1,720,985 research outputs found
Scattering matrix for the reflection-transmission problem in a viscoelastic medium
No full textThe reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed
Phase separation in lava flow
No full textIn this paper we propose a model to study the phenomenon of phase separation during lava flow. Lava is considered as a mixture of two incompressible fluids with different density, in that the mass density of the mixture is determined by the concentrations of the two constituents. We consider as state variables the order parameter, describing the difference in concentration of the fluids, the velocity of the mixture and the absolute temperature. We assume that the order parameter satisfies a Cahn-Hilliard equation, where the chemical potential depends on the velocity and we model lava as a Bingham fluid whose apparent viscosity and yield stress increase exponentially as temperature decreases, according to experimental data. The heat equation provides the evolution equation for temperature. We prove that this model is consistent with the principles of thermodynamics
Existence and uniqueness for the reflection and transmission problem in stratified electromagnetic media
No full textThe reflection-transmission problem of time-harmonic waves in a stratified electromagnetic medium is investigated. The waves are sent from upward or downward with oblique incidence. By means of the energy flux, up-going and down-going waves are distinguished and the reflection and transmission matrices are introduced. When the solid occupies a strip between two homogeneous media, the existence and uniqueness of the reflected and transmitted waves are proved. The same conclusions are obtained for a dielectric without memory extended in the whole space
A Ginzburg–Landau model for material aging depending on temperature
No full textWe consider a model describing the behavior of a body subject to aging and fatigue. These phenomena are supposed to be affected by both mechanical and thermal effects. The material is assumed to be viscoelastic where
the stress–strain relation is based on a new fractional derivative proposed in Caputo and Fabrizio. The order of derivative is regarded as a new variable whose evolution is ruled by a Ginzburg–Landau equation. The model also
includes an evolutive equation for the temperature deducing from the first law of thermodynamics. In this article, thermodynamic compatibility is shown and some numerical simulations are performed
Derivation of the Landau-Lifshitz-Bloch equation from continuum Thermodynamics
No full textWithin the continuum thermodynamic framework, we derive the evolution equation for the magnetization vector in a ferromagnetic body. This procedure leads to an evolution equation that generalizes the well-known Landau–Lifshitz model for magnetically saturated bodies and looks very similar to the Landau–Lifshitz–Bloch equation which was obtained by Garanin in 1997 from statistical mechanics. As a byproduct, we also obtain a generalization of the Gilbert equation when the magnetic field is far from saturation. By virtue of a suitable choice of the Gibbs free energy, this phenomenological model is able to describe the phase transition occurring from the paramagnetic to the ferromagnetic regime in anisotropic ferromagnets
A thermodynamically consistent Ginzburg-Landau model for superfluid transition in liquid helium
No full textIn this paper, we propose a thermodynamically consistent model for superfluid-normal phase transition in liquid helium, accounting for variations of temperature and density. The phase transition is described by means of an order parameter, according to the Ginzburg-Landau theory, emphasizing the analogies between superfluidity and superconductivity. The normal component of the velocity is assumed to be compressible, and the usual phase diagram of liquid helium is recovered. Moreover, the continuity equation leads to a dependence between density and temperature in agreement with the experimental data
A thermodynamic approach to isotropic-nematic phase transitions in liquid crystals
No full textWe propose a dynamical model for (non-isothermal) phase transitions in liquid crystals. Macroscopic motions of the liquid crystal (LC) are neglected, while the coupling with the electromagnetic field is considered. The LC is described in terms of the classical order tensor Q, which is split as Q=s N, where N is a normalized tensor; two independent evolution laws are given for s and N. The model includes an evolutive equation for the temperature field obtained from an appropriate form of the energy balance, in which the internal powers associated to the equations for s and N are accounted for. The thermodynamic restrictions in the constitutive relations which ensure the Clausius-Duhem inequality have been pointed out
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