arXiv subjects

A. R. Méndez

Publications and source records attributed to A. R. Méndez.

5 recordsLinked to original sources

arXiv2026

First-order general constitutive equations for relativistic fluids using the projection method in the Chapman-Enskog expansion of the Boltzmann equation

The first-order out of equilibrium correction to the distribution function, obtained by implementing the projection method for the perturbed relativistic Boltzmann equation using the Chapman-Enskog method, is generalized in order to explicitly include the freedom of choice for frame and representation. It is shown how this procedure leads to general constitutive equations that couple the dissipative fluxes to all derivatives of the state variables (forces), including a weak external electromagnetic field. Special cases of the resulting force-flux relations have been shown to lead to physically sound theories for relativistic fluids.

gr-qc↗

arXiv2025

Existence of the Chapman-Enskog solution and its relation with first-order dissipative fluid theories

The conditions for the existence of the Chapman-Enskog first-order solution to the Boltzmann equation for a dilute gas are examined from two points of view. The traditional procedure is contrasted with a somehow more formal approach based on the properties of the linearized collision operator. It is shown that both methods lead to the same integral equation in the non-relativistic scenario. Meanwhile, for relativistic systems, the source term in the integral equation adopts two different forms. However, as we explain, this does not lead to an inconsistency. In fact, the constitutive equations that are obtained from both methods are shown to be equivalent within relativistic first-order theories. The importance of stating invariant definitions for the transport coefficients in this context is emphasized.

gr-qc↗

arXiv2019

Thermal dissipation in two dimensional relativistic Fermi gases with a relaxation time model

The thermal transport properties of a two dimensional Fermi gas are explored, for the full range of temperatures and densities. The heat flux is established by solving the Uehling-Uhlebeck equation using a relaxation approximation given by Marle's collisional kernel and considering the temperature and chemical potential gradients as independent thermodynamic forces. It is shown that the corresponding transport coefficients are proportional to each other, which leads to the possibility of defining a generalized thermal force and a single transport coefficient. The behavior of such conductivity with the temperature and chemical potential is analyzed and a discussion on its dependence with the relaxation parameter is also included. The relevance and applications of the results are briefly addressed.

cond-mat.stat-mech↗

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↗

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↗