Hydrodynamics, Electrostatics, and Brownian Motion: Some Rigorous, Tight Bounds
Joseph Hubbard
Chemical Science and Technology Laboratory, Biotechnology Division
Tuesday, April 6, 2004 15:00-16:00,
NIST North (820), Room 145
Gaithersburg
Tuesday, April 6, 2004 13:00-14:00,
Room 4550
Boulder
Abstract:
The mathematical structures of hydrodynamics, electrostatics, and Brownian motion, though not identical,
do exhibit strikingly similar features.
Moreover, certain hydrodynamic phenomena, such as sedimentation, electrophoretic migration,
and pressure gradient driven flow through a porous medium, can be shown to have a common physical basis.
Though some of these connections are obvious, others are more subtle, requiring arguments based on symmetry
(spatial isotropy, Galilean invariance, etc.) and statistical regularity.
Following a brief survey of these issues, I will outline a technique that we have used to obtain rigorous bounds
on certain hydrodynamic properties that are notoriously difficult to compute for systems with complex geometries.
These include friction coefficients for bodies with translation-rotation coupling, and the permeability
of porous media having various statistical properties for the solid-void distribution.
In many cases the bounds can become highly accurate, and this implies that algorithms based on Brownian motion with sources and sinks
can provide very good estimates for these hydrodynamic quantities.
I'll discuss the reasons for this fortuitous behavior from a variational point of view.
I'll also describe the stochastic algorithms that have been developed, as well as provide a few numerical examples.
Speaker Bio:
Dr. Hubbard received his PhD in Physical Chemistry from Rice University in 1969 followed by a Postdoctoral Fellowship at
Yale University from 1971-1972.
He accepted a position as Associate Fellow at the University of Miami Center for Theoretical Studies in Coral Gables, Florida,
from 1972-1977.
He subsequently held positions as Research Associate at Harvard University and as Staff Analyst at the Institute for Defense Analyses
in Washington, DC.
Dr. Hubbard joined NIST in 1980 as a Staff Research Scientist and currently holds a guest researcher position in
the Chemical Science and Technology Laboratory.
His research interests include molecular dynamics simulations of interfacial properties of immiscible binary fluids,
development of statistical methods for fluctuation (noise)-based infrared spectroscopy of protein solutions and other biophysical systems,
and statistical characterization of rough metallic surfaces under various conditions of plastic strain.
Contact: F. HuntNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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