Regensburg 2022 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 40: Brownian Motion and Anomalous Diffusion
DY 40.6: Vortrag
Donnerstag, 8. September 2022, 11:30–11:45, H20
Generalised master equation for diffusion and reaction problems in heterogeneous media — Daniela Frömberg1 and •Felix Höfling1,2 — 1Department of Mathematics and Computer Science, Freie Universität Berlin — 2Zuse Institute Berlin
The kinetics of chemical reactions in a heterogeneous or crowded medium significantly deviates from that in a well-mixed, aqueous environment. One example is the partitioning of cell membranes and intracellular spaces, e.g., into cytoplasm and nucleus. For reaction–diffusion problems in such compartmentalised spaces, we extend a recently proposed generalised master equation (GME) for non-Markovian jump processes [1]. The GME governs the time evolution of the occupation probability of the spatial domains, its main ingredient are first-passage time densities encoding the transport behaviour in each domain. The domains can differ with respect to their diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. We discuss further the inclusion of barriers and the Markovian limit of the GME.
For a cherry-pit geometry with a reactive inner domain, we obtain the first-reaction time density and infer the effective reaction rate constant. This rate constant is timescale dependent and exhibits an enhancement at intermediate times by orders of magnitude and an algebraically slow convergence to the long-time limit. Our stochastic approach does not depend on the existence of a stationary distribution and thus overcomes a limitation of the classical Smoluchowski theory.
[1] D. Frömberg and F. Höfling, J. Phys. A 54, 215601 (2021).