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Algorithm for mesoscopic advection-diffusion
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Noel, Adam and Makrakis, Dimitrios (2018) Algorithm for mesoscopic advection-diffusion. IEEE Transactions on NanoBioscience, 17 (4). pp. 543-554. doi:10.1109/TNB.2018.2878065 ISSN 1536-1241.
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Official URL: https://doi.org/10.1109/TNB.2018.2878065
Abstract
In this paper, an algorithm is presented to calculate the transition rates between adjacent mesoscopic subvolumes in the presence of flow and diffusion. These rates can be integrated in stochastic simulations of reaction-diffusion systems that follow a mesoscopic approach, i.e., that partition the environment into homogeneous subvolumes and apply the spatial stochastic simulation algorithm (spatial SSA). The rates are derived by integrating Fick's second law over a single subvolume in one dimension (1D), and are also shown to apply in three dimensions (3D). The proposed algorithm corrects the derived rates to ensure that they are physically meaningful and it is implemented in the AcCoRD simulator (Actor-based Communication via Reaction-Diffusion). Simulations using the proposed method are compared with a naive mesoscopic approach, microscopic simulations that track every molecule, and analytical results that are exact in 1D and an approximation in 3D. By choosing subvolumes that are sufficiently small, such that the Peclet number associated with a subvolume is sufficiently less than 2, the accuracy of the proposed method is comparable with the microscopic method, thus enabling the simulation of advection-reaction-diffusion systems with the spatial SSA.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||||
| Library of Congress Subject Headings (LCSH): | Algorithms, Reaction-diffusion equations | ||||||||
| Journal or Publication Title: | IEEE Transactions on NanoBioscience | ||||||||
| Publisher: | IEEE | ||||||||
| ISSN: | 1536-1241 | ||||||||
| Official Date: | 1 October 2018 | ||||||||
| Dates: |
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| Volume: | 17 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 543-554 | ||||||||
| DOI: | 10.1109/TNB.2018.2878065 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Copyright Holders: | IEEE | ||||||||
| Date of first compliant deposit: | 20 March 2018 | ||||||||
| Date of first compliant Open Access: | 20 March 2018 | ||||||||
| Funder: | Natural Sciences and Engineering Research Council of Canada (NSERC) | ||||||||
| RIOXX Funder/Project Grant: |
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