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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.), v. 186.
Edition/Format:   Print book : Manuscript   Archival Material : EnglishView all editions and formats

Brownian Dynamics at Boundaries and Interfaces


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Additional Physical Format: (GyWOH)har130418244
Material Type: Manuscript
Document Type: Book, Archival Material
All Authors / Contributors: Zeev Schuss
ISBN: 9781461476863 1461476860
OCLC Number: 839388739
Description: xx, 322 pages : illustrations (some color) ; 24 cm.
Contents: Mathematical Brownian motion --
Definition of Mathematical Brownian motion --
Mathematical Brownian motion in Rd --
Construction of Mathematical Brownian motions --
Analytical and statistical properties of Brownian paths --
Integration with respect to MBM : the Itô integral --
Stochastic differentials --
The chain rule and Itô's formula --
Stochastic differential equations --
The Langevin equation --
Itô stochastic differential equations --
SDEs of Itô type --
Diffusion processes --
SDEs and PDEs --
The Kolmogorov representation --
The Feynman-Kac representation and terminating Trajectories --
The Pontryagin-Andronov-Vitt equation for the MFPT --
The exit distribution --
The PDF of the FPT --
The Fokker-Planck equation --
The backward Kolmogorov equation --
The survival probability and the PDF of the FPT --
Euler's scheme and Wiener's measure --
Euler's scheme for Itô SDEs and its convergence --
The pdf of Euler's scheme in R and the FPE --
Euler's scheme in Rd --
The convergence of the pdf in Euler's scheme in Rd --
Unidirectional and net probability Flux --
Brownian dynamics at Boundaries --
Absorbing boundaries --
Unidirectional Flux and the survival probability --
Reflecting and partially reflecting boundaries --
Reflection and partial reflection in one dimension --
Partially reflected diffusion in Rd --
Partial reflection in a half-space : constant diffusion matrix --
State-dependent diffusion and partial oblique reflection --
Curved boundary --
Boundary conditions for the backward equation --
Discussion and annotations --
Brownian simulation of Langevin's --
Diffusion limit of physical Brownian motion --
The Overdamped Langevin equation --
Diffusion approximation to the Fokker-Planck equation --
The Unidirectional current in the Smoluchowski equation --
Trajectories between fixed concentrations --
Trajectories, Fluxes, and boundary concentrations --
Connecting a simulation to the continuum --
The interface between simulation and the continuum --
Brownian dynamics simulations --
Application to channel simulation --
Annotation --
The first passage time to a boundary --
The FPT and escape from a domain --
The PDF of the FPT and the density of the mean time spent at a point --
The exit density and probability Flux density --
Conditioning --
Conditioning on Trajectories that reach A before B --
Application of the FPT to diffusion theory --
Stationary absorption flux in one dimension --
The probability law of the first arrival time --
The first arrival time for steady-state diffusion in R³ --
The next arrival times --
The exponential decay of G(r, t) --
Brownian models of Chemical reactions in microdomains --
A stochastic model of a non-arrhenius reaction --
Calcium dynamics in Dendritic spines --
Dendritic spines and their function --
Modeling dendritic spine dynamics --
Biological simplifications of the model --
A simplified physical model of the spine. A schematic model of spine twitching --
Final model simplifications --
The mathematical model --
Mathematical simplifications --
The Langevin equations --
Reaction-diffusion model of binding and unbinding --
Specification of the Hydrodynamic flow --
Chemical Kinetics of binding and unbinding Reactions --
Simulation of calcium kinetics in dendritic spines --
A Langevin (Brownian) dynamics simulation --
An estimate of a decay rate --
Summary and discussion --
Annotations --
Interfacing at the Stochastic separatrix --
Transition state theory of thermal activation --
The diffusion model of activation --
The FPE and TST --
Reaction rate and the principal eigenvalue --
The rate k abs (D), MFPT (... (D)), an eigenvalue ... (D) --
MFPT for domains of types I and II in Rd --
Recrossing, Stochastic Separatrix, Eigenfunctions --
The Eigenvalue problem --
Can recrossings be neglected? --
Accounting for recrossings and the MFPT --
The transmission coefficient Ktr --
Summary and discussion --
Annotations --
Narrow escape in R² --
Introduction --
The NET problem in Neuroscience --
NET, Eigenvalues, and time-scale separation --
A neumann-Dirichlet boundary value problem --
The Neumann function and an integral equation --
The NET problem in two dimensions --
Brownian motion in Dire straits --
The MFPT to a bottleneck --
Exit from several bottlenecks --
Diffusion and NET on a surface of revolution --
A composite domain with a bottleneck --
The NET from domains with bottlenecks in R² and R³ --
The principal Eigenvalue and bottlenecks --
Connecting head and neck --
The principal Eigenvalue in Dumbbell-Shaped domains --
A Brownian needle in Dire straits --
The diffusion law of a Brownian needle in a planar strip --
The turnaround time ... L-R --
Applications of the NET --
Annotations --
Annotation to the NET problem --
Narrow escape in R³ --
The Neumann function in Regulär domains in R³ --
Elliptic absorbing window --
Second-order asymptotics for a circular window --
Leakage in a conductor of Brownian particles --
Activation through a narrow opening --
The Neumann function --
Narrow escape --
Deep well : a Markov chain model --
The NET in a solid funnel-shaped domain --
Selected applications in molecular biophysics --
Leakage from a cylinder --
Applications of the NET --
Annotations --
Bibliography --
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 186.
Responsibility: Zeev Schuss.


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From the book reviews: "This book uniquely combines an introduction to the mathematical theory of Brownian motion with applications to chemical kinetics, primarily in biology and physiology. ... this Read more...

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