Diffuse-interface model for rapid phase transformations in nonequilibrium systems

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe the transformation within the diffuse interface, we use the phase-field model which allows us to follow the steep but smooth change of phases within the width of diffuse interface. The governing equations of the phase-field model are derived for the hyperbolic model, model with memory, and for a model of nonlinear evolution of transformation within the diffuse-interface. The consistency of the model is proved by the condition of positive entropy production and by the outcomes of the fluctuation-dissipation theorem. A comparison with the existing sharp-interface and diffuse-interface versions of the model is given.Comment: 15 pages, regular article submitted to Physical Review

Stability of inflationary solutions driven by a changing dissipative fluid

In this paper the second Lyapunov method is used to study the stability of the de Sitter phase of cosmic expansion when the source of the gravitational field is a viscous fluid. Different inflationary scenarios related with reheating and decay of mini-blackholes into radiation are investigated using an effective fluid described by time--varying thermodynamical quantities.Comment: 17 pages, LaTeX 2.09, 2 figures. To be published in Classical and Quantum Gravit

Why hyperbolic theories of dissipation cannot be ignored: Comments on a paper by Kostadt and Liu

Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality and stability of the relativistic diffusion equation"), experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It is stressed that the existence of a non--negligible relaxation time does not imply for the system to be out of the hydrodynamic regime.Comment: 8 pages Latex, to appear in Phys.Rev.

Nonequilibrium Temperature and Thermometry in Heat-Conducting Phi-4 Models

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We show in detail, for both two- and three-dimensional systems, that the ideal gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the Phi-4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between kinetic temperature and the nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that kinetic temperature, as modeled and imposed by the Nos\'e-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.Comment: 20 pages with six figures, revised following review at Physical Review

Some analytical models of radiating collapsing spheres

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.Comment: 17 pages Late

Ideal gas sources for the Lemaitre-Tolman-Bondi metrics

New exact solutions emerge by replacing the dust source of the Lem\^aitre-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic gas equation of state. The solutions have a consistent thermodynamical interpretation. The most general transport equation of Extended Irreversible Thermodynamics is satisfied, with phenomenological coefficients bearing a close resemblance to those characterizing a non relativistic Maxwell-Bolzmann gas.Comment: 7 pages, Plain TeX with IOP macros, important corrections to previous version, 3 figures (to appear in Classical and Quantum Gravity, June 1998

The dynamics of dissipative multi-fluid neutron star cores

We present a Newtonian multi-fluid formalism for superfluid neutron star cores, focussing on the additional dissipative terms that arise when one takes into account the individual dynamical degrees of freedom associated with the coupled "fluids". The problem is of direct astrophysical interest as the nature of the dissipative terms can have significant impact on the damping of the various oscillation modes of the star and the associated gravitational-wave signatures. A particularly interesting application concerns the gravitational-wave driven instability of f- and r-modes. We apply the developed formalism to two specific three-fluid systems: (i) a hyperon core in which both Lambda and Sigma^- hyperons are present, and (ii) a core of deconfined quarks in the colour-flavour-locked phase in which a population of neutral K^0 kaons is present. The formalism is, however, general and can be applied to other problems in neutron-star dynamics (such as the effect of thermal excitations close to the superfluid transition temperature) as well as laboratory multi-fluid systems.Comment: RevTex, no figure

Hydrodynamical Models of Superfluid Turbulence

This review paper puts together some of our results concerning the application of non equilibrium Thermodynamics to superfluid liquid helium. Two of the most important situations of this quantum fluid are rotating superfluid and superfluid turbulence, both characterized by the presence of quantized vortices (vortex lines whose core is about 1 Angstrom and the quantum of circulation is $h/m$, $h$ being the Plank's constant and $m$ the mass of helium atom). In the first part of the work a non-standard model of superfluid helium, which considers heat flux as independent variable, is briefly recalled, and compared with the well known two-fluid model, in absence of vortices, proposed by Tisza and Landau more than half a century ago. The model is generalized taking into account the presence of vortices in different cases of physical interest: rotating superfluids, counterflow superfluid turbulence (a particular situation in which no mass flux but only heat flux is present) and combined situations of counterflow and rotation. Since vortices are not fixed when all the hydrodynamical fields change, an additional scalar quantity, the averaged vortex line density per unit volume $L$, {\it line density} for short, is introduced in the model as a new field variable and an evolution equation is written for it, both in linear and in nonlinear regimes, via Extended Thermodynamics. Finally, to encompass more general situations, the model is further extended considering the flux of vortex line density as an independent new variable. In all these models the propagation of harmonic waves is studied, motivated by the fact that vortex lines density is experimentally detected via the attenuation of second sound. A new kind of waves, vortex density waves, is also dealt with

Attenuation and damping of electromagnetic fields: Influence of inertia and displacement current

New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation time for the current density in the realm of an extended Ohm's law. The classical notions of poor and good conductors are rediscussed on the basis of an effective electric conductivity, depending on both wave frequency and relaxation time. It is found that the attenuation for good conductors at high frequencies depends solely on the relaxation time. This means that the penetration depth saturates to a minimum value at sufficiently high frequencies. It is also shown that the actions of inertia and displacement current on damping of magnetic fields are opposite to each other. That could explain why the classical decay time of magnetic fields scales approximately as the diffusion time. At very small length scales, the decay time could be given either by the relaxation time or by a fraction of the diffusion time, depending whether inertia or displacement current, respectively, would prevail on magnetic diffusion.Comment: 21 pages, 1 figur

Cosmological solutions with nonlinear bulk viscosity

A recently proposed nonlinear transport equation is used to model bulk viscous cosmologies that may be far from equilibrium, as happens during viscous fluid inflation or during reheating. The asymptotic stability of the de Sitter and Friedmann solutions is investigated. The former is stable for bulk viscosity index $q1$. New solutions are obtained in the weakly nonlinear regime for $q=1$. These solutions are singular and some of them represent a late-time inflationary era.Comment: 16 pages Latex (IOP style); to appear Class. Quantum Gra