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Numerical Modeling Of Capillary-Driven Flow In Open Microchannels: An Implication Of Optimized Wicking Fabric Design, Mehrad Gholizadeh Ansari

Masters Theses

"The use of microfluidics to transfer fluids without applying any exterior energy source is a promising technology in different fields of science and engineering due to their compactness, simplicity and cost-effective design. In geotechnical engineering, to increase the soil's strength, hydrophilic wicking fibers as type of microfluidics have been employed to transport and drain water out of soil spontaneously by taking advantage of natural capillary force without using any pumps or other auxiliary devices. The objective of this study is to understand the scientific mechanisms of the capability for wicking fiber to drain both gravity and capillary water out of …

On Modeling Quantities For Insurer Solvency Against Catastrophe Under Some Markovian Assumptions, Daniel Jefferson Geiger

Doctoral Dissertations

"Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop …

Incremental Proper Orthogonal Decomposition For Pde Simulation Data: Algorithms And Analysis, Hiba Fareed

Doctoral Dissertations

"We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. We introduce an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD). The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. We also modify the algorithm to initialize and incrementally update both the SVDand an error bound during the …

Cox-Type Model Validation With Recurrent Event Data, Muna Mohamed Hammuda

Doctoral Dissertations

"Recurrent event data occurs in many disciplines such as actuarial science, biomedical studies, sociology, and environment to name a few. It is therefore important to develop models that describe the dynamic evolution of the event occurrences. One major problem of interest to researchers with these types of data is models for the distribution function of the time between events occurrences, especially in the presence of covariates that play a major role in having a better understanding of time to events.

This work pertains to statistical inference of the regression parameter and the baseline hazard function in a Cox-type model for …

Hdg Methods For Dirichlet Boundary Control Of Pdes, Yangwen Zhang

Doctoral Dissertations

"We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems for PDEs. These problems can involve atypical variational formulations, and often have solutions with low regularity on polyhedral domains. These issues can provide challenges for numerical methods and the associated numerical analysis. In this thesis, we use an existing HDG method for a Dirichlet boundary control problem for the Poisson equation, and obtain optimal a priori error estimates for the control in the high regularity case. We also propose a new HDG method to approximate the solution of a Dirichlet boundary …