Browsing Applied mathematics by Title
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The stability and instabilities of stationary solutions to the nonlinear Schroedinger equation and the sineGordon equation
I present an analysis of the stability spectrum of all stationary elliptictype solutions to the focusing Nonlinear Schroedinger equation and the sineGordon equation. An analytical expression for the spectrum is given. ... 
This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks
At first glance, the neuronal network seems like a tangled web in many areas throughout the nervous system. Often, our best guess is that such “messy” connections are close to random, while obeying certain statistical ... 
Towards PatientSpecific Mathematical Radiation Oncology
(20131114)The war against cancer continues to take its toll on society, even after many decades of focused, intensive research into its origins and cures. Increasingly, efforts are being made to incorporate physical sciences and ... 
Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations
In this thesis, we consider an uncertainty quantification (UQ) problem that arises from tsunami modeling, namely the probabilistic tsunami hazard assessment (PTHA) problem. The goal of PTHA is to compute the probability ... 
Value function approximation methods for Linearlysolvable Markov Decision Process
(20140224)Optimal control provides an appealing machinery to complete complicated control tasks with limited prior knowledge. Both global methods and online trajectory optimization methods are powerful techniques for solving optimal ... 
Variability in Modified Estimators of VaR and ES
Modified ValueatRisk (mVaR) and Modified Expected Shortfall (mES) are risk estimators that can be calculated without modelling the distribution of asset returns. These modifided estimators use skewness and kurtosis ... 
Vortex Dynamics of Geostrophically Adjusted Density Perturbations in TriplyPeriodic Models of Stratified Incompressible Fluids
(20130225)A model exploring contributions to lateral dispersion in the oceanic submesoscale is presented. Wellmixed patches of fluid, produced by turbulent mixing events, are geostrophically adjusted to create compound vortices. ... 
Vortex Dynamics of Geostrophically Adjusted Density Perturbations in TriplyPeriodic Models of Stratified Incompressible Fluids
(20120913)A model exploring contributions to lateral dispersion in the oceanic submesoscale is presented. Wellmixed patches of uid, produced by turbulent mixing events, are geostrophically adjusted to create compound vortices. ... 
Wave propagation algorithms for multicomponent compressible flows with applications to volcanic jets
(2005)Numerical algorithms are developed for compressible multicomponent flow problems in the framework of wave propagation finite volume methods based on approximate Riemann solvers. Both models for multifluid flows, which ...