Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 43: Einstein Symposium Brownian Motion, Diffusion and Beyond (SYBM) – Contributed Talks I

DY 43.6: Vortrag

Dienstag, 8. März 2005, 15:45–16:00, TU H2032

On the proper boundary conditions for the anomalous subdiffusion–reaction processes — •Igor Goychuk and Peter Hänggi — Institut für Physik, Universität Augsburg, Germany

Diffusion can be of substantial importance for many processes in nature, e.g. for biochemical reactions occurring in the living cells. Due to the molecular crowding in the cytoplasm of the biological cells as well as in their membranes (which normally is the case) the molecular diffusion may become anomalously slow. The fractional diffusion equation presents a convenient mathematical tool to describe non-Markovian subdiffusion processes. Its application to the subdiffusion-reaction kinetics requires that the corresponding boundary conditions must be derived properly from the underlying physical consideration. There are two different kinds of the radiation boundary condition for the fractional diffusion equation at use. We justify the correctness and the physical relevance of one of them by invoking (i) the continuous time random walk picture of subdiffusional encounters, (ii) the probability conservation law and (iii) the standard assumption on the Markovian character of the chemical transformations at the encounter events. This justifies the correct use of the fractional Riemann-Liouville derivative for the diffusion part of the (sub)diffusion-reaction equations only. This implies also the failure of the known scaling recipe (in the Laplace-transformed time picture) to obtain the correct solution of a subdiffusion problem involving a pseudo-first order chemical reaction from its normal diffusion counterpart.