/LC.GIF&client=easterncarolinaedu)
Brownian dynamics at boundaries and interfaces in physics, chemistry, and biology / Zeev Schuss.
| Author/creator | Schuss, Zeev, 1937- |
| Format | Electronic |
| Publication Info | New York : Springer, [2013] |
| Description | xx, 322 pages : illustrations (some color) ; 24 cm. |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2013 English International |
| Supplemental Content | Full text available from Springer Books |
| Subjects |
| Series | Applied mathematical sciences, 0066-5452 ; Volume 186 Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 186. |
| 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 -- |
| Contents | 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 -- 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 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 -- Index. |
| Bibliography note | Includes bibliographical references (pages 285-306) and index. |
| Access restriction | Available only to authorized users. |
| Other forms | Also issued online. |
| Technical details | Mode of access: World Wide Web |
| Issued in other form | 9781461476870 |
| Genre/form | Electronic books. |
| LCCN | 2013944682 |
| ISBN | 9781461476863 (acid-free paper) |
| ISBN | 1461476860 (acid-free paper) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |