del Razo, M.J. and Qian, H. and Noé, F. (2018) Grand canonical diffusioninfluenced reactions: a stochastic theory with applications to multiscale reactiondiffusion simulations. J. Chem. Phys., 149 (4). 044102. ISSN 00219606, ESSN: 10897690

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Official URL: https://dx.doi.org/10.1063/1.5037060
Abstract
Smoluchowskitype models for diffusioninfluenced reactions (A+B > C) can be formulated within two frameworks: the probabilisticbased approach for a pair A, B of reacting particles and the concentrationbased approach for systems in contact with a bath that generates a concentration gradient of B particles that interact with A. Although these two approaches are mathematically similar, it is not straightforward to establish a precise mathematical relationship between them. Determining this relationship is essential to derive particlebased numerical methods that are quantitatively consistent with bulk concentration dynamics. In this work, we determine the relationship between the two approaches by introducing the grand canonical Smoluchowski master equation (GCSME), which consists of a continuoustime Markov chain that models an arbitrary number of B particles, each one of them following Smoluchowski's probabilistic dynamics. We show that the GCSME recovers the concentrationbased approach by taking either the hydrodynamic or the large copy number limit. In addition, we show that the GCSME provides a clear statistical mechanical interpretation of the concentrationbased approach and yields an emergent chemical potential for nonequilibrium spatially inhomogeneous reaction processes. We further exploit the GCSME robust framework to accurately derive multiscale/hybrid numerical methods that couple particlebased reactiondiffusion simulations with bulk concentration descriptions, as described in detail through two computational implementations.
Item Type:  Article 

Additional Information:  SFB1114Preprint in arXiv:1804.07743 (https://arxiv.org/abs/1804.07743) 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Comp. Molecular Biology 
ID Code:  2290 
Deposited By:  Silvia Hoemke 
Deposited On:  06 Feb 2019 15:57 
Last Modified:  26 Jun 2019 12:39 
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