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Crossover from kinetic to diffusive behaviour for a class of generalized models of the Lorentz gas

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  • Jasiukiewicz, Cz.
  • Paszkiewicz, R.
  • Woźny, J.

Abstract

The rarefied Lorentz gas with anisotropic scattering is considered. The collision integral contains terms related to the isotropic and anisotropic scattering. The Cauchy problem for the Boltzmann equation is studied. Assuming that the Fourier transform of the initial distribution function depends on the wave-vector k, the modulus of velocity v and the cosine of the angle between them, the Fourier-Laplace transform of the distribution function is expanded into a series in the Legendre polynomials. The explicit time dependence of the coefficients of this series is studied. In this way the crossover from kinetic to diffusive stage of evolution is discussed. As a special case the gas of neutrinos in stellar matter is considered.

Suggested Citation

  • Jasiukiewicz, Cz. & Paszkiewicz, R. & Woźny, J., 1989. "Crossover from kinetic to diffusive behaviour for a class of generalized models of the Lorentz gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 158(3), pages 864-893.
    • Handle: RePEc:eee:phsmap:v:158:y:1989:i:3:p:864-893
    DOI: 10.1016/0378-4371(89)90495-0
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    References listed on IDEAS

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    1. Piasecki, J. & Wajnryb, E., 1985. "The Lorentz model for neutrinos: Exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(1), pages 291-301.
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    Cited by:

    1. Paszkiewicz, T. & Pruchnik, M., 1996. "Kinetic description of the phonon-pulse propagation and phonon images of crystalline solids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 747-768.

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