Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths

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...

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Bibliographic Details
Published in:Physica A 2016-05, Vol.450, p.205-216
Main Author: Rukolaine, Sergey A.
Format: Article
Language:English
Subjects:
Active transport processes
Approximation
Asymptotic properties
Boltzmann equation
Boltzmann transport equation
Generalized linear Boltzmann equation
Kinetic theory
Linear transport theory
Mathematical analysis
Mathematical models
Mean free path
Transport
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Summary: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.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2015.12.105