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Continuous versus discrete description of the transport in a membrane system

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  • Kosztołowicz, Tadeusz

Abstract

The continuous (macroscopic) and the discrete (microscopic) description of the membrane transport are related to each other. Specifically, we construct the Green's functions for a diffusive-convective system with a membrane (which is treated as a partially permeable wall) in three cases: in the first one the Smoluchowski (diffusion) equation (SE) is used, in the second case one applies the birth-death (BDE) equation, and finally, we combine the continuous and discrete description in such a way that in the space outside the wall the SE acts, whereas the passing through the membrane is described in terms of BDE. To obtain the Green's functions in the above-mentioned cases, we introduced a new generalized method of images.

Suggested Citation

  • Kosztołowicz, Tadeusz, 1998. "Continuous versus discrete description of the transport in a membrane system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 44-56.
    • Handle: RePEc:eee:phsmap:v:248:y:1998:i:1:p:44-56
    DOI: 10.1016/S0378-4371(97)00450-0
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    References listed on IDEAS

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    1. Van Kampen, N.G., 1987. "A set of oscillators in a common bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 165-183.
    2. Widder, M.E. & Titulaer, U.M., 1989. "Brownian motion in a medium with inhomogeneous temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(3), pages 452-466.
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