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The p-q model Boltzmann equation

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  • Futcher, E.J.
  • Hoare, M.R.

Abstract

The “p-q” model earlier introduced by the authors to describe persistent scattering under a scalar Boltzmann equation is here examined in detail. After deriving the scattering kernel and exhibiting its properties we obtain moment and similarity solutions and show how the model effectively parametrizes all intermediate conditions between the extremes of diffusion-like “small-scattering” and the strong-collisional limit of “diffuse-scattering” characteristic of earlier, more restrictive models. Both continuous and discrete-variable versions of the model are discussed and shown to be straightforwardly interrelated. Our derivations, carried out in natural energy-like variables, parallel those given recently by Ernst and Hendriks using transform methods.

Suggested Citation

  • Futcher, E.J. & Hoare, M.R., 1983. "The p-q model Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 516-546.
    • Handle: RePEc:eee:phsmap:v:122:y:1983:i:3:p:516-546
    DOI: 10.1016/0378-4371(83)90047-X
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    References listed on IDEAS

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    1. Hendriks, A.J., 1981. "Theoretische en practische problemen van het distributieplanologisch onderzoek : Referaten themadag RSA op 14 mei 1981," Research Memorandum FEW 98, Tilburg University, School of Economics and Management.
    2. Hoare, M.R. & Rahman, M., 1979. "Distributive processes in discrete systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(1), pages 1-41.
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