Repository: Freie Universität Berlin, Math Department

A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures

Montefusco, Alberto and Schütte, Christof and Winkelmann, Stefanie (2023) A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures. Society for Industrial and Applied Mathematic (siam), 83 (2). pp. 836-861.

Full text not available from this repository.

Official URL: https://doi.org/10.1137/22M1488831

Abstract

The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations (RDPDEs). Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas, A. Mielke: Modeling of chemical reactions systems with detailed balance using gradient structures. J. Stat. Phys. (181), 2257-2303 (2020)] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2963
Deposited By: Monika Drueck
Deposited On:20 Apr 2023 10:52
Last Modified:02 Feb 2024 13:00

Repository Staff Only: item control page