`Name: Prof. Michael Mascagni
Address: Department of Computer Science `*and*
School of Computational Science
Florida State University
Tallahassee, FL 32306-4530 * USA
*Offices: 498 Dirac Science Library/172 Love Building
Phone: +1.850.644.3290
FAX: +1.732.601.4470
e-mail: mascagni@fsu.edu

**Title:
First- and Last-Passage Random Walk Algorithms**

**Abstract:**

### We present two complimentary Monte Carlo methods for
computing the charge density on a
conductor when that conductor is at potential V_{0 }with respect to
infinity. The first method extends our previous first-passage algorithm for
calculating the capacitance of an arbitrarily shaped conducting object.
The capacitance of an object can be probabilistically calculated finding the
probability that a Brownian walker starting at infinity hits the region before
returning to infinity. It is a standard result from probabilistic
potential theory that the absorption locations of the first-passage capacitance calculation give
the charge distribution on the conducting object. The second Monte Carlo method utilizes the last-passage
concept. This last-passage method stems from the consideration of the
isomorphism between the electrostatic potential and the probability of going to
infinity without touching a conducting object at a certain distance from the
conductor. This is analogous to "adjoint" methods, where time-reversed
walks are used to solve the adjoint problem. We demonstrate our methods
for computing an analytically known charge
density on a two dimensional thin disk in three dimensions. In addition we
solve for the charge distribution on the unit
cube using an edge distribution concept. Computing the capacitance of the
unit cube is considered the most important open problem in electrostatics, and
we not only have the most accurate calculation, but the edge distribution
computation provides results never before computed.

### This is joint work with Dr.
Chi-Ok Hwang of Inha University and Dr. James Given of the Naval Research Lab.

Home | Educational
Background | Research
Experience | Curriculum
Vitae | Research
Interests | Research
Projects | Recent
Papers | Courses |
Abstracts of Talk