Asymptotics of Elliptic and Parabolic PDEs
and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics
Authors: Holcman, David, Schuss, Zeev
- Discusses asymptotic formulae in the context of the life sciences
- Presents applications in molecular and cellular biology, biophysics, as well as computational neuroscience
- Contains over 100 figures
- Includes bibliographical notes
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- About this book
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This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.
In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory.
Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles. - About the authors
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David Holcman is an applied mathematician and computational biologist. He developed mathematical modeling and simulations of molecular dynamics in micro-compartments in cell biology using stochastic processes and PDEs. He has derived physical principles of physiology at various scales, including diffusion laws in dendritic spines, potential wells hidden in super-resolution single particle trajectories or first looping time in polymer models. Together with Zeev Schuss, he developed the Narrow escape and Dire strait time theory.
Zeev Schuss is an applied mathematician who significantly shaped the field of modern asymptotics in PDEs with applications to first passage time problems. Methods developed have been applied to various fields, including signal processing, statistical physics, and molecular biophysics. - Reviews
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“The monograph under review deals with asymptotic methods for the construction of solutions to boundary value problems for partial differential equations arising in applications, as molecular and cellular biology and biophysics. … The monograph is well written, interesting, and surely recommended to applied mathematicians, engineers, physicists, chemists, and neuroscientists interested into analytical methods for the asymptotic analysis of elliptic and parabolic PDEs of relevance in applications.” (Paolo Musolino, zbMATH 1402.35004, 2019)
- Table of contents (12 chapters)
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Second-Order Elliptic Boundary Value Problems with a Small Leading Part
Pages 3-9
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A Primer of Asymptotics for ODEs
Pages 11-48
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Singular Perturbations in Higher Dimensions
Pages 49-113
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Eigenvalues of a Non-self-adjoint Elliptic Operator
Pages 115-158
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Short-Time Asymptotics of the Heat Kernel
Pages 159-187
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Asymptotics of Elliptic and Parabolic PDEs
- Book Subtitle
- and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics
- Authors
-
- David Holcman
- Zeev Schuss
- Series Title
- Applied Mathematical Sciences
- Series Volume
- 199
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-76895-3
- DOI
- 10.1007/978-3-319-76895-3
- Hardcover ISBN
- 978-3-319-76894-6
- Softcover ISBN
- 978-3-030-08319-9
- Series ISSN
- 0066-5452
- Edition Number
- 1
- Number of Pages
- XXIII, 444
- Number of Illustrations
- 47 b/w illustrations, 56 illustrations in colour
- Topics
