Related papers: The Relativistic Maxwell-J\"uttner Velocity Distri…
We derive a Lorentz invariant distribution of velocities for a relativistic gas. Our derivation is based on three pillars: the special theory of relativity, the central limit theorem and the Lobachevskyian structure of the velocity space of…
Two relativistic distributions which generalizes the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-J{\"u}ttner (MJ) distribution. For the two distributions we derived in terms of special functions the…
In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-Juttner probability distribution for the four-momentum $p^{\alpha}$. We investigate…
The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Juttner's as the relativistic generalization of Maxwell's distribution…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
We are interested in electrons kinetics in a stellar atmosphere to validate or invalidate the usually accepted hypothesis of thermalisation of electrons. For this purpose, we calculate the velocity distribution function of electrons by…
The radial neoclassical fluxes of electrons in the 1/nu regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is based on the relativistic drift-kinetic…
The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is…
The particle distribution function that describes two interpenetrating plasma streams is re-investigated. It is shown how, based on the Maxwell-Boltzmann-J\"uttner distribution function that has been derived almost a century ago, a…
Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in…
The various distribution functions can encompass the diverse characteristics of the magnetospheric plasma of surrounding neutron stars in both hot and cold environments; however, the Maxwell-J\"uttner distribution is so far widely used to…
In this article we study a fully relativistic model of a two dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects…
We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation…
We examine numerically and analytically the problem of the relativistic velocity distribution in a 1-dim relativistic gas in thermal equilibrium. Our derivation is based on the special theory of relativity, the central limit theorem and the…
In this work two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external…
There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Juettner function as well as…
In solar interior, it is the equilibrium velocity distribution of few high-energy protons and nuclei that participates in determining nuclear fusion reaction rates. So, it is inappropriate to use the Maxwellian velocity distribution to…
The current standard solar models can be improved by substituting the relativistic equilibrium velocity distribution for the Maxwellian velocity distribution. The relativistic equilibrium velocity distribution is close- fitting to the…
We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…
In 1911, J\"uttner proposed the generalization, for a relativistic gas, of the Maxwell-Boltzmann distribution of velocities. Here we want to discuss, among others, J\"uttner probability density function (PDF). Both the velocity space and,…