The blending region hybrid framework for the simulation of stochastic reaction–diffusion processes
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Published version
Author(s)
Type
Journal Article
Abstract
The simulation of stochastic reaction–diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to ignore stochastic fluctuations and use a more efficient coarse-grained simulation approach. Nevertheless, for multiscale systems which exhibit significant spatial variation in concentration, a coarse-grained approach may not be appropriate throughout the simulation domain. Such scenarios suggest a hybrid paradigm in which a computationally cheap, coarse-grained model is coupled to a more expensive, but more detailed fine-grained model, enabling the accurate simulation of the fine-scale dynamics at a reasonable computational cost. In this paper, in order to couple two representations of reaction–diffusion at distinct spatial scales, we allow them to overlap in a ‘blending region’. Both modelling paradigms provide a valid representation of the particle density in this region. From one end of the blending region to the other, control of the implementation of diffusion is passed from one modelling paradigm to another through the use of complementary ‘blending functions’ which scale up or down the contribution of each model to the overall diffusion. We establish the reliability of our novel hybrid paradigm by demonstrating its simulation on four exemplar reaction–diffusion scenarios.
Date Issued
2020-10
Date Acceptance
2020-09-29
Citation
Journal of The Royal Society Interface, 2020, 17 (171), pp.1-19
ISSN
1742-5689
Publisher
The Royal Society
Start Page
1
End Page
19
Journal / Book Title
Journal of The Royal Society Interface
Volume
17
Issue
171
Copyright Statement
© 2020 The Authors.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Identifier
https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0563
Subjects
General Science & Technology
Publication Status
Published
Date Publish Online
2020-10-21