Search results for "Boltzmann equation"

Relative importance of second-order terms in relativistic dissipative fluid dynamics

2013

In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of …

Modified Boltzmann Transport Equation

2005

Recently several works have appeared in the literature in which authors try to describe Freeze Out (FO) in energetic heavy ion collisions based on the Boltzmann Transport Equation (BTE). The aim of this work is to point out the limitations of the BTE, when applied for the modeling of FO or other very fast process, and to propose the way how the BTE approach can be generalized for such a processes.

Hot electron noise in n-type GaAs in crossed electric and magnetic fields

2006

A Monte Carlo analysis of hot electron transport properties of bulk \textit{n}-type GaAs in crossed electric and magnetic fields is presented. %Magnetic field strengths allowing negligible quantum effects in the electron dynamics during free flights are considered. Effects due to the nonparabolicity of bands are properly taken into account by means of a local parabolic approximation. Stochastic properties of electron transport are analyzed by computing the velocity auto-correlation function and the spectral density of fluctuations. It is shown how the presence of the magnetic field is able to deeply modify electron noise up to high electric field strengths. The resulting features of the vel…

Modelling of Boltzmann transport equation for freeze-out

2005

The freeze-out (FO) in high-energy heavy-ion collisions is assumed to be continuous across finite layer in space–time. Particles leaving local thermal equilibrium start to freeze out gradually till they leave the layer, where all the particles are frozen out. To describe such a kinetic process we start from Boltzmann transport equation (BTE). However, we will show that the basic assumptions of BTE, such as molecular chaos or spatial homogeneity do not hold for the above-mentioned FO process. The aim of the presented work is to analyse the situation, discuss the modification of BTE and point out the physical causes, which yield to these modifications of BTE for describing FO.

A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows

2013

In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…

On the existence of kinetic equations

1974

The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.

Exact results for the homogeneous cooling state of an inelastic hard-sphere gas

1998

The infinite set of moments of the two-particle distribution function is found exactly for the uniform cooling state of a hard-sphere gas with inelastic collisions. Their form shows that velocity correlations cannot be neglected, and consequently the 'molecular chaos' hypothesis leading to the inelastic Boltzmann and Enskog kinetic equations must be questioned. © 1998 Cambridge University Press.

Solving the heat-flow problem with transient relativistic fluid dynamics

2014

Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes important. In principle, it should also be applicable to situations where heat flow becomes important. However, it has been shown that there are cases where Israel-Stewart theory cannot reproduce phenomena associated with heat flow. In this paper, we derive a relativistic dissipative fluid-dynamical theory from kinetic theory which provides a good description of all dissipative phenomena, including heat flow. We explicitly demonstrate this by comparing th…

2019

Abstract Heavy quarkonium related observables are very useful to obtain information about the medium created in relativistic heavy ion collisions. In recent years the theoretical description of quarkonium in a medium has moved towards a more dynamical picture in which decay and recombination processes are very important. In this talk we will discuss the equations that describe the evolution of the heavy quark reduced density matrix in different approximations, highlighting the color dynamics that is absent in the Abelian case, and we will study their semi-classical limit. This will allow us to obtain stochastic equations (similar to Langevin or Boltzmann equations) that can be useful to obt…

Qualitative characterisation of effective interactions of charged spheres on different levels of organisation using Alexander’s renormalised charge a…

2005

Abstract Effective interactions are conveniently determined from experimental or numerical data by fitting a Debye–Huckel potential with an effective charge Z ∗ and an effective electrolyte concentration c ∗ as free parameters. In this contribution we numerically solved the Poisson–Boltzmann equation to obtain the so-called renormalised charge Z PBC ∗ . For sufficiently large bare charge Z one finds a saturation of Z ∗ which scales as Z ∗ = A a / λ B , where a is the particle radius, λ B the Bjerrum length and A a proportionality factor of order (8–10). The saturation value increases with increased total micro-ion concentration and shows a shallow minimum as a function of packing fraction. …