Defect Diffusion with Drift and the Kinetics of Reactions
Part of the
Condensed Matter Theories
book series (COMT, volume 8)
A considerable amount of work has been devoted to the study of biased random walks. The effects of a random bias and of random jump rates have been taken into account. Random distributions of traps have also been added.1–7 However, aside from some calculations for walks on finite segments,3, 7 the systems considered have been, in general, homogeneous on the average. The purpose of this paper is to present results for one-dimensional biased random walks where this “average homogeneity” has been destroyed by the introduction of a partially absorbing boundary. The boundary may represent a defect-mediated relaxation process, as in the Glarum model of dielectric relaxation,8–10 or a chemical reaction occurring at the surface of a sample if one of the reactants is allowed to diffuse in the sample interior. It may also be a special site in a protein where a process is triggered by the arrival of a diffusing catalyst.11–14 The sensitivity of ionic channels in cell membranes to applied voltages is currently the object of intense study.15–16 Biological systems are of particular interest, because of the many spatial constraints they impose on particle motion.17 A different application would be to the problem of particle diffusion in a liquid when gravity effects are nonnegligible.
KeywordsBromide Stein Isoamyl
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