Leonardo Seccia

Continuum approach to phonon gas and shape changes of second sound via shock waves theory

SummaryA continuum approach, based on the principles of modern extended thermodynamics, describing the model of a phonon gas is performed. The main difference with the ideal phonon gas theory consists in the presence of athermal inertia. We apply the shock wave theory and discuss the selection rules for physical shocks (theLax conditions and theentropy growth). In this way the existence of two new kinds of shocks (hot andcold shocks) in rigid heat conductors at low temperature is pointed out. In particular a critical temperature, characteristic of each material, changing the structure of the previous types of shocks is analytically deduced. This characteristic temperature permits also to explain the modification of the received second sound wave form with respect to the initial wave profile. Finally, the results are applied to the case of high-purity crystals (NaF, Bi,3He and4He) and compared with experimental results.

Dispersion relation in the high frequency limit and non linear wave stability for hyperbolic dissipative systems

We consider a quasi-linear first order hyperbolic dissipative system in a one-dimensional space, and we prove that, if the constant solutions are stable for the linearized system, then they are also non-linear asymptotically λ-stable, i.e. the amplitude of the discontinuity wave vanishes, when t increases, provided that the initial amplitude is sufficiently small. In order to give the proof an evaluation of the dispersion law in the limit of high frequencies is accomplished, and the results are applied to the case of the Extended Thermodynamics for a non-equilibrium monatomic classical gas.

Wave propagation in relativistic Extended Thermodynamics

We classify the thermodynamical waves that propagate in a non-equilibrium gas governed by the field equations of relativistic extended thermodynamics. The calculations are carried out for a generic state function appropriate to mon-atomic ideal gases. In the particular cases of the non-degenerate gas specific wave speeds are calculated. In the limit of the non-relativistic and the ultra-relativistic gas the results agree with those given before in literature.

Shock wave propagation and admissibility criteria in a nonlinear dielectric medium

We study the propagation of electromagnetic shock waves in an isotropic nonlinear dielectric medium. In order to select the physical shocks among all the mathematical solutions the usualLax conditions are applied. However, here they do not appear sufficient since strong shocks are present and the differential system is not strictly hyperbolic. So, two additional criteria are studied, theentropy growth condition and thereflection and transmission criterion, and a comparative analysis is developed. Finally, some experimental checks are suggested considering in particular the possible shape changes of an initial shock wave during its propagation.