Related papers: Probability distribution for the relative velocity…
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…
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 paper we clarify the relation between the invariant relativistic relative velocity $V_\text{r}$, the M\o{}ller velocity $\bar{v}$, and the non-relativistic relative velocity $v_r$. Adopting $V_{\text{r}}$ as the true physical…
The distribution function of the relative velocity in a two-body reaction of nonrelativistic uncorrelated particles is derived for general cases of given distribution functions of single particle velocities. The distribution function is…
In this paper, the expression of the relativistic Maxwell-J\"uttner velocity distribution was deduced in a detailed and didactic way. This distribution was compared with the well-known Maxwell-Boltzmann distribution, which does not take…
High energy infers high velocity and high velocity is a concept of special relativity. The Maxwellian velocity distribution is corrected to be consistent with special relativity. The corrected velocity distribution reduces to the Maxwellian…
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 velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles…
We discuss the probability distribution of relative speed $\Delta V$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise…
We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the…
Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…
We study the joint probability distributions of separation, $R$, and radial component of the relative velocity, $V_{\rm R}$, of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and…
We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the…
The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.
The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and…
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…
The relativistic equilibrium velocity distribution coincides with the Maxwellian distribution for small velocities and vanishes at c, the velocity of light. Based on the decay pattern of high-energy tail in the relativistic equilibrium…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
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,…