Simple Brownian Diffusion An Introduction to the Standard Theoretical Models

by Gillespie, Daniel Thomas; Seitaridou, Effrosyni

• ISBN13: 9780199664504
• ISBN10: 0199664501
• Format: Hardcover
• Copyright: 2012-12-12
• Publisher: Oxford University Press

Summary

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This bookfocuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Twoself-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

Table of Contents

The Fickian theory of diffusion

A review of random variable theory

Einstein's theory of diffusion

Implications and limitations of the Einstein theory of diffusion

The discrete-stochastic approach

Master equations and simulation algorithms for the discrete-stochastic approach

Continuous Markov process theory

Langevin's theory of diffusion

Implications of Langevin's theory

Diffusion in an external force field

The first-passage time approach

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