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Brownian MotionFluctuations, Dynamics, and Applications$
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Robert M. Mazo

Print publication date: 2008

Print ISBN-13: 9780199556441

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199556441.001.0001

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Brownian Motion

Robert M. Mazo

Oxford University Press

This chapter begins the study of the physical study of Brownian motion. The theory of Smoluchowski is based on a kinetic model of colliding spheres, at first for an ambient dilute gaseous medium. This result is then generalized, approximately to a dense ambient medium. It is indicated how fluctuations may give an appreciable effect when the effect of an individual collision is negligible. Essentially the same result is obtained by Einstein's theory, using probabilistic, instead of kinetic reasoning. The relation of the friction constant to the diffusion coefficient is obtained. The Langevin equation, expressing the foregoing ideas in dynamical terms is discussed.

Keywords:   Einstein, Smoluchowski, Langevin equation, Stokes–Einstein, rotation, fluctuation, viscosity, root-mean-square displacement, random force, friction

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