Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Hardcover | November 15, 2012

byDaniel Thomas Gillespie, Effrosyni Seitaridou

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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 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.

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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 bookfocuses on the four simplest models of Brow...

Dan Gillespie is a physicist, with a B.A. from Rice University (1960) and a Ph.D. from Johns Hopkins University (1968). He is well known in the field of stochastic chemical kinetics as the inventor of a computer algorithm for simulating the discrete-stochastic time evolution of a chemically reacting system. Dan has written two books in...
Format:HardcoverDimensions:256 pagesPublished:November 15, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199664501

ISBN - 13:9780199664504

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Table of Contents

1. The Fickian theory of diffusion2. A review of random variable theory3. Einstein's theory of diffusion4. Implications and limitations of the Einstein theory of diffusion5. The discrete-stochastic approach6. Master equations and simulation algorithms for the discrete-stochastic approach7. Continuous Markov process theory8. Langevin's theory of diffusion9. Implications of Langevin's theory10. Diffusion in an external force field11. The first-passage time approach

Editorial Reviews

"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 ofnumerical 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