Simple Brownian diffusion : an introduction to the standard theoretical models / Daniel T. Gillespie & Effrosyni Seitaridou.

Format:

Book

Author/Creator:

Gillespie, Daniel Thomas.

Contributor:

Seitaridou, Effrosyni.

Language:

English

Subjects (All):

Brownian motion processes.

Diffusion processes.

Physical Description:

1 online resource (288 p.)

Edition:

1st ed.

Place of Publication:

New York : Oxford University Press, 2013.

Language Note:

English

Summary:

Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.

Contents:

Cover; Contents; 1 The Fickian theory of diffusion; 1.1 Fick's Law and the diffusion equation; 1.2 Some one-dimensional examples; 1.3 The road ahead; Note to Chapter 1; 2 A review of random variable theory; 2.1 Probability; 2.2 Definition of a random variable; 2.3 Some commonly encountered random variables; 2.4 Multivariate random variables; 2.5 Functional transformations of random variables: the RVT theorem; 2.6 Some useful consequences of the RVT theorem; 2.7 The bivariate normal random variable; 2.8 Generating numerical samples of random variables; 2.9 Integer-valued random variables

Notes to Chapter 23 Einstein's theory of diffusion; 3.1 Einstein's derivation of the diffusion equation; 3.2 A critique of Einstein's derivation; 3.3 Einstein's new perspective; 3.4 The covariance and correlation; 3.5 The relative diffusion coefficient; 3.6 The probability flux: boundary conditions; 3.7 The stochastic bimolecular chemical reaction rate: Part I; Notes to Chapter 3; 4 Implications and limitations of the Einstein theory of diffusion; 4.1 Numerical simulation strategies; 4.2 A serious problem; 4.3 Proof of Eqs (4.12) and (4.13) in two dimensions

4.4 Implications of Eqs (4.12) and (4.13)4.5 A hint of a quantitative lower bound on Δt in Eqs; 4.6 The small-scale motion of a solute molecule; 4.7 Collision probability of a solute molecule with a surface; 4.8 The stochastic bimolecular chemical reaction rate: Part II; Notes to Chapter 4; Appendix 4A: Proof of the reflecting boundary point simulation procedure; Appendix 4B: Proof of the absorbing boundary point simulation procedure; Appendix 4C: The Maxwell-Boltzmann distribution; 5 The discrete-stochastic approach; 5.1 Specification of the system; 5.2 The key dynamical hypothesis

5.3 Connection to the classical Fickian model5.4 Connection to the Einstein model; 5.5 Constraints on l and δt; 5.6 A more accurate formula for K[sub(l)]; 5.7 The discrete-stochastic model's version of Fick's Law; 5.8 Does the concentration gradient "cause" diffusion?; 5.9 A microfluidics diffusion experiment; Notes to Chapter 5; 6 Master equations and simulation algorithms for the discrete-stochastic approach; 6.1 The single-molecule diffusion master equation; 6.2 Relation to the Einstein model of diffusion; 6.3 Solutions to the single-molecule master equation

6.4 Simulating the discrete-stochastic motion of a single solute molecule6.5 Some examples of single-molecule simulations; 6.6 The many-molecule diffusion master equation; 6.7 The case M = 2: an exact solution of a different kind; 6.8 The moments of the cell populations: recovering the diffusion equation; 6.9 Simulating the discrete-stochastic motion of an ensemble of solute molecules; 6.10 Some examples of many-molecule simulations; 6.11 A simulation study of Fick's Law; Appendix 6A: General solution to the single-molecule master equation

Appendix 6B: Confidence intervals in Monte Carlo averaging

Notes:

Includes index.

Description based on online resource; title from PDF title page (viewed on Oct. 31, 2012).

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-164153-7

0-19-164152-9

0-19-174851-X

OCLC:

922971428