Brownian Dynamics at Boundaries and Interfaces: In Physics, Chemistry, and Biology / Edition 1

by Zeev Schuss

Overview

Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of shastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Shastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or sk prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein’s and Langevin’s theories of Brownian motion could predict.

This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout.

Product Details

ISBN-13:	9781461476863
Publisher:	Springer New York
Publication date:	08/13/2013
Series:	Applied Mathematical Sciences , #186
Edition description:	2013
Pages:	322
Product dimensions:	6.30(w) x 9.20(h) x 1.00(d)

About the Author

Zeev Schuss is a Professor at Tel Aviv University.

Table of Contents

The Mathematical Brownian Motion.- Euler Simulation of Ito SDEs.- Simulation of the Overdamped Langevin Equation.- The First Passage Time of a Diffusion Process.- Chemical Reaction in Microdomains.- The Shastic Separatrix.- Narrow Escape in R2.- Narrow Escape in R3.

Editorial Reviews

From the book reviews:

“This text provides an excellent entry point for applied mathematicians who would like to get a first understanding of the field of neuronal modeling, with a bold motivation and immediate application to highly relevant phenomena in the science … . this text may serve as an excellent basis for a specialized course on neuronal modeling or biophysics at master’s level and as a common reference text for interdisciplinary teams, which perfectly reflects the author’s long working experience.” (P. R. C. Ruffino, zbMATH, Vol. 1305, 2015)

“This book uniquely combines an introduction to the mathematical theory of Brownian motion with applications to chemical kinetics, primarily in biology and physiology. … this a unique and valuable book. … Exercises are included throughout the book, particularly relating to the mathematical theory. The book will be extremely useful to both mathematicians and biologists/physiologists, etc., who work at the interface of these two subjects.” (D. J. W. Simpson, SIAM Review, Vol. 56 (4), December, 2014)

“This book will be of interest to a broad group of students and researchers. It presents a style of analysis that is typical of applications in physics and applied sciences—an explicit transition-density style based on the Fokker-Planck and Langevin equations, and the forward Kolmogorov equation, and defining solutions to shastic differential equations through the Euler scheme of successive approximations … .” (David R. Steinsaltz, Mathematical Reviews, November, 2014)

From the Publisher