13 research outputs found
On the illposedness and stability of the relativistic heat equation
In this article, we analyze, in terms of a simple example, the incompatibility of parabolic evolution and general covariance. For this, we introduce a unit time-like four-vector and study the simplest heat flux equation with respect to it. In cases where this vector field is surface forming, then the local high wave number limit shows well posedness, but as soon as that property is lost, the Cauchy problem becomes ill-posed. We also discuss how the Maxwell-Cattaneo type modification of the system renders it well posed and link the amplitude of the modification, which is related to the so-called second wave speed of the system, to the size of the failure of surface orthogonality.Fil: GarcĂa-Perciante, A. L.. Universidad AutĂłnoma Metropolitana; MĂ©xicoFil: Reula, Oscar Alejandro. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - CĂłrdoba. Instituto de FĂsica Enrique Gaviola. Universidad Nacional de CĂłrdoba. Instituto de FĂsica Enrique Gaviola; Argentin
The Simple Non-degenerate Relativistic Gas: Statistical Properties and Brownian Motion
This paper shows a novel calculation of the mean square displacement of a
classical Brownian particle in a relativistic thermal bath. The result is
compared with the expressions obtained by other authors. Also, the
thermodynamic properties of a non-degenerate simple relativistic gas are
reviewed in terms of a treatment performed in velocity space.Comment: 6 pages, 2 figure
Hyperbolic heat equation in Kaluza's magnetohydrodynamics
This paper shows that a hyperbolic equation for heat conduction can be
obtained directly using the tenets of linear irreversible thermodynamics in the
context of the five dimensional space-time metric originally proposed by T.
Kaluza back in 1922. The associated speed of propagation is slightly lower than
the speed of light by a factor inversely proportional to the specific charge of
the fluid element. Moreover, consistency with the second law of thermodynamics
is achieved. Possible implications in the context of physics of clusters of
galaxies of this result are briefly discussed.Comment: 14 pages, no figure
On the inertia of heat
Does heat have inertia? This question is at the core of a long-standing
controversy on Eckart's dissipative relativistic hydrodynamics. Here I show
that the troublesome inertial term in Eckart's heat flux arises only if one
insists on defining thermal diffusivity as a spacetime constant. I argue that
this is the most natural definition, and that all confusion disappears if one
considers instead the space-dependent comoving diffusivity, in line with the
fact that, in the presence of gravity, space is an inhomogeneous medium.Comment: 3 page
Gravitational instability of a dilute fully ionized gas in the presence of the Dufour effect
The gravitational instability of a fully ionized gas is analyzed within the
framework of linear irreversible thermodynamics. In particular, the presence of
a heat flux corresponding to generalized thermodynamic forces is shown to
affect the properties of the dispersion relation governing the stability of
this kind of system in certain problems of interest.Comment: 8 pages, 2 figure