Compact modeling of semiconductor devices
Collaborators: Henok Abebe, Ellis Cumberbatch, Uno Shigeyasu
Solitary elastic waves in a heterogeneous medium Randy
LeVeque and I investigated how elastic waves in a
heterogeneous medium support solitary wave behavior.
Multiple-scale homogenization for the initial-boundary value
problem for hyperbolic conservation systems with rapid spatial
fluctuations
When hyperbolic conservation laws involve large, rapidly
fluctuating quantities, the natural solution technique is
multiple-scale homogenization. Although the initial-value
problem has been well-studied, a general theory for
initial-boundary value problems using the method of
multiple-scales is missing. This work is under the supervision
of Jirair
Kevorkian.
Here is a copy of my thesis.
Nutational movement of plant cotyledons Please see this awesome video. Worked with Mele Sato and James Moore, summer of 2004 and 2005, respectively.
Dynamics of modelocking optical fiber lasers
One way to generate stable solitons along an optical fiber is by
taking advantage of the nonlinearity of its polarization
rotation. In our model, a train of solitons is trapped in a
optical fiber ring with a polarization control. Our goal is to
understand the dynamics of this optical system, governed by a
coupled pair of nonlinear Schrodinger equations. Arnold Kim and
I are working with Kristin Spaulding, Nathan Kutz and
David Muraki.