Vyankat Pawar, Maharashtra Udayagiri Mahavidyalaya, Physics and Electronics, India
Abstract: The dielectric relaxation study of diethanolamine with triethanolamine binary mixture have been determined over the frequency range of 10 MHz to 20 GHz, at 15, 20, 25, 28, and 30oC using time domain reflectometry (TDR) method for 11 concentrations of the system. The present work reveals molecular interaction between same multi-functional groups [−OH and –NH2] of the alkanolamines (diethanolamine and triethanolamine) using different models (Such as Debye model, Excess model, Kirkwood model and Bruggeman model). The dielectric parameters viz. static dielectric constant (0), dielectric constant at high frequency (∞) and relaxation time () have been obtained with Debye equation characterized by a single relaxation time without relaxation time distribution by the least squares fit method. The values of static dielectric constant increases up to their melting points and then it decreases with increasing temperatures. This behavior of the static dielectric constant indicates the change of phase from semi-solid to liquid state of the system. At the melting points, the values of relaxation time suddenly drop down.
1
Julio S Espinoza Ortiz, Universidade Federal de Goias, Departamento de Física, Brazil
Roberto E Lagos, IGCE Universidade Estadual Paulista, Física, Brazil
Abstract: Research on modeling the mechanical behavior of soft tissue has growing demand for applications on surgical simulations, pursuing in real time, precise and fast calculations of tissue mechanical deformations. For almost all biological soft tissue, the stress-strain curve exhibit a hysteresis loop showing a nonlinear relationship, meanwhile under different strain rates they are mechanically not very sensitive. Moreover, their hysteresis loop-area does not depend on the strain rate. Hysteresis, relaxation and creep are common features of viscoelastic mechanical behavior. As for most materials, their mechanical properties depend to a large extent on the environmental conditions, mainly the temperature and the type of loading regime applied to the material. The time dependence of a viscoelastic material could be better understood by considering it as composed by an elastic solid and a viscous fluid. Different types of mechanical devices can be constructed provided a particular configuration of elastic springs and dashpots. In this work we explore the possibility to obtain most of the soft tissue mechanical behavior by considering a Kelvin's device coupled to a set of {\it\,in parallel} Maxwell's devices. Then, the resulting model composed of a long series of modified Kelvin bodies must span a broad range of characteristic times resulting in a suitable model for soft tissue simulation. Soft tissue mechanical response under driving static and dynamic deformations on {\it\,2-Dim} system are considered, given the applied stress. We compute the strain deformations as a function of time. We obtain a set of coupled Volterra integral equations, solved via the extended trapezoidal rule scheme, and we use the Newton-Raphson method when solving the remaining coupled equations.
2
Rémi Léandre, Université de Franche-Comté, Laboratoire de Mathématiques, France
Abstract: There are much more semi-groups than semi-groups which are represented by stochastic processes. On the other hand, there are a lot of formulas in stochastic analysis which are natural. The theory of pseudodifferential operators allow to understand a lot of partial differential equations, including parabolic equations. On the other hand we have imported in the theory of non-markovian semi-groups a lot of tools of stochastic analysis. Stochastic analysis formulas are valid for the whole process. Their interpretation for non-markovian semi-groups work only for the semi-group.
3
Back to Top