Related papers: Regularized $\kappa$-distributions with non-diverg…
For kinetic modeling of plasma processes in space, a rejection-sampling procedure for generating a Kappa distribution in particle-in-cell (PIC) simulation is proposed. A Pareto distribution is employed as an envelope distribution. The…
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time…
We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa}…
Using a geometric averaging procedure applied to a non-affine linear connection, we prove that for a narrow one particle distribution function and in the ultra-relativistic limit, a bunch of point charged particles can be described by a…
Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, the…
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…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Accurate estimation of the T-year return levels of climate extremes using statistical distribution is a critical step in the projection of future climate and in engineering design for disaster response. We show how the estimation of such…
We develop a new method for describing the dynamics of 3-dimensional thermal plasmas. Using a piecewise constant 1-particle distribution, we reduce the Vlasov equation to a generalized Lorentz force equation for a family of vector fields…
Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…
The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the…
In a classical plasma the momentum distribution, $n(k)$, decays exponentially, for large $k$, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay,…
This article reviews two currently available analytic models of the dielectric function of a plasma consisting of quantum particles interacting via Coulomb forces, namely the Random Phase Approximation (RPA) and the Standard (Simple)…
The linear and nonlinear properties of large amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a…
Broad classes of plasma phenomena can be understood in terms of phase-space rearrangements. For example, the net effect of a wave-particle interaction may consist of moving populations of particles from one region of phase space to another.…
We investigate a particle velocity in the $\kappa$-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy $\gamma$-rays or neutrinos, which have been…
The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a…
The nonlinear propagation of electron-acoustic solitary structures is investigated in a plasma containing kappa-distributed (superthermal) electrons. Different types of localized structures are shown to exist. The occurrence of modulational…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response…
Recently Sasane defined a notion of evaluating a distribution at a point using delta sequences. In this paper, we explore the relationship between generalizations of his definition and the standard definition of distributional point values.…