Brownian dynamics at boundaries and interfaces [electronic resource] : in physics, chemistry, and biology / Zeev Schuss.

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Bibliographic Details
Main Author: Schuss, Zeev, 1937- (Author)
Language:English
Published: New York : Springer, [2013]
Series:Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 186.
Subjects:
Brownian motion processes > Computer simulation.
Boundary value problems > Computer simulation.
Stochastic differential equations > Computer simulation.
Online Access:
Springer English/International eBooks 2013 - Full Set: 2013 (Springer Link)
Variant Title:
Brownian Dynamics at Boundaries and Interfaces: In Physics, Chemistry, and Biology
Format: Electronic eBook

MARC

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100 1 |a Schuss, Zeev,  |d 1937-,  |e author. 
245 1 0 |a Brownian dynamics at boundaries and interfaces  |h [electronic resource] :  |b in physics, chemistry, and biology /  |c Zeev Schuss. 
246 2 |a Brownian Dynamics at Boundaries and Interfaces: In Physics, Chemistry, and Biology 
264 1 |a New York :  |b Springer,  |c [2013] 
264 4 |c ©2013 
490 1 |a Applied mathematical sciences,  |x 0066-5452 ;  |v Volume 186 
504 |a Includes bibliographical references (pages 285-306) and index. 
505 0 0 |t Mathematical Brownian motion --  |t Definition of Mathematical Brownian motion --  |t Mathematical Brownian motion in Rd --  |t Construction of Mathematical Brownian motions --  |t Analytical and statistical properties of Brownian paths --  |t Integration with respect to MBM : the Itô integral --  |t Stochastic differentials --  |t The chain rule and Itô's formula --  |t Stochastic differential equations --  |t The Langevin equation --  |t Itô stochastic differential equations --  |t SDEs of Itô type --  |t Diffusion processes --  |t SDEs and PDEs --  |t The Kolmogorov representation --  |t The Feynman-Kac representation and terminating Trajectories --  |t The Pontryagin-Andronov-Vitt equation for the MFPT --  |t The exit distribution --  |t The PDF of the FPT --  |t The Fokker-Planck equation --  |t The backward Kolmogorov equation --  |t The survival probability and the PDF of the FPT --  |t Euler's scheme and Wiener's measure --  |t Euler's scheme for Itô SDEs and its convergence --  |t The pdf of Euler's scheme in R and the FPE --  |t Euler's scheme in Rd --  |t The convergence of the pdf in Euler's scheme in Rd --  |t Unidirectional and net probability Flux --  |t Brownian dynamics at Boundaries --  |t Absorbing boundaries --  |t Unidirectional Flux and the survival probability --  |t Reflecting and partially reflecting boundaries --  |t Reflection and partial reflection in one dimension --  |t Partially reflected diffusion in Rd --  |t Partial reflection in a half-space : constant diffusion matrix --  |t State-dependent diffusion and partial oblique reflection --  |t Curved boundary --  |t Boundary conditions for the backward equation --  |t Discussion and annotations --  |t Brownian simulation of Langevin's --  |t Diffusion limit of physical Brownian motion --  |t The Overdamped Langevin equation --  |t Diffusion approximation to the Fokker-Planck equation --  |t The Unidirectional current in the Smoluchowski equation --  |t Trajectories between fixed concentrations --  |t Trajectories, Fluxes, and boundary concentrations --  |t Connecting a simulation to the continuum --  |t The interface between simulation and the continuum --  |t Brownian dynamics simulations --  |t Application to channel simulation --  |t Annotation --  |t The first passage time to a boundary --  |t The FPT and escape from a domain --  |t The PDF of the FPT and the density of the mean time spent at a point --  |t The exit density and probability Flux density --  |t Conditioning --  |t Conditioning on Trajectories that reach A before B --  |t Application of the FPT to diffusion theory --  |t Stationary absorption flux in one dimension --  |t The probability law of the first arrival time --  |t The first arrival time for steady-state diffusion in R³ --  |t The next arrival times --  |t The exponential decay of G(r, t) --  |t Brownian models of Chemical reactions in microdomains --  |t A stochastic model of a non-arrhenius reaction --  |t Calcium dynamics in Dendritic spines --  |t Dendritic spines and their function --  |t Modeling dendritic spine dynamics --  |t Biological simplifications of the model --  |t A simplified physical model of the spine -- 
505 0 0 |t A schematic model of spine twitching --  |t Final model simplifications --  |t The mathematical model --  |t Mathematical simplifications --  |t The Langevin equations --  |t Reaction-diffusion model of binding and unbinding --  |t Specification of the Hydrodynamic flow --  |t Chemical Kinetics of binding and unbinding Reactions --  |t Simulation of calcium kinetics in dendritic spines --  |t A Langevin (Brownian) dynamics simulation --  |t An estimate of a decay rate --  |t Summary and discussion --  |t Annotations --  |t Interfacing at the Stochastic separatrix --  |t Transition state theory of thermal activation --  |t The diffusion model of activation --  |t The FPE and TST --  |t Reaction rate and the principal eigenvalue --  |t MFPT --  |t The rate k abs (D), MFPT (...(D)), an eigenvalue ... (D) --  |t MFPT for domains of types I and II in Rd --  |t Recrossing, Stochastic Separatrix, Eigenfunctions --  |t The Eigenvalue problem --  |t Can recrossings be neglected? --  |t Accounting for recrossings and the MFPT --  |t The transmission coefficient Ktr --  |t Summary and discussion --  |t Annotations --  |t Narrow escape in R² --  |t Introduction --  |t The NET problem in Neuroscience --  |t NET, Eigenvalues, and time-scale separation --  |t A neumann-Dirichlet boundary value problem --  |t The Neumann function and an integral equation --  |t The NET problem in two dimensions --  |t Brownian motion in Dire straits --  |t The MFPT to a bottleneck --  |t Exit from several bottlenecks --  |t Diffusion and NET on a surface of revolution --  |t A composite domain with a bottleneck --  |t The NET from domains with bottlenecks in R² and R³ --  |t The principal Eigenvalue and bottlenecks --  |t Connecting head and neck --  |t The principal Eigenvalue in Dumbbell-Shaped domains --  |t A Brownian needle in Dire straits --  |t The diffusion law of a Brownian needle in a planar strip --  |t The turnaround time ...L-R --  |t Applications of the NET --  |t Annotations --  |t Annotation to the NET problem --  |t Narrow escape in R³ --  |t The Neumann function in Regulär domains in R³ --  |t Elliptic absorbing window --  |t Second-order asymptotics for a circular window --  |t Leakage in a conductor of Brownian particles --  |t Activation through a narrow opening --  |t The Neumann function --  |t Narrow escape --  |t Deep well : a Markov chain model --  |t The NET in a solid funnel-shaped domain --  |t Selected applications in molecular biophysics --  |t Leakage from a cylinder --  |t Applications of the NET --  |t Annotations --  |g Bibliography --  |g Index. 
650 0 |a Brownian motion processes  |x Computer simulation. 
650 0 |a Boundary value problems  |x Computer simulation. 
650 0 |a Stochastic differential equations  |x Computer simulation. 
773 0 |t Springer English/International eBooks 2013 - Full Set   |d Springer Nature 
776 0 |z 9781461476870 
776 0 |w (GyWOH)har130418244 
776 1 |t Brownian dynamics at boundaries and interfaces  |w (OCoLC)ocn839388739  |w (DLC)2013944682 
830 0 |a Applied mathematical sciences (Springer-Verlag New York Inc.) ;  |v v. 186. 
856 4 0 |y Access Content Online(from Springer English/International eBooks 2013 - Full Set)  |u https://ezproxy.msu.edu/login?url=https://link.springer.com/10.1007/978-1-4614-7687-0  |z Springer English/International eBooks 2013 - Full Set: 2013