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A. Sandoval-Villalbazo

Publications and source records attributed to A. Sandoval-Villalbazo.

At least 37 records · Page 2Linked to original sources
arXiv2011

Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies

Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter $ε$. We demonstrate, that within Gaussian noise, the variance of the resulting wealth distribution will significantly decrease, and the equilibrium state is reached faster than in the case of a uniform distributed $ε$ parameter. Also, we show that the system with Gaussian noise strongly resembles a deterministic system which is solved by means of a Z-Transform based technique.

q-fin.GN↗
arXiv2011

Jeans instability analysis in the presence of heat in Eckart's frame

It is shown that the coupling of heat with acceleration first proposed by Eckart would have an overwhelming effect in the growth of density mass fluctuations, even in non-relativistic fluids in the presence of a gravitational field. Gravitational effects would be negligible if the heat-acceleration relation is assumed to be valid for the hydrodynamic equations. A direct implication of this result is that recent alternative first order in the gradients theories must be taken into account while describing a special relativistic fluid.

gr-qc↗
arXiv2010

Light Cone analysis of relativistic first-order in the gradients hydrodynamics

This work applies a Rayleigh-Brillouin light spectrum analysis in order to establish a causality test by means of a frequency cone. This technique allows to identify forbidden and unforbidden regions in light scattering experiments and establishes if a set of linearized transport equations admits causal solutions. It is shown that, when studying a relativistic fluid with its acoustic modes interacting with light, Eckart's formalism yields a non causal behavior. In this case the solutions describing temperature, density and pressure fluctuations are located outside the frequency cone. In contrast, the set of equations that arises from modified Eckart's theory (based on relativistic kinetic theory) yields solutions that lie within the cone, so that they are causal.

gr-qc↗
arXiv2010

Remarks on relativistic kinetic theory to first order in the gradients

In this paper we emphasize some conceptual points related to the kinetic foundations of relativistic hydrodynamics. We summarize previous work and focus on the construction of the heat flux from a kinetic theory point of view. A thorough discussion addressing aspects concerning stability and causality under linear perturbations, and the construction of an appropriate stress-energy tensor, in the case of a high temperature (special relativistic) single component dilute fluid is included.

gr-qc↗
arXiv2010

On the microscopic nature of dissipative effects in special relativistic kinetic theory

A microscopic formulation of the definition of both the heat flux and the viscous stress tensor is proposed in the framework of kinetic theory for relativistic gases emphasizing on the physical nature of such fluxes. A Lorentz transformation is introduced as the link between the laboratory and local comoving frames and thus between molecular and chaotic velocities. With such transformation, the dissipative effects can be identified as the averages of the chaotic kinetic energy and the momentum flux out of equilibrium, respectively. Within this framework, a kinetic foundation of the ensuing transport equations for the relativistic gas is achieved. To our knowledge, this result is completely novel.

gr-qc↗
arXiv2010

A causality analysis of the linearized relativistic Navier-Stokes equations

It is shown by means of a simple analysis that the linearized system of transport equations for a relativistic, single component ideal gas at rest obeys the \textit{antecedence principle}, which is often referred to as causality principle. This task is accomplished by examining the roots of the dispersion relation for such a system. This result is important for recent experiments performed in relativistic heavy ion colliders, since it suggests that the Israel-Stewart like formalisms may be unnecessary in order to describe relativistic fluids.

gr-qc↗
arXiv2009

Relativistic transport theory for simple fluids at first order in the gradients: a stable picture

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called \textit{first order in the gradients} theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.

gr-qc↗
arXiv2009

The Rayleigh-Brillouin Spectrum in Special Relativistic Hydrodynamics

In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to non-equilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic non-equilibrium thermodynamics. The answer will clearly require deeper examination of this problem.

gr-qc↗
arXiv2009

Thermal fluctuations propagation in the relativistic Euler regime: a causal appraisal

It is shown that thermal fluctuations present in a simple non-degenerate relativistic fluid satisfy a wave equation in the Euler regime. The characteristic propagation speeds are calculated and the classical expression for the speed of sound is recovered at the non relativistic limit. Implications and generalizations of this work are analyzed.

gr-qc↗
arXiv2009

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.

gr-qc↗
arXiv2009

The heat flux from a relativistic kinetic equation with a simplified collision kernel

We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.

gr-qc↗
arXiv2008

On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics, describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart's formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of linear irreversible thermodynamics (LIT), namely a violation of Onsager's hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.

gr-qc↗
arXiv2008

Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation

The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are thoroughly discussed regarding the nature of heat as chaotic energy transfer in the context of relativity theory.

gr-qc↗
arXiv2007

Magnetic field effects in the heat flow of charged fluids

Heat conduction in ionized plasmas in the presence of magnetic fields is today a fashionable problem. The kinetic theory of plasmas, in the context of non-equilibrium thermodynamics, predicts a Hall-effect-like heat flow due to the presence of a magnetic field in ionized gases. This cross effect, the Righi-Leduc effect together with a heat flow perpendicular to the magnetic field are shown to yield significant contributions, under certain conditions to the ordinary Fourier component of the heat flow. The thermal conductivities associated with these effects change with the strength of the magnetic field for a given temperature and density and are shown to be significant compared with the parallel conductivity for a whole range of values of \vec{B}.

astro-ph↗
arXiv2007

Dufour and Soret effects in a magnetized and non-magnetized plasma

It is well known that magnetic fields affect heat conduction in a different way in the direction parallel and perpendicular to the field. In this paper a formal derivation of this phenomenon and analytical expressions for the transport coefficients based in the Boltzmann equation are presented. Moreover, the Dufour effect or diffusion thermo effect is usually ignored in plasma transport theory. In this work, analytic expressions for the parallel and perpendicular thermal conductivities as well as the coefficients for both the thermal diffusion, or Soret, effect and the Dufour effect are formally derived. It is also shown how the heat conduction in the perpendicular direction decreases with increasing magnetic field and how in both directions the diffusion thermo effect is significant compared to thermal conduction. Other aspects of this work are also emphasized.

astro-ph↗
arXiv2006

Thermoelectric and Thermomagnetic Effects in Dilute Plasmas

When an electrically charged system is subjected to the action of an electromagnetic field, it responds by generating an electrical current. In the case of a multicomponent plasma other effects, the so called cross effects, influence the flow of charge as well as the heat flow. In this paper we discuss these effects and their corresponding transport coefficients in a fully ionized plasma using Boltzmann's equation. Applications to non-confined plasmas, specially to those prevailing in astrophysical systems are highlighted. Also, a detailed comparison is given with other available results.

astro-ph↗
arXiv2006

Oskar Klein, the sixth dimension and the strength of a magnetic pole

This work extends to six dimensions the idea first proposed by Klein regarding a closed space in the context of a fifth dimension and its link to quantum theory. The main result is a formula that expresses the value of the characteristic length of the sixth dimension in terms of the strength of a magnetic monopole $g$. It is shown that in the case of Dirac's monopole, the ratio of the characteristic lengths of the fifth and sixth dimension corresponds to twice the fine structure constant $α$. Possible consequences of the idea are discussed.

gr-qc↗