Computational
and Applied Mathematics Seminar
Fall
2008
September
15
Howard
Levine
Classical properties of solutions of some elliptic boundary value
problems
October
6
Krishna
Athreya
Probabilistic
model for population growth and migration.
October
13
Xinwei
Wang
Shock
Waves in Laser-material Interaction: Atomistic to Macroscale Study
ABSTRACT: The dynamics evolution of shock waves in laser-material
interaction involves a wide spectrum of physical processes, including
phase explosion, abrupt structural change, deceleration, attenuation
and thermalization of molten nanoparticles, as well as diffusion,
recombination and formation of the shock waves. Although a substantial
amount of research on laser ablation has been conducted, the underlying
effects and the mechanism of laser induced plume expansion in an
ambient environment still remains relatively unclear. This talk will
present our very recent work on shock waves in laser-material
interaction, which pioneers the study of shock wave in the presence of
phase explosion using large-scale molecular dynamics simulation. The
position of shock wave front has been defined and studied over
nanoseconds. Extensive research is elaborated upon to study the inside
structural evolution of the shock wave and the effect of optical
absorption depth, ambient gas pressure, laser fluence, and backward
plume motion. The physics behind plume splitting and secondary shock
wave will be discussed based on the detaild atomistic structural
evolution in our study. Furthermore, the shock waves formed in
laser-assisted surface nanostructuring will be presented to show the
unique phenomena in nanoscale surface modification.
October
20
Karin
Dorman
Title: Disentangling the selection
pressures acting on overlapping
reading frames
Authors: K. S. Dorman, W. Chen
Abstract: We describe a strategy for modeling the evolution
of overlapping reading frames, where gene products are coded in
different phases by the same genetic sequence. Continuous time Markov
models of evolution do not extend easily to overlapping reading frames
because codon overlap abrogates the usual assumption of iid sites
(nucleotides,
amino acids, or codons). We focus on relatively conserved
sequences and identify mutating codon blocks. Assuming these codon
blocks are independent, we can test the hypothesis that both
reading frames are under the same selection pressure. When applied to
sequence data from the Equine Infectious Anemia Virus, we find a
surprising abundance of changes nonsynonymous in both reading frames.
This observation contrasts with conclusions based on an
analysis of the same region in the related Human Immunodeficiency
Virus, where changes nonsynonymous in both reading frames are
disfavored. While both viruses seem to tolerate fewer amino
acid changes in the Rev protein overall, differences in the specific
balance of mutations could reflect distinct strategies of these viruses
to adapt to the immune response in their respective hosts.
November
7
Tuncay
Aktosun (University of Texas at Arlington)
Exact Solutions to the Nonlinear Schrodinger Equation
ABSTRACT:
A method is presented to onstruct exact solutions to the nonlinear
Schrodinger equation on the line. An explicit formula and its
equivalents are obtained to express such exact solutions in a compact
form in terms of matrix exponentials. Such exact solutions can
alternatively be written explicitly as algebraic combinations of
exponential, trigonometric, and polynomial functions of the spatial and
temporal coordinates. The method is generalizable to some other
nonlinear partial differential equations such as the Korteweg-de Vries
equation on the half line and the sine-Gordon equation.
November
17
Jue
Yan
The
Direct Discontinuous Galerkin (DDG) Methods for Diffusion
with
interface correction
