In this work, we consider a convexity splitting scheme for a coupled phase field and energy equation, a modification of Stefan problem. The Stefan problem is a free boundary value problem that models the temperature in a homogeneous multiphase medium. Each phase is modeled using a heat diffusion parabolic partial...
Smart weapons promise to provide leap ahead capability with regard to accuracy and engagement range for medium and large caliber projectiles. One of the most critical components of a smart weapon system is its sensor suite that provides position, orientation, and velocity information as the projectile flies down range so...
In this dissertation, we introduce a family of fully discrete finite difference time-domain (FDTD) methods for Maxwell’s equations in linear and nonlinear materials. Onecategory of methods is constructed using multiscale techniques involving operator splittings. We present the sequential splitting scheme, the Strang Marchuk splitting scheme,the weighted sequential splitting scheme including...
Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
Many geophysical phenomena exhibit complicated dynamics that, due to a variety of factors, diverge quickly from physical models. The arrival of new observations allows researchers to combine the model estimate with measurements in a statistical process called data assimilation to produce a revised estimate of the phenomenon. This assimilation of...
Maintaining the sustainability of the earth’s ecosystems has attracted much attention as these ecosystems are facing more and more pressure from human activities. Machine learning can play an important role in promoting sustainability as a large amount of data is being collected from ecosystems. There are at least three important...
In this thesis we study a numerical analysis problem motivated by the need to simulate an event such as an oil spill in a deep water environment. Numerical simulation can help to mitigate the disastrous effects of such events by aiding the management of risk assessment and recovery efforts.
However,...
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately...
A numerical model for the simulation of fully-coupled fluid-structure
interaction is developed in this study. In modeling the fluid, the Reynolds
Averaged Navier-Stokes equations are solved for an incompressible viscous
fluid field and a k-ε model is employed for turbulence computations.
Hydrodynamic forces obtained by the integration of the fluid...
Protecting end-users privacy and building trust are the two most important factors needed to support the growth of ecommerce. The increased dependence on the Internet for a wide variety of daily transactions causes a corresponding loss in privacy for many users, as virtually all websites collect data from users directly...