In some previous papers it has been shown that dielectric after-effects may be studied with the a... more In some previous papers it has been shown that dielectric after-effects may be studied with the aid of thermodynamic vectorial internal variables. In this paper it is assumed that n "hidden" vectorial degrees of freedom 2t\ which influence the polarization of the medium, give rise to dielectric relaxation phenomena and it is shown that with the aid of such vector fields the specific polarization vector p may be split in n + 2 parts:p\p\ ...,p\p+\p has the property that it vanishes for all values of p, p\ ... 5 p\ if the medium is in a state where the electric field and the mechanical stress tensor vanish and the temperature of the medium equals some reference temperature. The n specific polarization vectors p may replace the n vectorial variables Z k = 1,2,..., n) as internal degrees of freedom. /j is a constant vector. Furthermore, it is shown that the two expressions for the entropy production derived by using either the n variables Z or the n variables p are equivalent.
DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2019
In this paper a Boillat's methodology is applied to investigate discontinuity waves of a syst... more In this paper a Boillat's methodology is applied to investigate discontinuity waves of a system of quasi-linear hyperbolic partial differential equations (PDEs), describing the interactions between the electronic and dislocation fields in extrinsic semiconductors with defects of dislocation. The thermodynamic model for the semiconductors under consideration was deduced in previous papers, in the frame of extended irreversible thermodynamics with internal variables, but here it is assumed that these semiconductors are not polarized. The solutions of the PDEs system considered are looked for in an approximate form, presenting a jump in the first order derivatives crossing the associated wave fronts. In particular, in the one-dimensional case, we study the propagation of one solution into a uniform unperturbed state, deriving the expression of the velocity along the characteristic rays, the associated wave front equation in the first approximation and Bernoulli's equation governing the propagation of the discontinuity amplitude.
Our principal result is the description of the constitutive surfaces S of the material point mode... more Our principal result is the description of the constitutive surfaces S of the material point model as the Legendre submanifolds of the TPS shifted by the flow of Reeb vector field. This shift is controlled, at the points of Legendre submanifold by the entropy production function $\sigma$.
In some previous papers it has been shown that dielectric after-effects may be studied with the a... more In some previous papers it has been shown that dielectric after-effects may be studied with the aid of thermodynamic vectorial internal variables. In this paper it is assumed that n "hidden" vectorial degrees of freedom 2t\ which influence the polarization of the medium, give rise to dielectric relaxation phenomena and it is shown that with the aid of such vector fields the specific polarization vector p may be split in n + 2 parts:p\p\ ...,p\p+\p has the property that it vanishes for all values of p, p\ ... 5 p\ if the medium is in a state where the electric field and the mechanical stress tensor vanish and the temperature of the medium equals some reference temperature. The n specific polarization vectors p may replace the n vectorial variables Z k = 1,2,..., n) as internal degrees of freedom. /j is a constant vector. Furthermore, it is shown that the two expressions for the entropy production derived by using either the n variables Z or the n variables p are equivalent.
DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2019
In this paper a Boillat's methodology is applied to investigate discontinuity waves of a syst... more In this paper a Boillat's methodology is applied to investigate discontinuity waves of a system of quasi-linear hyperbolic partial differential equations (PDEs), describing the interactions between the electronic and dislocation fields in extrinsic semiconductors with defects of dislocation. The thermodynamic model for the semiconductors under consideration was deduced in previous papers, in the frame of extended irreversible thermodynamics with internal variables, but here it is assumed that these semiconductors are not polarized. The solutions of the PDEs system considered are looked for in an approximate form, presenting a jump in the first order derivatives crossing the associated wave fronts. In particular, in the one-dimensional case, we study the propagation of one solution into a uniform unperturbed state, deriving the expression of the velocity along the characteristic rays, the associated wave front equation in the first approximation and Bernoulli's equation governing the propagation of the discontinuity amplitude.
Our principal result is the description of the constitutive surfaces S of the material point mode... more Our principal result is the description of the constitutive surfaces S of the material point model as the Legendre submanifolds of the TPS shifted by the flow of Reeb vector field. This shift is controlled, at the points of Legendre submanifold by the entropy production function $\sigma$.
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