This thesis describes the Immersed Interface Method (IIM) for interface problems, in which the partial differential equations have discontinuities and singularities in the coefficients and the solutions. A typical example ...
The goal of my thesis is to provide a theoretical demonstration of how dimension reduc- tion, control and machine learning techniques can be applied to optimize the performance of complex nonlinear systems. Specifically, ...
Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley ...
There is a broad need in the neuroscience, neurological and biomedical engineering communities to better classify, quantify and diagnose Focal Axonal Swellings (FAS) and their impact on cognitive deficits and/or neural ...
In this dissertation, mathematical models for two biophysically related topics are investigated: facilitated diffusion and the Brownian ratchet. Both phenomena exhibit counterintuitive behavior: in the case of facilitated ...
This work studies the problem of model-based hand posture estimation via monocular camera. Generally, a model-based posture estimation method manipulates a 3D hand model whose posture is determined by a set of parameters. ...
Poroelasticity theory models the mechanics of porous, fluid-saturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ...
Poroelasticity theory models the mechanics of porous,
uid-saturated, deformable solids. It
was originally developed by Maurice Biot to model geophysical problems, such as seismic
waves in oil reservoirs, but has also ...
In this dissertation, I address mathematical problems arising from the field of theo- retical neuroscience that share a common theme: temporally driven neural networks treated as perturbed, coupled nonlinear dynamical ...
We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advection-diffusion and reaction-diffusion ...
We analyze the stability of solutions to Euler's equations in the presence of surface tension. First we compute stationary solutions to periodic Euler's equations in a travelling frame of reference and then we analyze their ...
A widely-accepted technique for the analysis of rigid mechanical systems with unilateral contact and Coulomb friction is to formulate the contact forces (or impulses) as the unknowns of a linear complementarily problem ...
This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing ...
The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the ...
In many areas of research, robust and efficient data-mining, and data-driven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered ...
The reconfigurable holographic metamaterial antenna is an attractive new technology for satellite communications, particularly in mobile applications. This antenna is thin, light-weight, consumes little power to operate, ...
Subtropical stratocumulus clouds are important part of the Earth's energy budget. The response of low clouds to Earth's changing climate is one of the dominant uncertainties in global warming projections, due primarily ...
Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundary-value problems associated with Euler's equations. My approach is motivated ...
Mathematical models for waves on shallow water surfaces has been of interest to researchers dating back to the 1800's. These models are governed by partial differential equations, and many of them have rich mathematical ...
With water in short supply and utility deregulation imminent, the problem of long-term scheduling on a hydroelectric power system has become increasingly important.Many of the algorithms developed for this large-scale ...