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QA274.75 .S38 2013
Generalized diffusion processes
1990
Portenko, N. I. (Nikolaĭ Ivanovich)
Math & Statistics Library » QA274.75 .P6713 1990
Option pricing in fractional browni...
2009
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Brownian dynamics at boundaries and...
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Schuss, Zeev, 1937
»
Brownian dynamics at boundaries and...
2013
Schuss, Zeev, 1937
Math & Statistics Library » QA274.75 .S38 2013
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Brownian dynamics at boundaries and interfaces : in physics, chemistry, and biology / Zeev Schuss.
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QA274.75 .S38 2013
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QA274.75 .S38 2013
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Author/Creator:
Schuss, Zeev, 1937
author.
Language:
English.
Publication date:
2013
Imprint:
[New York] : Springer, [2013]
Format:
Book
xx, 322 pages : illustrations (some color) ; 24 cm.
Bibliography:
Includes bibliographical references (pages 285306) and index.
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 FeynmanKac representation and terminating Trajectories
The PontryaginAndronovVitt equation for the MFPT
The exit distribution
The PDF of the FPT
The FokkerPlanck 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 halfspace : constant diffusion matrix
Statedependent 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 FokkerPlanck 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 steadystate 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 nonarrhenius 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
Reactiondiffusion 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
MFPT
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 timescale separation
A neumannDirichlet 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 DumbbellShaped domains
A Brownian needle in Dire straits
The diffusion law of a Brownian needle in a planar strip
The turnaround time ...LR
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
Secondorder 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 funnelshaped domain
Selected applications in molecular biophysics
Leakage from a cylinder
Applications of the NET
Annotations
Bibliography
Index.
Note:
Also issued online.
Available in another form:
9781461476870 (online)
(GyWOH)har130418244
Series:
Applied mathematical sciences, 00665452 ; Volume 186
Applied mathematical sciences (SpringerVerlag New York Inc.) ;
v. 186.
Subjects:
Brownian motion processes.
ISBN:
1461476860
9781461476863
Catkey: 10281928
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