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

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  • Rukolaine, Sergey A.

Abstract

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.

Suggested Citation

  • Rukolaine, Sergey A., 2016. "Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 205-216.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:205-216
    DOI: 10.1016/j.physa.2015.12.105
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    References listed on IDEAS

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    1. Uchaikin, Vladimir V., 1998. "Anomalous transport equations and their application to fractal walking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(1), pages 65-92.
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