Vincenzo Ciancio

On linear dynamical equations of state for isotropic media I: General formalism☆

In this paper we investigate the relation (dynamical equation of state) among the (mechanical hydrostatic) pressure P, the volume ν and the temperature T of an isotropic medium with an arbitrary number, say n, of scalar internal degrees of freedom. It is assumed that the irreversible processes in the medium are due to volume viscosity and to changes in the internal variables and that these processes can be described with the aid of non-equilibrium thermodynamics. It is shown that an explicit form for the dynamical equation of state may be obtained if in the neighbourhood of some state of thermodynamic equilibrium it is permissible to consider the equilibrium pressure and the thermodynamic affinities (conjugate to the internal degrees of freedom) as linear functions of ν, T and the internal variables and if, moreover, the phenomenological coefficients, which occur in the equations for the irreversible processes, may be considered as constants. This dynamical equation of state has the form of a linear relation among P, ν, T, the first n derivatives with respect to time of P and of T and the first n+1 derivatives with respect to time of ν.

On linear dynamical equations of state for isotropic media II: Some cases of special interest

In a previous paper we have investigated the relation (dynamical equation of state) among the hydrostatic pressure P, the volume v and the temperature T of an isotropic medium with an arbitrary number, say n, of scalar internal degress of freedom. It has been shown that linearization of the theory leads to a dynamical equation of state which has the form of a linear relation among P, v, T, the first n derivatives with respect to time of P and T and the first n+1 derivatives with respect to time of v. In this paper we give a more detailed investigation of the coefficients of P, v and T in the linear dynamical equation of state. Furthermore, we consider the case of media without volume viscosity. It is shown that for these media the derivative with respect to time of order n+1 of the volume does not occur in the dynamical equation of state. Finally, we pay special attention to media with one and with two scalar internal variables.

On the propagation of linear transverse acoustic waves in isotropic media with mechanical relaxation phenomena due to viscosity and a tensorial internal variable

In this paper we consider the propagation of linear transverse acoustic waves in isotropic media in which mechanical relaxation phenomena occur. It is assumed that the irreversible mechanical processes in the medium are due to viscosity and to changes in a tensorial internal variable and that these processes can be described with the aid of non-equilibrium thermodynamics. The viscous flow phenomenon is analogous to the viscous flow of ordinary fluids. In particular we investigate the velocity and attenuation of the waves and we consider the limiting cases of waves high and low frequencies. For high frequencies we obtain expressions for the phase velocity and attenuation which are analogous to those for viscous fluids and it is seen that the tensorial internal variables does not influence the propagation of waves. If the frequencies are sufficiently low, the expression for the phase velocity is analogous to the expression for the phase velocity in purely elastic media, while the damping is influenced by both irreversible phenomena and the imaginary part of the complex wave number is proportional to the square of the frequency.

Asymptotic waves in anelastic media without memory (Maxwell media)

A general method devised to construct oscillatory approximate solutions is applied to a system of equations which describes the behaviour of isotropic media in which mechanical relaxation phenomena occur. The propagation into a uniform unperturbed state is explicitly worked out and the growth equation is established. Finally, the critical time is evaluated.

On the representation of dynamic degrees of Freedom

The different possibilities for choosing dynamic state variables are analyzed, with the dielectric polarization in an isothermic electric conductor being taken as an example. The advantage of a canonical choice for the dynamic variables is shown. Several questions involving non-linear theories are also discussed.

Non-linear dissipative waves in viscoanelastic media

The propagation of non-linear dissipative waves in viscoanelastic media without memory is considered. By applying an asymptotic perturbative method the transport equation for the first perturbation term is obtained. Finally, it is shown that this equation can be reduced to an equation similar to Burgers equation.

On the propagation of linear transverse acoustic waves in isotropic media with mechanical relaxation phenomena due to viscosity and a tensorial internal variable. II. Some cases of special interest (Poynting-Thomson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media)

The propagation of linear transverse acoustic waves in isotropic media in which mechanical relaxation phenomena occur was considered in a previous paper. In particular expressions for the velocity and attenuation of the waves were obtained and the limiting cases of waves with high and low frequencies were discussed. In the present paper we investigate the propagation of linear transverse acoustic waves in Poynting-Thomson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media. We show that the dispersion relations for these waves may be considered as degeneracies of the dispersion relation which we derived in the general case of a viscoanelastic medium with memory. In particular we investigate the explicit dependence of the dispersion relations on the thermodynamic parameters and the phenomenological coefficients.

On the evolution of higher order fluxes in non-equilibrium thermodynamics

The connection between the balance structure of the evolution equations of higher order fluxes and different forms of the entropy current is investigated using the example of rigid heat conductors. Compatibility conditions of the theories are given. Thermodynamic closure relations are derived.

The generalized Burgers equation in viscoanelastic media with memory

Abstract In this paper the propagation of non-linear dissipative waves in viscoanelastic media with memory is considered using a thermodynamic theory for mechanical relaxation phenomena proposed in some previous papers. In particular we investigate the contributions of the memory effects on the transport equation which governs the first perturbation term of the asymptotic solution of the basic equation. Finally, it is shown that the transport equation can be reduced to a generalized Burgers equation.

A Thermodynamic Theory for Heat Radiation Through the Atmosphere

Basing on the conclusions of a previous work [1], a simple thermodynamic model is established for radiating heat transfer through the air. The model is applied to the temperature distribution of the atmosphere and the radiating heat loss of the Earth.