Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

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

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 science: A Quantum Mechanics Primer (in print from 1970 to 1986 from International Textbook Co.), and Markov Processes: An Introduction for Physical Scientists (1992, Academic Press). From 1971 to 2001, Dan was a civilian research scientist for the U. S. Navy in China Lake, California. Since his retirement from there in 2001, he has been a private consultant in stochastic chemical kinetics, working under contracts with researchers at the University of California at Santa Barbara and the California Institute of Technology.

Effrosyni Seitaridou is an Assistant Professor of Physics at Oxford College of Emory University in Atlanta, Georgia. She received her B.A. in Physics from Smith College (2002), and received a B.E. in Materials Science from Dartmouth College (2002). Effrosyni did her post-graduate studies at the California Institute of Technology (Caltech), where she was a Moore Fellow. Her research work has been published in such diverse journals as the American Journal of Physics, The Journal of Physical Chemistry B, and Nucleic Acid Research. Effrosyni is currently conducting experiments with undergraduate students to understand how the stage of development of a biofilm affects the process of diffusion within the biofilm. She is also designing interdisciplinary experiments for the introductory physics curriculum, as she is especially interested in the teaching of freshman-level and sophomore-level physics courses. In 2009, Effrosyni received formal recognition from Phi Beta Kappa for her excellence in teaching.