Frömberg, Daniela and Höfling, Felix (2020) Generalized master equation for firstpassage problems in partitioned spaces. Journal of Physics A . pp. 123. (Submitted)

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Official URL: https://arxiv.org/abs/2010.04854
Abstract
Abstract Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat firstpassage problems for diffusion in partitioned spaces. The spatial 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. The approach relies on a coarsegraining of the motion by dissecting the trajectories on domain boundaries or when the mode of transport changes, yielding a small set of states. The time evolution of the reduced model follows a generalized master equation, which takes the form of a set of linear integrodifferential equations in the occupation probabilities of the states and the corresponding probability fluxes. Further building blocks of the model are partial firstpassage time (FPT) densities, which encode the transport behavior in each domain or state. The approach is exemplified and validated for a target search problem with two domains in one and threedimensional space, first by exactly reproducing known results for an artificially divided, homogeneous space, and second by considering the situation of domains with distinct diffusivities. Analytical solutions for the FPT densities are given in Laplace domain and are complemented by numerical backtransform yielding FPT densities over many decades in time, confirming that the geometry and heterogeneity of the space can introduce additional characteristic timescales.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2471 
Deposited By:  Monika Drueck 
Deposited On:  19 Oct 2020 12:48 
Last Modified:  19 Oct 2020 12:48 
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