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 …
The derivation of fluid equations from the Boltzmann equation is a fundamental problem in kinetic theory. In this paper, we investigate several results concerning the …
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 …
This thesis contains two parts, including the development of a modified total variation bounded (TVB) limiter applied to the discontinuous Galerkin (DG) methods, and the …
This thesis consists of two topics on discontinuous Galerkin (DG) finite element methods for time-dependent problems. In the first part of the thesis, we analyze …
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 …
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections to a wide range of scientific disciplines including optimal control, differential games, imaging sciences, and machine …
In this work, we develop and analyze solvers and preconditioners designed for the implicit time integration of discontinuous Galerkin (DG) discretizations. The discontinuous Galerkin method …
In this thesis, we study the elliptic boundary value problems on irregular domains. We first obtain the $W^{2,p}$ and $C^2$ regularity theories for second-order, non-divergence …
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, …
This paper measures both the correlation and causal relationship between startups and urban economic growth in the U.S. over the past thirty years. Correlation results …
In this thesis, we explore the behavior of interacting particle systems. The first part of the thesis investigates the long-time behavior of sparsely interacting particles …
Stochastic networks arise in a variety of real world applications including telecommunications, service systems such as call centers, computer networks, health care services and biological …
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 …