Browsing Applied mathematics by Title
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Energy and Charge Transfer in Open Plasmonic Systems
Coherent and collective charge oscillations in metal nanoparticles (MNPs), known as localized surface plasmons, offer unprecedented control and enhancement of optical processes on the nanoscale. Since their discovery in ... 
ETGETL Portfolio Optimization
(20130225)Modern Portfolio Theory dates back to 1950s, when Markowitz proposed meanvariance portfolio optimization to construct portfolios. It provided a systematic approach to determine portfolio allocation when one is facing ... 
Exploiting Low Dimensionality in Nonlinear Optics and Other Physical Systems
(20120913)Dimensionality reduction techniques have long been used in a number of fields including nonlinear optics and fluid dynamics. Regardless of the specific technique, the underlying idea is to generate a reduced order model ... 
Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges
(20110711)Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these ... 
Finite volume methods for Tsunamis genereated by submarine landslides
(20140430)Submarine landslides can generate tsunamis, and the generated waves can be catastrophic when a large volume of landslide material is involved. Moreover, large earthquakes are often accompanied by submarine landslides that ... 
Geographic Range Shifts under Climate Warming
(20130725)Rapid climate warming has caused species across the globe to shift their geographic ranges, and ecologists are increasingly concerned about whether species are able to track climate warming. Early efforts to predict species ... 
Green's Law and the Riemann Problem in Layered Media
The propagation of long waves onto a continental shelf is of great interest in tsunami modeling, where understanding the amplification of waves during shoaling is of significant importance. When the linearized shallow water ... 
High order shock capturing methods with compact stencils for use with adaptive mesh refinement and mapped grids
This thesis focuses on several developments toward creating a high order shock capturing method that can be used on mapped grids with blockstructured adaptive mesh refinement (AMR). The discontinuous Galerkin (DG) method ... 
The immersed interface method: a numerical approach for partial differential equations with interfaces
(1994)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 ... 
Integrating DataDriven Methods in Nonlinear Dynamical Systems: Control, Sparsity and Machine Learning
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, ... 
Interface Problems using the Fokas Method
Interface problems for partial differential equations are initial boundary value problems for which the solution of an equation in one domain prescribes boundary conditions for the equations in adjacent domains. These ... 
Irreversibility in Stochastic Dynamic Models and Efficient Bayesian Inference
This thesis is the summary of an excursion around the topic of reversibility. We start the journal from a classical mechanical view of the “time reversal symmetry”: we look into the details to track the movements of all ... 
Kspectral Sets and Functions of Nonnormal Matrices
In this thesis, we study Kspectral sets and use them to bound norms of functions of nonnormal matrices. For a fixed constant K > 0, the set Ω is said to be a Kspectral set for a matrix A if the spectrum Λ(A) is contained ... 
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 paracrine PDGFdriven glioma growth and invasion
The most common primary brain tumor in adults, glioma claims thousands of lives each year. Despite efforts to improve survival rates, the standard of care has remain unchanged for more than a decade. Recent research has ... 
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 ...