Stochastic modelling of reaction-diffusion processes

by Erban, Radek

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Title Statements

Full title :Stochastic modelling of reaction-diffusion processes / Radek Erban (University of Oxford), S. Jonathan Chapman (University of Oxford).

Summary

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Edition Statements

Publication Date:©2020

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:©2020

The Physical Object

Description:1 online resource

Edition Identifiers

ISBN:9781108628389, 1108628389
oclc:on1128863867
LC Classification:QA274
Dewey Decimal:515/.3534

Cover -- Half-title page -- Series page -- Title page -- Copyright page -- Contents -- Preface -- 1 Stochastic Simulation of Chemical Reactions -- 1.1 Stochastic Simulation of Degradation -- 1.2 Stochastic Simulation of Production and Degradation -- 1.3 Higher-Order Chemical Reactions -- 1.4 Stochastic Simulation of Dimerization -- 1.5 Gillespie Algorithm -- Exercises -- 2 Deterministic versus Stochastic Modelling -- 2.1 Systems with Multiple Favourable States -- 2.2 Self-Induced Stochastic Resonance -- 2.3 Stochastic Focusing -- 2.4 Designing Stochastic Chemical Systems -- Exercises

3 Stochastic Differential Equations -- 3.1 A Computational Definition of SDE -- 3.2 Examples of SDEs -- 3.3 Fokker-Planck Equation -- 3.4 Boundary Conditions on the Fokker-Planck Equation -- 3.5 Kolmogorov Backward Equation -- 3.6 SDEs with Multiple Favourable States -- 3.7 Chemical Fokker-Planck Equation -- 3.8 Analysis of Problem from Section 2.1 -- 3.9 Analysis of Problem from Section 2.2 -- Exercises -- 4 Diffusion -- 4.1 Diffusion Modelled by SDEs -- 4.2 Compartment-Based Approach to Diffusion -- 4.3 Diffusion and Velocity-Jump Processes -- 4.4 Diffusion to Adsorbing Surfaces

4.5 Reactive Bound…