Browsing Applied mathematics by Title
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Lagrangian coherent structures and the dynamics of inertial particles
Dynamics of inertial particles in twodimensional planar flow have been investigated by evaluating finitetime Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The MaxeyRiley ... 
Machine learning and data decompositions for complex networked dynamical systems
Machine learning has become part of our daily lives. Its applications include personalized advertisements, stock price predictions, and selfdriving cars. The goal of this thesis is to study ways to apply machine learning ... 
Mathematical modeling of focal axonal swellings arising in traumatic brain injuries and neurodegenerative diseases
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 ... 
Mathematical Models for Facilitated Diffusion and the Brownian Ratchet
(20110831)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 ... 
ModelBased Hand Posture Estimation Using Monocular Camera
(20130225)This work studies the problem of modelbased hand posture estimation via monocular camera. Generally, a modelbased posture estimation method manipulates a 3D hand model whose posture is determined by a set of parameters. ... 
Multiscale Modeling of Esophageal Adenocarcinoma
Over the past three to four decades, esophageal adenocarcinoma (EAC) incidence has increased dramatically in the Western world due to causes that are not well understood. Current screening strategies for early detection ... 
Numerical Modeling of PoroelasticFluid Systems Using HighResolution Finite Volume Methods
(20130624)Poroelasticity theory models the mechanics of porous, uidsaturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ... 
Numerical Modeling of PoroelasticFluid Systems Using HighResolution Finite Volume Methods
(20130725)Poroelasticity theory models the mechanics of porous, fluidsaturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also ... 
On driven neural assemblies: synchrony, chaos and entropy.
(20140224)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 ... 
On the asymptotic behavior of internal layer solutions of advectiondiffusionreaction equations
(2001)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 advectiondiffusion and reactiondiffusion ... 
On the instability of water waves with surface tension.
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 ... 
Optimizationbased analysis of rigid mechanical systems with unilateral contact and kinetic friction
(2008)A widelyaccepted 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 ... 
Reproducing color images with custom inks
(1998)This dissertation investigates the general problem of reproducing color images on an offset printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing ... 
RiemannHilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions
(20131114)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 ... 
Robust RealTime Image Processing Through Dynamic Mode Decomposition
(20131114)In many areas of research, robust and efficient datamining, and datadriven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered ... 
SelfOptimizing Metamaterial Antennas
The reconfigurable holographic metamaterial antenna is an attractive new technology for satellite communications, particularly in mobile applications. This antenna is thin, lightweight, consumes little power to operate, ... 
Singlecolumn and mixedlayer model analysis of subtropical stratocumulus response mechanisms relevant to climate change
(20131114)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 ... 
Some BoundaryValue Problems for Water Waves
(20120913)Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundaryvalue problems associated with Euler's equations. My approach is motivated ... 
Spectral Methods for Partial Dierential Equations that Model Shallow Water Wave Phenomena
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 ... 
A splitting algorithm for multistage stochastic programming with application to hydropower scheduling
(1997)With water in short supply and utility deregulation imminent, the problem of longterm scheduling on a hydroelectric power system has become increasingly important.Many of the algorithms developed for this largescale ...