Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths
| Autor: | Sergey A. Rukolaine |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
010504 meteorology & atmospheric sciences Mathematical analysis Statistical and Nonlinear Physics Kinetic energy Heavy traffic approximation 01 natural sciences Exponential function Distribution (mathematics) 0103 physical sciences Path (graph theory) Kinetic theory of gases Linear transport theory Initial value problem 010306 general physics 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 450:205-216 |
| ISSN: | 0378-4371 |
| Popis: | In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt’s model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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