Meshless methods provide an ideal framework for scalably simulating Lagrangian hydrodynamics in domains undergoing large deformation. For these schemes, interfaces can easily be treated without …
The problem of detecting changes in images taken by a stationary camera has been well studied and many algorithms now exist which perform robustly in …
This thesis is a mathematical and statistical study of conditional modeling and conditional inference. Two applications are covered: (1) Stock Prices and the Statistics of …
Representation and comparison of shapes is a central problem in computer vision. In this dissertation, we continue investigation of a relatively recent approach, based on …
A space filling curve (or mapping) is a parametric map from a one-dimensional unit interval to a n-dimensional hypercube that traverses every point in its …
This thesis takes aim at two directions. The first direction involves setting the foundations for a new type of data-driven scientific computing, essentially creating a …
This thesis discusses two topics, both related to the goal of determining tumor blood flow parameters from time-sequenced contrast-enhanced medical imaging data in an effort …
This thesis is concerned with the applicationof a certain class of eigenvalue algorithmsto random matrix initial data. In particularwe study numerically the time to first …
This dissertation focuses on studies of two different discontinuous Galerkin (DG) methods for general convection-diffusion equations. One preserves the strict maximum principle for general nonlinear …
Dissipative Particle Dynamics (DPD) is a Lagrangian type mesoscopic method widely applied in mesoscale hydrodynamics and complex fluids simulations. DPD can be understood as coarse-grained …
Dissipative Particle Dynamics (DPD) is a mesoscopic simulation method, potentially very effective in simulating mesoscale hydrodynamics and soft matter. This thesis addresses open theoretical and …
Micron-size paramagnetic particles suspended in viscous fluid will aggregate to form linear chains when subject to a uniform magnetic field. This process provides a way …
This thesis studies the application of the Wiener chaos expansion in the analysis of stochastic partial differential equations (SPDEs). Specifically, linear parabolic SPDEs and the …
Queuing systems are one of the most prominent technological evolution in today's digital world. Data centers and cloud networks operated by large companies like Microsoft, …
A Monte-Carlo Simulation is presented for Radiation Transport in water. This process is of outmost importance, having applications in oncology and therapy of cancer, in …
Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
This dissertation aims to study finite element methods for two-dimensional stationary second order interface model problems on homogeneous and heterogeneous media, under discretizations non-fitted with …
In this dissertation, we mainly discuss two topics of partial differential equations in fluid dynamics and kinetic theory: viscous surface wave and diffusive limit. With …