Simple Brownian Diffusion

• Carefully describes and assesses the four standard models of molecular diffusion
• Addresses issues relevant to modelling chemical reactions in living cells
• Gives special attention to the numerical simulation of diffusion
• Tutorial chapters on random variable theory and stochastic differential equations provide the requisite beyond-calculus mathematics background
• Self-contained didactic presentation fosters accessibility to many disciplines
• A revised/corrected Section 5.6, along with other current errata is available

Readership: Graduate students, post-doctoral students, professors, and researchers in physics, chemistry, biology, computer science, and engineering, whose theoretical or experimental work concerns the chemistry of living cells.

Daniel Thomas Gillespie and Effrosyni Seitaridou

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 Assistant 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.

"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

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