Stochastic Modelling of Reaction-Diffusion Processes

✍ Scribed by Radek Erban, S. Jonathan Chapman

• Publisher: Cambridge University Press
• Year: 2020
• Tongue: English
• Leaves: 321
• Series: Cambridge Texts in Applied Mathematics (60)
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Front Matter
......Page 2
Cambridge Texts in Applied Mathematics......Page 3
Stochastic Modelling of
Reaction–Diffusion Processes......Page 4
Copyright
......Page 5
Contents
......Page 6
Preface
......Page 10
1 Stochastic Simulation of Chemical Reactions......Page 14
2 Deterministic versus Stochastic Modelling......Page 46
3 Stochastic Differential Equations......Page 72
4 Diffusion......Page 108
5 Efficient Stochastic Modelling of Chemical
Reactions......Page 150
6 Stochastic Reaction–Diffusion Models......Page 173
7 SSAs for Reaction–Diffusion–Advection
Processes......Page 205
8 Microscopic Models of Brownian Motion......Page 239
9 Multiscale and Multi-Resolution Methods......Page 281
References......Page 306
Appendix......Page 314
Index......Page 318