English
Related papers

Related papers: On Modeling and Solving the Boltzmann Equation

200 papers

The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…

Optimization and Control · Mathematics 2018-04-06 J. Tervo , P. Kokkonen , M. Frank , M. Herty

The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…

Analysis of PDEs · Mathematics 2019-12-02 Jouko Tervo

A semi-classical approach to the study of the evolution of anyonic excitations--elementary particles with fractional statistics, complementing bosons and fermions--is through the Boltzmann equation for anyons. This work reviews a…

Mathematical Physics · Physics 2025-05-29 Niclas Bernhoff

We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even and especially for finite systems. Inspired by these…

Statistical Mechanics · Physics 2009-11-13 Mehmet Kadiroglu , Jochen Gemmer

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…

Fluid Dynamics · Physics 2025-02-25 Boyuan Wang , Zhaoyuan Meng , Yaomin Zhao , Yue Yang

This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…

Numerical Analysis · Mathematics 2009-11-19 Akil Narayan , Andreas Klöckner

The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called…

Mathematical Physics · Physics 2016-08-03 Manabu Machida

In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer…

Computational Engineering, Finance, and Science · Computer Science 2023-01-26 T. R. F. Phillips , C. E. Heaney , C. Boyang , A. G. Buchan , C. C. Pain

This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…

We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation}…

Statistical Mechanics · Physics 2009-11-13 M. I. Garcia de Soria , P. Maynar , G. Schehr , A. Barrat , E. Trizac

Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…

Statistical Mechanics · Physics 2007-05-23 A. N. Gorban , I. V. Karlin

Over the past few years it has been discovered that an "observable" can be set up on the lattice which obeys the discrete Cauchy-Riemann equations. The ensuing condition of discrete holomorphicity leads to a system of linear equations which…

Mathematical Physics · Physics 2013-09-17 Murray T. Batchelor

A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…

Computational Physics · Physics 2013-11-19 Gian Pietro Ghiroldi , Livio Gibelli

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…

Analysis of PDEs · Mathematics 2025-03-18 Ki-Nam Hong , Marwa Shahine , Seok-Bae Yun

The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from Molecular Dynamics and from Direct Monte Carlo simulation of the Boltzmann equation are compared. It is…

Statistical Mechanics · Physics 2009-11-10 J. Javier Brey , M. J. Ruiz-Montero

The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…

Analysis of PDEs · Mathematics 2025-05-20 Koudzo Togbévi Selom Sobah , Amah Séna d'Almeida

It is a fundamental problem in mathematical physics to derive macroscopic transport equations from microscopic models. In this paper we derive the linear Boltzmann equation in the low-density limit of a damped quantum Lorentz gas for a…

Mathematical Physics · Physics 2023-03-29 Jory Griffin

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal…

Quantum Physics · Physics 2010-09-28 Bassano Vacchini , Klaus Hornberger

We review the derivation of the Boltzmann equation and its cosmological applications in this paper. The derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of the quantum field theory…

High Energy Physics - Phenomenology · Physics 2023-03-02 Seishi Enomoto , Yu-Hang Su , Man-Zhu Zheng , Hong-Hao Zhang

Understanding how new physics influences the dynamics of cosmic neutrinos during their decoupling is crucial in light of upcoming precise cosmological observations and the need to reconcile cosmological and laboratory probes. Existing…

High Energy Physics - Phenomenology · Physics 2025-03-13 Maksym Ovchynnikov , Vsevolod Syvolap