arXiv subjects

A. R. Mendez

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

9 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

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↗

arXiv2019

Fundamental Diagram of Traffic Flow from Prigogine-Herman-Enskog Equation

Recent applications of a new methodology to measure fundamental traffic relations on freeways shows that many of the critical parameters of the flow-density and speed-spacing diagrams depend on vehicle length. In response to this fact, we present in this work a generalization of the Prigogine-Herman traffic equation for aggressive drivers which takes into account the fact that vehicles are not point-like objects but have an effective length. Our approach is similar to that introduced by Enskog for dense gases and provides the construction of fundamental diagrams which are in excellent agreement with empirical traffic data.

physics.soc-ph↗

arXiv2019

Multi-class fundamental diagrams from the Prigogine-Herman-Boltzmann equation

Our aim in this paper is to establish a theoretical fundamental diagram for a multi-class traffic flow from a gas-kinetic-like traffic model. We start with a multi-class generalization of the Prigogine-Herman-Boltzmann equation to construct the fundamental relation for this system. We show that there exists a critical density which depends on the relative concentration of slow and fast users and describe a procedure to find the threshold value. Finally, our flow-density relation for a two-class mixture of vehicles is contrasted with empirical data in the literature.

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↗

arXiv2016

On the role of dissipation in structure formation for dilute relativistic gases: the static background case

A correction to the Jeans stability criterion due to heat conduction is established for the case of high temperature gases. This effect is only relevant for relativistic fluids and includes an additional term due to a density gradient driven heat flux. The result is obtained by thoroughly analyzing the exponentially growing modes present in the dynamics of density fluctuations in the linearized relativistic Navier-Stokes regime. The corrections to the corresponding Jeans mass and wavenumber are explicitly obtained and are compared to the non-relativistic and non-dissipative values using the transport coefficients obtained in the BGK approximation.

gr-qc↗

arXiv2010

On the kinetic theory of vehicular traffic flow: Chapman-Enskog expansion versus Grad's moment method

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier-Stokes equations for viscous fluids by applying two well-known methods of gas-kinetic theory, namely: the Chapman-Enskog method and the method of moments of Grad. The viscosity coefficient appearing in our macroscopic traffic model is not introduced in an ad hoc way - as in other second-order traffic flow models - but comes into play through the derivation of a first-order constitutive relation for the traffic pressure. Numerical simulations show that our Navier-Stokes-like traffic model satisfies the anisotropy condition and produces numerical results which are consistent with our daily experiences in real traffic.

math-ph↗

arXiv2010

Relativistic heat conduction: the kinetic theory approach and comparison with Marle's model

In order to close the set of relativistic hydrodynamic equations, constitutive relations for the dissipative fluxes are required. In this work we outline the calculation of the corresponding closure for the heat flux in terms of the gradients of the independent scalar state variables: number density and temperature. The results are compared with the ones obtained using Marle's approximation in which a relativistic correction factor is included for the relaxation time parameter. It is shown how including such correction this BGK-like model yields good results in the relativistic case and not only in the non-relativistic limit as was previously found by other authors.

gr-qc↗

arXiv2010

Heat conduction in relativistic neutral gases revisited

The kinetic theory of dilute gases to first order in the gradients yields linear relations between forces and fluxes. The heat flux for the relativistic gas has been shown to be related not only to the temperature gradient but also to the density gradient in the representation where number density, temperature and hydrodynamic velocity are the independent state variables. In this work we show the calculation of the corresponding transport coefficients from the full Boltzmann equation and compare the magnitude of the relativistic correction.

gr-qc↗