Related papers: Numerical simulation of non-extensive Boltzmann eq…
A time-dependent statistical description of multiple particle breakage is presented. The approach combines the Tsallis non-extensive entropy with a fractal kinetic equation for the time variation of the number of fragments. The obtained…
A new protocol for linearization of the Poisson-Boltzmann equation is proposed and the resultant electrostatic equation coincides formally with the Debye-Huckel equation, the solution of which is well known for many electrostatic problems.…
We consider the existence of steady rarefied flows of polyatomic gas between two parallel condensed phases, where evaporation and condensation processes occur. To this end, we study the existence problem of stationary solutions in a…
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…
We calculate the distribution of electrons in clusters of galaxies, resulting from thermalization processes in the presence of stochastic acceleration due to plasma waves. We show that the electron distribution can deviate from a…
A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate…
We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything…
The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…
A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models…
Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the electron density.
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann…
The formation of the electron energy distribution function in nanosecond atmospheric nitrogen discharges is investigated by means of self-consistent solution of the chemical kinetics and the Boltzmann equation for free electrons. The…
Following the basic prescriptions of the Tsallis' nonextensive thermodynamics, we study the relativistic nonextensive thermodynamics and the equation of state for a perfect gas at the equilibrium. The obtained results are used to study the…
The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities…
Analytic solutions $F(v,t)$ of the nonlinear Boltzmann equation in $d$-dimensions are studied for a new class of dissipative models, called inelastic repulsive scatterers, interacting through pseudo-power law repulsions, characterized by a…
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that…