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.
Dan Gillespie is a physicist, with a B.A. from Rice University and a Ph.D. from Johns Hopkins University. He is best known as the inventor of the Gillespie algorithm for numerically simulating the discrete-stochastic time evolution of chemical reactions inside living cells. He has written two previous 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). He was for 30 years 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 collaboratively with researchers at the University of California at Santa Barbara and the California Institute of Technology. Effrosyni Seitaridou is an Associate Professor of Physics at Oxford College of Emory University in Atlanta, Georgia. In 2002 she received a B.A. in physics from Smith College and also a B.E. in Materials Science from Dartmouth College. She did post-graduate studies at the California Institute of Technology as a Moore Fellow in the Rob Phillips research group. There she received her M.S. (2004) and Ph.D. (2008) in applied physics, with a focus on biochemical systems and microfluidics devices. She is currently conducting experiments with undergraduate students on diffusion in biofilms. She is also designing interdisciplinary experiments for the introductory physics curriculum. In 2009 she received formal recognition from Phi Beta Kappa for her excellence in teaching.
1. The Fickian theory of diffusion ; 2. A review of random variable theory ; 3. Einstein's theory of diffusion ; 4. Implications and limitations of the Einstein theory of diffusion ; 5. The discrete-stochastic approach ; 6. Master equations and simulation algorithms for the discrete-stochastic approach ; 7. Continuous Markov process theory ; 8. Langevin's theory of diffusion ; 9. Implications of Langevin's theory ; 10. Diffusion in an external force field ; 11. The first-passage time approach