Re: Brownian motion.
From: Andy Resnick (axr67_at_op.cwru.edu)
Date: 12/01/04
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Date: Wed, 01 Dec 2004 11:04:39 -0500
LEJ Brouwer wrote:
>Suppose at time T=0 we have a very large number N of tiny hard
>spherical particles enclosed in a small sphere of radius epsilon, each
>with the same kinetic energy and travelling in random directions. If
>we set them free and allow them to take part in elastic collisions,
>they will presumably diffuse outwards with the distribution of the
>particles being spherical Gaussian with spread ~sqrt(T) at time T.
>
>Can anyone point me towards a simple derivation of this?
>
Your question, as stated, is too general. If you are simply asking how
a (initally packed) cloud of hard spheres at some initial temperature T
evolves over time, simply look at the thermodynamics of ideal gases.
The gas will freely expand and cool. Pretty much any thermodynamics and
statistical mechanics textbook will cover free expansion.
If, as another example, you are interested in the dynamics of an
initially packed cloud of hard spheres immersed in a fluid, that is
considerably more difficult- start by reading:
Mazur, P., Physica 110A, 128 (1982)
The origin of the difficulty is the hydrodynamic interactions between
the particles as they move.
-- Andrew Resnick, Ph.D. Department of Physiology and Biophysics CWRU School of Medicine tanspose 'op' for mail
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