Simple Brownian Diffusion

An Introduction to the Standard Theoretical Models

By: Daniel Thomas Gillespie, Effrosyni Seitaridou

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Hardcover | 25 October 2012 | Edition Number 1

At a Glance

Hardcover
288 Pages

Dimensions(cm)
24.64 x 17.27 x 2.03

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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 book focuses 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. Two self-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.

A revised/corrected Section 5.6, along with other current errata, can be obtained as a PDF document by emailing a request to gillespiedt@mailaps.org or eseitar@emory.edu

Industry Reviews

`I appreciate the attention Gillespie and Seitaridou pay to matters of principle and to important detail. I sense that I am in the hands of masters when reading Simple Brownian Diffusion and trust the authors to do a good job. Simple Brownian Diffusion has the potential to become a standard reference book and learning tool for decades to come.' Don S. Lemons, Emeritus Professor of Physics, Bethel College, and author of An Introduction to Stochastic Processes in Physics. `Simple Brownian Diffusion provides a solid introduction to the physics and chemistry of diffusive processes. This book offers a wonderfully complete treatment of the numerical simulation of diffusion problems (with many well-explained examples). ' William Peter, Applied Physics Laboratory, John Hopkins University `In this volume, Gillespie and Seitaridou have given an introductory, self contained, and thorough discussion of the motion of heavy particles in a milieu of light particles. In addition to the analytic techniques and physical assumptions needed to study the model, a very welcome treatment of numerical simulation methods for probabilistic problems is included. A person who works through this material will be well prepared for research on random processes in chemistry and physics.' R. M. Mazo, Emeritus Professor of Chemistry, University of Oregon

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