ArticleJournal of computational physics2015
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Article in Journal of computational physics, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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Who cites it
14 citing papers in PubMed.
- Approximate Bayesian inference in a model for self-generated gradient collective cell movement.Computational statistics · 2025Article
- Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles.PLoS computational biology · 2023Article
- Incorporating domain growth into hybrid methods for reaction-diffusion systems.Journal of the Royal Society, Interface · 2021Article
- The blending region hybrid framework for the simulation of stochastic reaction-diffusion processes.Journal of the Royal Society, Interface · 2020Article
- Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations.Bulletin of mathematical biology · 2019Article
- Spatially extended hybrid methods: a review.Journal of the Royal Society, Interface · 2018Review
- Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.The Journal of chemical physics · 2017Article
- Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.Journal of computational physics · 2017Article
- Modeling, signaling and cytoskeleton dynamics: integrated modeling-experimental frameworks in cell migration.Wiley interdisciplinary reviews. Systems biology and medicine · 2017Review
- Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.Journal of theoretical biology · 2016Article
- A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.Journal of the Royal Society, Interface · 2016Article
- Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.Journal of the Royal Society, Interface · 2016Article
- Hybrid finite element and Brownian dynamics method for charged particles.The Journal of chemical physics · 2016Article
- Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics.Journal of biomechanical engineering · 2016Review
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Authors and funding
5 authors.
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No grant is acknowledged in the PubMed record.
Abstract
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.