power polynomials: u(x,t) jN a (t)xj , and to perform multiple integration of the parabolic partial differential j xx equation over the region x 0,s(t) with the use of the integral operators n dx...()dx. The following 00 n variants of the Stefan problem for a two-phase model were considered and analyzed: 1) the Dirichlet boundary condition at a constant value of the function u(0,t) : u(0,t) 1 and at variable temperatures (concentrations) u(0,t)1/Steexp(k2t)1, u(0,t)exp(Stet),and u(0,t)1sin(t),whereSteistheStefannumber; 2) the Neumann boundary condition u(0,t)/xexp(t); 3) the Robin boundary condition u(0,t)u(0,t)/x2exp(t)1. Our calculations have shown that the solutions obtained for the temperature (concentration) profiles with the use of the BChIM are of one and the same order of accuracy with the analogous numerical solutions and that the BChIM surpasses the numerical methods in accuracy of calculating the position of the interphase boundary by several orders of magnitude. For example, for the Dirichlet boundary condition u(0,t) 1 , a calculation of the solidification constant in the classical Stefan formula s(t) 2 t with the use of the sixth-degree polynomial has given an error only in the fifteenth decimal place. For the Robin boundary condition, the absolute error in calculating the temperature (concentration) with the use of the fifth-degree polynomial was of the order of 10^(-6).

232

**Zhu Wen Zhou**, Guizhou Education University, Physics and Electronic Science College, China

**Abstract:**We have developed an analytical dual-frequency model, which results in accurate dual-peaks of the ion energy distributions (IEDs) for the given control parameters. The model can analytically calculate and predict the IEDs dual peaks and energy width with necessary plasma parameters. This model can also predict the IEDs from dual frequencies’ drives at any voltage, the associated results are compared with particle-in-cell (PIC) simulations. The IED at a surface is an important parameter for processing in dual radio frequencies driven capacitive couple discharges. The computing model is developed for the IED in a low pressure discharge based on a linear transfer function that relates the time-varying sheath voltage to the time-varying ion energy response at the surface. This model is in good agreement with PIC simulations over a wide range of dual frequencies driven capacitive couple discharge excitations.

233

**Constantino Tsallis**, Centro Brasileiro de Pesquisas Físicas, Theoretical Physics, Brazil

**Abstract:**Boltzmann-Gibbs (BG) statistical mechanics was formulated in the years 1870 and, like Maxwell electromagnetism and classical, quantum and relativistic mechanics, constitutes one of the pillars of contemporary physics. As such it is world-wide studied in the university courses of Physics, Chemistry, Computational Sciences, Economics, Biomedicine, Engineerings, and more. This magnificent theory is based on the paradigm that the entropy is universal, namely the BG one, which depends on no parameter at all. It was thought in 1985, and formally proposed in 1988, that this paradigm is not correct, and that it should be substituted by an adequate family of entropies, thus reflecting the various universality classes of natural, artificial and social systems. Today, three decades later, this simple idea has done a long and fruitful trajectory, and, as is natural, has also generated controversies. A plethora of predictions and applications has concomitantly emerged through analytical, experimental, observational and computational results: nearly 5.600 publications by close to 7.500 scientists and technologists are registered in the Bibliography at http://tsallis.cat.cbpf.br/biblio.htm A brief introduction of the central concepts, followed by some recent verifications of this generalization of the BG theory will be presented.

234

**George Spyrou**, Biomedical Research Foundation of the Academy of Athens, Center for Systems Biology, Greece

**Abstract:**Systemic approaches are essential in the discovery of disease-specific genes, offering a different perspective and new tools on the analysis of several types of molecular relationships, such as gene co-expression or protein-protein interactions. Model-based random walks either on isolated networks or on clusters of networks resist in the inherent complexity and provide insights regarding gene/protein significance and underlying molecular mechanisms as well as enhanced input in biomarker discovery and drug repurposing pipelines.

235

**Iannis Kominis**, University of Crete, Department of Physics, Greece

**Abstract:**Quantum information science has capitalized on the "quantum advantage" in information processing stemming from quantum coherence and entanglement. Naively, it was thought that such advantage pertains only to well-isolated quantum systems carefully engineered by man. Yet again, we now discover that Nature got there first. During her billion-year-old research and development program, Nature has already managed to harness non-trivial quantum effects. In this talk I will demonstrate that two major paradigms establishing the new interdisciplinary science of quantum biology, photosynthesis and avian magnetic compass, are surprisingly apt quantum-information-technology realizations.

236

**Kalman Varga**, Vanderbilt University, Department of Physics and Astronomy, United States

**Abstract:**The fundamental processes in materials are mediated by electronic and nuclear dynamics. The electronic dynamics inherent to these systems have attosecond time-scales. Comprehensive knowledge of the dynamic behavior of electrons and ions in materials is pertinent to the development of many modern technologies, such as semiconductor and molecular electronics, optoelectronics, information processing and photovoltaics. We will present our study of electron and nuclear dynamics induced by strong laser pulses in the framework of the time-dependent density functional theory in real-time and real-space. Several prototypical examples will be used to highlight the correlated electron and nuclear dynamics in strong fields, including Coulomb explosion of clusters, laser-enhanced field emission from nanostructures, and laser-assisted desorption of hydrogen from surfaces of silicon clusters and graphene flakes.

237

**Yannis Kominis**, National Technical University of Athens, School of Applied Mathematical and Physical Science, Greece

**Abstract:**We consider the role of asymmetry in the propagation of nonlinear waves in inhomogeneous photonic media with gain and loss. The combination of lossy dielectrics, metals and active parts in modern photonic structures introduces an inhomogeneous gain-loss landscape which, along with the conservative inhomogeneity, corresponding to refractive index modulations, determines the dynamics of wave propagation. In a large variety of such structures, gain and loss are not balanced, as in the typical case where high-gain active parts (“hot-spots”) of small extent are introduced in order to compensate losses due to more extended lossy parts. We study conditions for stable propagation of localized beams as well as continuous waves in such asymmetric structures. These conditions are a consequence of a dynamical balance between gain, loss, nonlinearity and asymmetric inhomogeneity and enable stable propagation for a wide range of wave launching conditions such as initial power, angle of incidence, and position. It is shown that the lack of symmetry allows for interesting applications related to nonreciprocal dynamics and directed power transfer.

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**Fabrizio Pinto**, Jazan University, Physics Dept., Saudi Arabia

**Abstract:**In this Invited talk, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing vertically on smooth glass.

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**Nikolaos Mavromatos**, King's College London, DEPARTMENT OF PHYSICS, United Kingdom

**Abstract:**In the modern framework of string/brane theory one may view our Universe as a three space-dimensional membrane propagating in a higher dimensional bulk. If, in addition, we consider the bulk as being populated by lower dimensional branes, say three branes of type IIB string theory (which is phenomenologically relevant) compactified on three cycles, then such entities appear from a low-energy-observer view point as `effective point-like' space-time defects which cross our brane world and can form bound states with the D-brane Universe. Such bound defects play a role of Dark matter (D-mater), consistently with current phenomenology. In the talk I discuss the evolution of such Universes, from inflationary eras (of Starobinsky type) to galactic epochs, where populations of D-particles may induce growth of large structure. I discuss lensing phenomenology, showing consistency, as well as propagation of gravitational waves in such media. The interaction of gravitons with recoiling D-matter may result in interesting refractive index and effective masses for the gravitons, which can be bound by current observations, including the LIGO-Virgo interferometers.

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**Ramin Zahedi**, Hokkaido University, , Japan

**Abstract:**This article is a summary of an expanded version of my previous publication [<https://inspirehep.net/record/1387680/>, 2015]. In this article I present a new axiomatic matrix approach based on the ring theory (including the integral domains) and the generalized Clifford algebra. On the basis of this (primary) mathematical approach, by linearization (and simultaneous parameterization, as necessary algebraic conditions), followed by first quantization of the relativistic energy-momentum relation (defined algebraically for a single particle with invariant mass m_0), a unique and original set of the general relativistic (single-particle) wave equations are derived directly. These equations are shown to correspond uniquely to certain massive forms of the laws governing the fundamental forces of nature, including the Gravitational (Einstein), Electromagnetic (Maxwell) and Nuclear (Yang-Mills) field equations (formulated solely in (1+3) dimensional space-time), in addition to the (half-integer spin) single-particle wave equations such as the Dirac equation (which are formulated solely in (1+2) dimensional space-time). In particular, a unique massive form of the general theory of relativity – with a definite complex torsion – is shown to be obtained solely by first quantization of a special relativistic algebraic matrix relation. In addition, it is shown that the "massive " Lagrangian density of the obtained Maxwell and Yang- Mills fields could be also locally gauge invariant – where these fields are formally re-presented on a background space-time with certain complex torsion which is generated by the invariant mass of the gauge field carrier particle. Subsequently, in agreement with certain experimental data, the invariant mass of a particle (that actually would be identified as massive photon) has been specified ( m_γ ≈ 1.4070696×10 *-41 kg), which is coupled with background space-time geometry. Moreover, based on the unique structure of general relativistic particle wave equations derived and also the assum ption of chiral symmetry as a basic discrete symmetry of the source-free cases of these fields, it has been proven that the universe cannot have more than four space-time dimensions. In addition, an argument for the asymmetry of left and right handed (interacting) particles is presented. Furthermore, on the basis of definite mathematical structure of the field equations derived, it is also shown that magnetic monopoles (in contrast with electric monopoles) could not exist in nature.

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**Odysseus Kosmas**, University of Peloponnese, Department of Informatics and Telecommunications, Greece

**Dimitrios Vlachos**, University of Peloponnese, Department of Informatics and Telecommunications, Greece

**Abstract:**The use of space-time geodesic approach of classical mechanics is investigated, in order to derive time adaptive high order phase fitted variational integrators. The proposed technique is employed for systems of which the Lagrangian is of separable form. To this end, first the unfolding of the standard Euler-Lagrange system to its space-time manifold is presented and then it is rewritten as a geodesic problem with zero potential energy. Preliminary simulation results (without optimizing the choice of step sizing) show that one can use the space- time geodesic formulation to generate an adaptive scheme that still preserves some underlying geometric structure.

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