Name: Prof. Michael Mascagni
Address: Department of Computer Science and
School of Computational Science
Florida State University
Tallahassee, FL 323064530 USA
Offices: 498 Dirac Science Library/172 Love Building
Phone: +1.850.644.3290
FAX: +1.850.644.0098
email: mascagni@fsu.edu
Title:
New Monte Carlo Methods for Problems in Materials and Biology
Abstract:
Probabilistic potential theory enables us to solve a large class of parabolic and elliptic
partial differential equations using diffusion techniques. Here, we
present new first and lastpassage Monte Carlo algorithms and show their
utility in problems coming from materials science and biology. These
techniques exploit the fact that the firstpassage probability function is
the Green's function for the Dirchlet problem of the Laplace equation. Firstpassage algorithms
allow the rapid simulation of diffusion using analytic or simulationbased
Green's functions in rather less complicated basic geometries. This
permits consideration of more complicated real geometries made up as
combinations of the simple geometries where Green's functions are
available. This new method is the extension of the well known "Walk on Spheres"
method. Harnessing these firstpassage algorithms, we have developed
the fastest algorithms known to compute:
The fluid permeability in
overlapping, nonoverlapping, and polydispersed spherical models of
random porous media
The SolcStockmayer model with zero
potential, a model of ligand binding

The mean trapping rate of a diffusing
particle in a domain of nonoverlapping spherical traps

The effective conductivity for
perfectly insulating, nonoverlapping spherical inclusions in a matrix of
conductivity
In certain problems,
such as that of computing the electrostatic charge distribution on a conductor,
using the lastpassage distribution is useful. Using these analogous lastpassage algorithms, we have solved
the test problem of computing the charge distribution on a circular
twodimensional disk in three dimensions.
Our plans for the future involve adding more surface Green's functions to our
present set of known Green's functions, and the application of these techniques
to more realistic problems in materials and biology.
This is joint work with Dr.
ChiOk Hwang of Florida State University, and Dr. James Given of Angle, Inc.
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