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Brownian dynamics at boundaries and interfaces : in physics, chemistry, and biology

Author: Zeev Schuss
Publisher: New York : Springer, [2013] ©2013
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), volume 186.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Zeev Schuss
ISBN: 9781461476870 1461476879 1461476860 9781461476863
OCLC Number: 858924139
Description: 1 online resource (xx, 322 pages) : illustrations (some color)
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 stochastic separatrix --
Narrow escape in R² --
Narrow escape in R³.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), volume 186.
Responsibility: Zeev Schuss.

Abstract:

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.

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