arXiv subjects

D. Brun-Battistini

Publications and source records attributed to D. Brun-Battistini.

8 recordsLinked to original sources

arXiv2019

Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model

This article shows a new focus of mathematic analysis for the Solow-Swan economic growth model, using the generalized conformal derivative Katugampola (KGCD). For this, under the same Solow-Swan model assumptions, the Inada conditions are extended, which, for the new model shown here, depending on the order of the KGCD. This order plays an important role in the speed of convergence of the closed solutions obtained with this derivative for capital (k) and for per-capita production (y) in the cases without migration and with negative migration. Our approach to the model with the KGCD adds a new parameter to the Solow-Swan model, the order of the KGCD and not a new state variable. In addition, we propose several possible economic interpretations for that parameter.

econ.TH↗

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 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

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↗

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↗

arXiv2011

Maxwell-Cattaneo's equation and the stability of fluctuations in the relativistic fluid

Extended theories are widely used in the literature to describe the relativistic fluid. The motivation for this is mostly due to the causality issues allegedly present in the first order theories. However, the decay of fluctuations in the system is also at stake when first order theories \emph{that couple heat with acceleration} are used. In this paper it is shown how the generic instabilities in relativistic fluids are not present when a Maxwell-Cattaneo type law is introduced in the system of hydrodynamic equations. Emphasis is made on the fact that the stabilization is only due to the difference in characteristic times for heat flux relaxation and instabilities onset. This gives further evidence that Eckart's like constitutive equations are responsible for the first order sytem exhibiting unphysical behavior.

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↗