Simple Brownian Diffusion

An Introduction to the Standard Theoretical Models

Nonfiction, Science & Nature, Science, Chemistry, Physical & Theoretical, Physics, Mathematical Physics
Cover of the book Simple Brownian Diffusion by Daniel Thomas Gillespie, Effrosyni Seitaridou, OUP Oxford
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Author: Daniel Thomas Gillespie, Effrosyni Seitaridou ISBN: 9780191641534
Publisher: OUP Oxford Publication: October 18, 2012
Imprint: OUP Oxford Language: English
Author: Daniel Thomas Gillespie, Effrosyni Seitaridou
ISBN: 9780191641534
Publisher: OUP Oxford
Publication: October 18, 2012
Imprint: OUP Oxford
Language: English

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

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Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

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