Propagation of an initial pulse in relativistic magneto-hydrodynamics with finite conductivity

The problem of the propagation of a small initial pulse in nonrelativistic magnetohydrodynamics with finite conductivity was solved completely by G. S. Golitsyn [1]. The solution proved to be relatively easy since the displacement current may be ignored in the Maxwell equations (the displacement current, as will be seen below, is of the order 1/c² in comparison with the remaining terms). The fact that the displacement current is small makes it possible to express the electric field in terms of the magnetic field and hence reduce the number of necessary equations to a minimum. Here, the Alfvén and magnetosonic waves are described by two independent systems of equations which indicate that they propagate without interaction even at finite conductivity.In conclusion, the author thanks K. P. Stanyukovich for his interest in the work.     

Non-equilibrium relativistic M.H.D. with finite electrical conductivity

A system of balance laws for relativistic m.h.d, with finite eIectrical conductivity, heat flux and viscosity is proposed, starting from the properties of the systems of conservation laws compatible with a supplementary balance law (entropy balance). Adopting a two-fluid scheme the plasma is treated as a mixture of a neutral fluid and a charged fluid. Following the approach ofextended thermodynamics heat flux, viscous stress and electric current density are considered as new field variables contributing to non equilibrium entropy density and flux.     

Extended thermodynamics of a non-Newtonian fluid

Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.     

Extended thermodynamics of dense gases

We study extended thermodynamics of dense gases by adopting the system of field equations with a different hierarchy structure to that adopted in the previous works. It is the theory of 14 fields of mass density, velocity, temperature, viscous stress, dynamic pressure, and heat flux. As a result, most of the constitutive equations can be determined explicitly by the caloric and thermal equations of state. It is shown that the rarefied-gas limit of the theory is consistent with the kinetic theory of gases. We also analyze three physically important systems, that is, a gas with the virial equations of state, a hard-sphere system, and a van der Waals fluid, by using the general theory developed in the former part of the present work.     

Extended thermodynamics of viscoelastic materials

Extended thermodynamics is a field theory with the principal objective of determining the fields of deformation, temperature, stress and heat flux. With its hyperbolic field equations it ensures finite speeds for shear waves and thermal waves. The theory has previously been formulated for gases where its tenets could be well motivated by the kinetic theory of gases. The present paper is an attempt to incorporate solids into extended thermodynamics. In particular, it considers linearly viscoelastic solids and provides generalizations of the standard stress-strain relations of classical viscoelasticity.     

Wave propagation in relativistic extended thermodynamics of a charged fluid

An analysis of discontinuity wave propagation across a constant state for a relativistic charged fluid with finite electric conductivity is performed. Beside thecontact wave usual in fluid dynamics, acharge wave arises which propagates with the drift speed of the ions. The remaining eight waves are all coupled together and reduce to magnetoacustic and Alfven waves when the electric conductivity tends to infinity, while they become purely electromagnetic waves when the electric permutivity and the magnetic permeability of the medium are the same as in vacuo.     

Extended thermodynamics of molecular ideal gases

The objective of extended thermodynamics of molecular ideal gases is the determination of the 17 fields ofmass density, velocity, energy density, pressure deviator, heat flux, intrinsic energy density and intrinsic heat flux. The intrinsic energy represents the rotational or the vibrational energy of the molecules. The necessary field equations are based upon balance laws and the system of equations is closed by constitutive relations which are characteristic for the gas under consideration. The generality of the constitutive relations is restricted by theprinciple of material frame indifference, and by the entropy principle. These principles reduce the constitutive coefficients of all fluxes to the thermal and caloric equation of state of the gas and provide inequalities for the transport coefficients. The transport coefficients can be related to the shear viscosity, the heat conductivity, and the coefficients of self-diffusion and attenuation of sound waves, so that the field equations become quite specific. The theory is in perfect agreement with the kinetic theory of molecular gases. It is shown that in non-equilibrium the temperature is discontinuous at thermometric walls. The dynamic pressure and the volume viscosity, are discussed and it is shown how extended thermodynamics and ordinary thermodynamics are related.     

On the relativistic thermodynamics of a continuous system in electromagnetic fields

Summary Whithout adopting a particular interaction between matter and fields, we deduce the relativistic equations of balance -for charged differential materials which move in electromagnetic fields. Successively, restriction for the relativistic constitutive equations are deduced by adopting a relativistic reduced dissipation inequality obtained from the 2nd principle of thermodynamics by P. M. Quan.

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Sommario Si determinano le equazioni relativistiche del bilancio per materiali differenziali carichi, con distribuzione continua di momento angolare interno, in moto in campi elettromagnetici senza ricorrere ad alcuna interazione particolare tra materia e campi. Successivamente si deducono delle restrizioni per le equazioni costitutive derivanti dall'imporre che esse rendano soddisfatta una diseguaglianza di dissipazione ridotta relativistica ottenuta dal2 ^o principio della termodinamica di P. M. Quan.

     

Variational irreversible thermodynamics of physical-chemical solids with finite deformation

A new thermodynamics of open thermochemical systems and a variational principle of virtual dissipation are applied to the finite deformation of a solid coupled to thermomolecular diffusion and chemical reactions. A variational derivation is obtained of the field differential equations as well as Lagrangian equations with generalized coordinates. New formulas for the affinity and a new definition of the chemical potential are presented. An outline is given of an unusually large field of applications, such as active transport in biological systems, finite element methods, plastic properties as analogous to chemical reactions, phase changes and recrystalization, porous solids, heredity and initially stressed solids. A new and unified insight is thus provided in highly diversified problems.     

Extended irreversible thermodynamics and its relation with other continuum approaches

We present an introduction to extended irreversible thermodynamics (EIT) as applied to polymer solutions in the presence of shear flow and of diffusion flux. We discuss with special attention the definition of chemical potential in non-equilibrium situations and its use in the analysis of shear-induced phase transitions. In the second part, we compare EIT with other contemporary continuum approaches: theories with internal variables, the GENERIC approach, and the matrix model. All these theories share an emphasis on the relations between dynamics and thermodynamics at a deeper level than in the classical theory, but each of them has some peculiar advantage in the analysis of some specific aspects of physical problems.     

Interaction of a shock wave with a magnetic field in a medium with finite conductivity

We consider the process of the interaction of aplanar shock wave with a magnetic field (impact on a magnetic wall) in a medium having finite conductivity.The problem cannot be solved analytically in the general form. Numerical methods are used to study the problem. A computer is used to calculate the complete system of one-dimensional nonsteady equations of MHD with finite conductivity which depends on temperature in a nonlinear fashion. Results are also presented of particular analytic solutions obtained under simplifying assumptions.We discuss the dependence of the process dynamics on the magnitude of the magnetic field intensity and the law of variation of the medium conductivity with temperature.In the numerical calculations we note the formation of a T-layer, a phenomenon which occurs under definite conditions in unsteady MHD problems [1].In conclusion the authors wish to thank N. G. Basov, A. A. Samarskli, and O. N. Krokhin for posing the problem and for fruitful discussions, and also D. A. Gol'din and A. A. Ivanov for carrying out the numerical calculations.     

Exploitation of the dissipation inequality in general relativistic continuum thermodynamics

The balance equations of energy-momentum and spin together with Einstein’s field equations are investigated by the Liu procedure to find constraints for the constitutive equations in such a way that the Second Law is satisfied. Special cases such as spinless systems and curvature insensitive materials are shortly discussed.     

Effect of finite conductivity in a medium on shock-wave interaction with a magnetic field

We consider the problem of shock-wave incidence on a magnetic wall, which has been studied in [1]. It is shown that the dynamics of the processes which take place in this case depend significantly on the behavior of the conductivity-temperature dependence (T) of the medium and also on the magnitude of the magnetic-field intensity H₀.An exact solution of the problem is constructed for a special form of the law (T). For an arbitrary law (T) the problem is studied numerically by means of digital computer computations; the results are compared with the exact results.Analysis of these solutions shows that the dissipative properties of the medium (electrical conductivity, viscosity), which determine the structure of the refracted wave front, affect the nature of the entire flow as a whole.The formulated problem also makes it possible to clarify the characteristic features of the decay of a discontinuity in a conducting medium.The authors wish to thank A. A. Samarskii, L. A. Zaklyaz'minskii, L. M. Degtyarev, and A. P. Favorskii for discussions of the study, D. A. Gol'dina and A. A. Ivanov for carrying out the numerical calculations, and also G. A. Lyubimov for several helpful comments.     

Extended thermodynamics of the Blotekjaer hydrodynamical model for semiconductors

The Blotekjaer hydrodynamical model for charge carriers transport in semiconductors is reconsidered from the viewpoint of extended thermodynamics. In particular the Blotekjaer original closure of the moment equations is shown to be equivalent to that obtained by applying the entropy principle.Work partially supported by C.N.R. (MMI-P.S IPPMI, U.O Mathematical Models of Semiconductors)