Brownian Dynamics at Boundaries and Interfaces
In Physics, Chemistry, and Biology
1st Edition
Published on 13. August 2013
Book
Hardback
XX, 322 pages
978-1-4614-7686-3 (ISBN)
Description
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 stochastic 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. Stochastic 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 stock 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.
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.
Reviews / Votes
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 stochastic differential equations through the Euler scheme of successive approximations ... ." (David R. Steinsaltz, Mathematical Reviews, November, 2014)More details
Product info
Book
Series
Language
English
Place of publication
New York, NY
United States
Target group
Graduate
Illustrations
37 schwarz-weiße und 9 farbige Abbildungen
Dimensions
Height: 241 mm
Width: 162 mm
Thickness: 25 mm
Weight
654 gr
ISBN-13
978-1-4614-7686-3 (9781461476863)
DOI
10.1007/978-1-4614-7687-0
Schweitzer Classification
Other editions
Additional editions
Book
08/2015
Springer
€53.49
Shipment within 15-20 days
E-Book
08/2013
Springer
€53.49
Available for download
Person
Zeev Schuss is a Professor at Tel Aviv University.
Content
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 Stochastic Separatrix.- Narrow Escape in R2.- Narrow Escape in R3.