Overview

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.

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9780199664504

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Reviews

In a lively tutorial style, the authors discuss some of the most widely used mathematical formulations of diffusion. They have endeavored to organize and present the subject matter from a purely logical perspective. They emphasize the basic physical assumptions and the conditions for the validity of each of the mathematical formalisms. No subtlety is bypassed, and no limitation of the theory is swept under the carpet. In a lively tutorial style, the authors discuss some of the most widely used mathematical formulations of diffusion. They have endeavored to organize and present the subject matter from a purely logical perspective . They emphasize the basic physical assumptions and the conditions for the validity of each of the mathematical formalisms. No subtlety is bypassed, and no limitation of the theory is swept under the carpet. Physics Today

`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

<br>. ..accessible to researchres from a broad spectrum of technical backgrounds. -- Mathematical Reviews<br><p><br>

Author Information

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.

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