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Title: Hybrid approaches for multiple-species stochastic reaction–diffusion models

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 accountmore » 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. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [6] ;  [7]
  1. Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States)
  2. (United States)
  3. Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom)
  4. Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain)
  5. (Barcelona) (Spain)
  6. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
  7. (United Kingdom)
Publication Date:
OSTI Identifier:
22465671
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 299; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; BACTERIA; CHAPMAN-KOLMOGOROV EQUATION; COMPUTERIZED SIMULATION; DETERMINISTIC ESTIMATION; DIFFUSION EQUATIONS; ERRORS; FOKKER-PLANCK EQUATION; MEAN-FIELD THEORY; MOLECULES; PARTICLES; STOCHASTIC PROCESSES; VOLTERRA INTEGRAL EQUATIONS