Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations
Two multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Ma...
| Main Authors: | , |
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| Format: | Journal article |
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Springer
2019
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| _version_ | 1797105379979558912 |
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| author | Kang, HW Erban, R |
| author_facet | Kang, HW Erban, R |
| author_sort | Kang, HW |
| collection | OXFORD |
| description | Two multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction–diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches. |
| first_indexed | 2024-03-07T06:46:42Z |
| format | Journal article |
| id | oxford-uuid:fb16a54a-4d33-46c5-b6b8-9e49a0dd791c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:46:42Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:fb16a54a-4d33-46c5-b6b8-9e49a0dd791c2022-03-27T13:11:17ZMultiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fb16a54a-4d33-46c5-b6b8-9e49a0dd791cSymplectic Elements at OxfordSpringer2019Kang, HWErban, RTwo multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction–diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches. |
| spellingShingle | Kang, HW Erban, R Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title | Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title_full | Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title_fullStr | Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title_full_unstemmed | Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title_short | Multiscale stochastic reaction–diffusion algorithms combining Markov chain models with stochastic partial differential equations |
| title_sort | multiscale stochastic reaction diffusion algorithms combining markov chain models with stochastic partial differential equations |
| work_keys_str_mv | AT kanghw multiscalestochasticreactiondiffusionalgorithmscombiningmarkovchainmodelswithstochasticpartialdifferentialequations AT erbanr multiscalestochasticreactiondiffusionalgorithmscombiningmarkovchainmodelswithstochasticpartialdifferentialequations |