arXiv subjects

A. L. Garcia-Perciante

Publications and source records attributed to A. L. Garcia-Perciante.

At least 19 recordsLinked to original sources

arXiv2021

Dissipation in 2D degenerate gases with non-vanishing rest mass

The complete set of transport coefficients for two dimensional relativistic degenerate gases is derived within a relaxation approximation in kinetic theory, by considering both the particle and energy frames. A thorough comparison between Marle and Anderson-Witting's models is carried out, pointing out the drawbacks of the former when compared both to the latter and to the full Boltzmann equation results in the non-degenerate limit. Such task is accomplished by solving the relativistic Uehling-Uhlenbeck equation, in both the particle and energy frames, in order to establish the constitutive equations for the heat flux and the Navier tensor together with analytical expressions for the transport coefficients in such representations. In particular, the temperature dependence of the thermal conductivity (associated with a generalized thermal force) and the bulk and shear viscosities are analyzed and compared within both models and with the non-degenerate, non-relativistic and ultra-relativistic limits.

cond-mat.quant-gas↗

arXiv2019

Generic instabilities in the relativistic Chapman-Enskog heat conduction law

We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the relativistic Chapman-Enskog procedure. The resulting system of equations is shown to be non hyperbolic, by considering general perturbations over the whole set of equations written with respect to a generic time direction. The obtained eigenvalues are not purely imaginary and their real part grows without bound as the wave-number increases. Unlike Eckart's theory, this instability is not present when the time direction is aligned with the fluid's direction. However, since in general the fluid velocity is not surface-forming, the instability can only be avoided in the particular case where no rotation is present.

gr-qc↗

arXiv2019

Bulk viscosity in 2D relativistic fluids: the effects of temperature and modifications to the Rayleigh-Brillouin spectrum

The dependence of the bulk viscosity with the relativistic parameter $z=kT/mc^{2}$, obtained through the complete Boltzmann equation [1,2], is thoroughly analyzed. A complete and rigorous examination of the relevant non-relativistic and ultra-relativistic limits is carried out in the case of a hard disk model and compared with the results obtained in the relaxation time approximation. The modifications of the non-vanishing bulk viscosity to the Rayleigh-Brillouin is briefly discussed.

cond-mat.stat-mech↗

arXiv2018

Mathematical analysis of unstable density fluctuations in the dissipative gravitational collapse

A detailed analysis of the dynamics of unstable modes present in the linearized Navier-Stokes-Fourier system in the presence of a gravitational field is carried out. The transition between the non-dissipative and dissipative regimes is explored from the mathematical point of view by considering the same equation of state in both cases, a procedure which sheds light on the discontinuity present in the critical parameter. It is also shown that two distinct behaviours for the propagation of unstable modes can be identified below the critical value for a gravitational instability to occur, depending on a parameter $r$ that quantifies the relevance of dissipation relative to gravitational effects.

physics.flu-dyn↗

arXiv2018

Dissipative properties of relativistic two-dimensional gases

The constitutive equations for the heat flux and the Navier tensor are established for a high temperature dilute gas in two spatial dimensions. The Chapman-Enskog procedure to first order in the gradients is applied in order to obtain the dissipative energy and momentum fluxes from the relativistic Boltzmann equation. The solution for such equation is written in terms of three sets of orthogonal polynomials which are explicitly obtained for this calculation. As in the three dimensional scenario, the heat flux is shown to be driven by the density, or pressure, gradient additionally to the usual temperature gradient given by Fourier's law. For the stress (Navier) tensor one finds, also in accordance with the three dimensional case, a non-vanishing bulk viscosity for the ideal monoatomic relativistic two-dimensional gas. All transport coefficients are calculated analytically for the case of a hard disk gas and the non-relativistic limit for the constitutive equations is verified.

cond-mat.stat-mech↗

arXiv2017

Thermoelectric and thermomagnetic effects in Kaluza's kinetic theory

A five-dimensional treatment of the Boltzmann equation is used to establish the constitutive equations that relate thermodynamic fluxes and forces up to first order in the gradients for simple charged fluids in the presence of electromagnetic fields. The formalism uses the ansatz first introduced by Kaluza back in 1921, proposing that the particle charge-mass ratio is proportional to the fifth component of its velocity field. It is shown that in this approach, space-time curvature yields thermodynamic forces leading to generalizations of the well-known cross-effects present in linear irreversible thermodynamics.

gr-qc↗

arXiv2016

Thermal conductivity for a general bidimensional dilute gas within the Chapman-Enskog approximation

In this work we explicitly calculate the thermal conductivity for a general bidimensional dilute gas of neutral molecules by solving Boltzmann's equation. Chapman-Enskog's method is used in order to analytically obtain this transport coefficient to first approximation in terms of a collision integral for an unspecified molecular interaction model. In the particular case of hard disks interactions, the result is shown to be consistent with previous work by J. V. Sengers \cite{Sengers}, yielding the expected $T^{1/2}$ dependence with the temperature. This dependence is widely used for dense gases as the low density limit in the Enskog expansion. The case of Maxwellian molecules is also explored where a linear dependence with the temperature is obtained.

physics.flu-dyn↗

arXiv2016

Heat flux in the presence of a gravitational field in a simple dilute fluid: an approach based in general relativistic kinetic theory to first order in the gradients

Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \textquotedblleft suppressing\textquotedblright{} the molecular acceleration in Boltzmann\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.

gr-qc↗

arXiv2015

Relativistic heat flux for a single component charged fluid in the presence of an electromagnetic field

Transport properties in gases are significantly affected by temperature. In previous works it has been shown that when the thermal agitation in a gas is high enough, such that relativistic effects become relevant, heat dissipation is driven not solely by a temperature gradient but also by other vector forces. In the case of relativistic charged fluids, a heat flux is driven by an electrostatic field even in the single species case. The present work generalizes such result by considering also a magnetic field in an arbitrary inertial reference frame. The corresponding constitutive equation is explicitly obtained showing that both electric and magnetic forces contribute to thermal dissipation. This result may lead to relevant effects in plasma dynamics.

gr-qc↗

arXiv2015

On the kinetic foundations of Kaluza's magnetohydrodynamics

Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field. The treatment in that work was limited to a four-dimensional Minkowksi space-time in which the Boltzmann equation was treated in a special relativistic approach. The more complete framework of general relativity can be introduced to kinetic theory in order to describe transport processes associated to electromagnetic fields. In this context the original Kaluza's formalism is a promising approach. The present work contains a kinetic theory basis for Kaluza's magnetohydrodynamics and gives a novel description for the establishment of thermodynamic forces beyond the special relativistic description.

gr-qc↗

arXiv2015

On the stability problem in relativistic thermodynamics: implications of the Chapman-Enskog formalism

Extended theories are widely used in the literature to describe relativistic fluids. The motivation for this is mostly due to the causality issues allegedly present in the first order in the gradients theories. However, the decay of fluctuations in the system is also at stake when first order theories that couple heat with acceleration are used. This paper shows that although the introduction of the Maxwell-Cattaneo equation in the description of a simple relativistic fluid formally eliminates the generic instabilities identified by Hiscock and Lindblom in 1985, the hypothesis on the order of magnitude of the corresponding relaxation term contradicts the basic ordering in Knudsen's parameter present in the kinetic approach to hydrodynamics. It is shown that the time derivative, stabilizing term is of second order in such parameter and thus does not belong to the Navier-Stokes regime where the so-called instability arises.

gr-qc↗

arXiv2013

On the role of the chaotic velocity in relativistic kinetic theory

In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.

cond-mat.stat-mech↗

arXiv2013

Entropy Production in Simple Special Relativistic Fluids

It is well known that, in the absence of external forces, simple non-relativistic fluids involve entropy production only through heat conduction and shear viscosity. In this work, it is shown that a number density gradient contributes to the local entropy production of a simple relativistic fluid using special relativistic kinetic theory. Also, the presence of an external field may cause strictly relativistic contributions to the entropy production, a fact not widely recognized. The implications of these effects are thoroughly discussed.

gr-qc↗

arXiv2013

Benedicks effect in a relativistic simple fluid

According to standard thermophysical theories, cross effects are mostly present in multicomponent systems. In this paper we show that for relativistic fluids an electric field generates a heat flux even in the single component case. In the non-relativistic limit the effect vanishes and Fourier's law is recovered. This result is novel and may have applications in the transport properties of very hot plasmas.

gr-qc↗

arXiv2012

Tolman's law in linear irreversible thermodynamics: a kinetic theory approach

In this paper it is shown that Tolman's law can be derived from relativistic kinetic theory applied to a simple fluid in a BGK-like approximation. Using this framework, it becomes clear that the contribution of the gravitational field can be viewed as a cross effect that resembles the so-called \emph{Thomson effect} in irreversible thermodynamics. A proper generalization of Tolman's law in an inhomogeneous medium is formally established based on these grounds.

gr-qc↗

arXiv2012

Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable first order in the gradients formalism

The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart's framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disapperance of the gravitational instability responsible for structure formation. In the present work the problem is revisited now using a constitutive equation derived from relativistic kinetic theory. The new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistc limit is recovered, opposite to what happens in Eckart's case.

gr-qc↗

arXiv2011

On the validity of the Onsager relations in relativistic binary mixtures

In this work we study the properties of a relativistic mixture of two non-reacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such effect, also present for the single component problem, has so far not been analyzed from the point of view of the Onsager resciprocity relations. In order to address this matter, we propose two alternatives for the Onsagerian matrix which comply with the corresponding reciprocity relations and also show that, as in the non-relativistic case, the chemical potential is not an adequate thermodynamic force. The implications of both representations are briefly analyzed.

cond-mat.stat-mech↗

arXiv2011

Entropy Production in Relativistic Binary Mixtures

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed.

cond-mat.stat-mech↗