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Stochastic modelling of reaction-diffusion processes /

Bibliographic Details
Main Authors: Erban, Radek (Author), Chapman, Jon (Author)
Corporate Author: Cambridge University Press
Format: eBook
Language:English
Published: Cambridge ; New York, NY : Cambridge University Press, [2020]
Series:Cambridge texts in applied mathematics.
Subjects:
Stochastic processes > Textbooks.
Reaction-diffusion equations > Textbooks.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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 Boundary Conditions
  • 4.6 Einstein-Smoluchowski Relation
  • Exercises
  • 5 Efficient Stochastic Modelling of Chemical Reactions
  • 5.1 A Simple Multiscale Problem
  • 5.2 Multiscale SSA with Partial Equilibrium Assumption
  • 5.3 Multiscale Modelling
  • 5.4 First-Reaction SSA
  • 5.5 Exact Efficient SSAs
  • Exercises
  • 6 Stochastic Reaction-Diffusion Models
  • 6.1 A Compartment-Based Reaction-Diffusion Algorithm
  • 6.2 A Reaction-Diffusion SSA Based on the SDE Model of Diffusion
  • 6.3 Compartment-Based SSA for Higher-Order Reactions
  • 6.4 A Choice of Compartment Size h
  • 6.5 Molecular-Based Approaches for Second-Order Reactions
  • 6.6 Reaction Radius and Reaction Probability
  • 6.7 Modelling Reversible Reactions
  • 6.8 Biological Pattern Formation
  • Exercises
  • 7 SSAs for Reaction-Diffusion-Advection Processes
  • 7.1 SSAs for Diffusion-Advection Processes
  • 7.2 Reaction-Diffusion-Advection SSAs
  • 7.3 Bacterial Chemotaxis
  • 7.4 Collective Behaviour of Locusts
  • 7.5 Ions and Ion Channels
  • 7.6 Metropolis-Hastings Algorithm
  • Exercises
  • 8 Microscopic Models of Brownian Motion
  • 8.1 One-Particle Solvent Model
  • 8.2 Generalized Langevin Equation
  • 8.3 Solvent as Harmonic Oscillators
  • 8.4 Solvent as Points Colliding with the Diffusing Particle
  • 8.5 Forces Between Atoms and Molecules
  • 8.6 Molecular Dynamics
  • Exercises
  • 9 Multiscale and Multi-Resolution Methods
  • 9.1 Coupling SDE-Based and Compartment-Based Models
  • 9.2 Coupling Molecular Dynamics with Langevin Dynamics
  • 9.3 Multi-Resolution Molecular and Brownian Dynamics
  • Exercises
  • Appendix
  • Appendix A Deterministic Modelling of Chemical Reactions
  • Appendix B Discrete Probability Distributions
  • Appendix C Continuous Probability Distributions
  • References
  • Index