Related papers: New probability distributions in astrophysics: IV.…
The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the…
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…
A simple numerical method for loading of a relativistic Maxwellian-type distribution is proposed based on inverse transform sampling. The relativistic Maxwellian energy distribution is introduced as an alternative to the Maxwell-J\"{u}ttner…
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 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…
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…
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are…
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…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…
Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar…
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…
Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…
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 obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
We demonstrate that certain astrophysical distributions can be modelled with the truncated Weibull distribution, which can lead to some insights: in particular, we report the average value, the $r$th moment, the variance, the median, the…
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.