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Generalized diffusion equation

Author

Listed:
  • Boon, Jean Pierre
  • Lutsko, James F.

Abstract

Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker–Planck equation to account for nonclassical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here, we introduce a nonlinear transformation by defining the q-generating function which, when applied to the intermediate scattering function of classical statistical mechanics, yields, in a mathematically systematic derivation, a generalized form of the advection–diffusion equation in Fourier space. Its solutions are discussed and suggest that the q-generating function approach should be a useful method to generalize classical diffusive transport formulations.

Suggested Citation

  • Boon, Jean Pierre & Lutsko, James F., 2006. "Generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 55-62.
    • Handle: RePEc:eee:phsmap:v:368:y:2006:i:1:p:55-62
    DOI: 10.1016/j.physa.2005.11.054
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    References listed on IDEAS

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    1. Silvio M. Duarte Queiros & Constantino Tsallis, 2004. "Bridging the ARCH model for finance and nonextensive entropy," Papers cond-mat/0401181, arXiv.org, revised Jan 2004.
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    Cited by:

    1. Alexanian, Moorad & McNamara, Dylan, 2018. "Anti-diffusion in continuous opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1256-1262.

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