Continuum Derrida approach to drift and diffusivity in random media
| Autor: | David S. Dean, R. R. Horgan, I T Drummond |
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| Rok vydání: | 1997 |
| Předmět: |
Physics
Molecular diffusion Condensed Matter (cond-mat) FOS: Physical sciences General Physics and Astronomy Order (ring theory) Statistical and Nonlinear Physics Condensed Matter Thermal diffusivity Renormalization Constraint (information theory) Probability distribution Statistical physics Continuum (set theory) Perturbation theory Mathematical Physics |
| Zdroj: | Journal of Physics A: Mathematical and General. 30:385-396 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/30/2/006 |
| Popis: | By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results. 18 pages, Latex, DAMTP-96-80 |
| Databáze: | OpenAIRE |
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