Applied Mathematical Sciences

Brownian Dynamics at Boundaries and Interfaces

In Physics, Chemistry, and Biology

Authors: Schuss, Zeev

  • ​Written in an accessible, easy to read manner without detailed rigorous proofs
  • Lots of examples and exercises throughout the book
  • Written from the scientists point of view with deep insight into several modelling situations in biology  ​
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About this Textbook

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.

About the authors

Zeev Schuss is a Professor at Tel Aviv University.

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 stochastic differential equations through the Euler scheme of successive approximations … .” (David R. Steinsaltz, Mathematical Reviews, November, 2014)

Table of contents (8 chapters)

  • Mathematical Brownian Motion

    Schuss, Zeev

    Pages 1-34

  • Euler’s Scheme and Wiener’s Measure

    Schuss, Zeev

    Pages 35-88

  • Brownian Simulation of Langevin’s

    Schuss, Zeev

    Pages 89-109

  • The First Passage Time to a Boundary

    Schuss, Zeev

    Pages 111-134

  • Brownian Models of Chemical Reactions in Microdomains

    Schuss, Zeev

    Pages 135-163

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-7687-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4614-7686-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Brownian Dynamics at Boundaries and Interfaces
Book Subtitle
In Physics, Chemistry, and Biology
Authors
Series Title
Applied Mathematical Sciences
Series Volume
186
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Author
eBook ISBN
978-1-4614-7687-0
DOI
10.1007/978-1-4614-7687-0
Hardcover ISBN
978-1-4614-7686-3
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XX, 322
Topics