I develop a numerical method that combines functional approximations and dynamic programming to solve high-dimensional discrete-time stochastic control problems under general constraints. The method relies on three building blocks: first, a quasi-random grid and the radial basis function method are used to discretize and interpolate the high-dimensional state space; second, to incorporate constraints, the method of Lagrange multipliers is applied to obtain the first order optimality conditions; third, the conditional expectation of the value function is approximated by a second order polynomial basis, estimated using ordinary least squares regressions. To reduce the approximation error, I introduce the test region iterative contraction (TRIC) method to shrink the approximation region around the optimal solution. I apply the method to two Finance applications: a) dynamic portfolio choice with constraints, a continuous control problem; b) dynamic portfolio choice with capital gain taxation, a high-dimensional singular control problem. / text

This thesis investigates the topology and geometry of hyperbolic knot complements that are commensurable with other knot complements. In chapter 3, we provide an infinite family examples of hyperbolic knot complements commensurable with exactly two other knot complements. In chapter 4, we exhibit an obstruction to knot complements admitting exceptional surgeries in conjunction with hidden symmetries. Finally, in chapter 5, we discuss the role of surfaces embedded in 3-orbifolds as it relates to hidden symmetries. / text

New survey technologies are able to provide detailed data on the form and topography of riverbeds. With this increased data resolution, the required computational time rather than data availability has become the limiting factor for river models. Detailed bathymetric data can be used to provide better empirical representation of drag and roughness at fine scales, allowing a priori selection of roughness using known physics rather than a posteriori calibration. However, we do not have sufficient guidance or understanding from the literature to represent known heterogeneities smaller than our practical grid scale. The problem is what to do with known subgrid-scale bathymetric features and roughness when our models must use a coarser computational grid. In this project, we simplify this complex problem to analyzing flow in a simple open channel with a single patch of relatively high roughness against an otherwise uniform background of low roughness. We model this open channel with a two-dimensional, depth-averaged river model. By running multiple simulations using different grid sizes we gain insight into how the relationship between the grid cell size and the patch size affects the appropriate physical selection of roughness parameter. As the primary focus, the present work proposes and investigates several methods for upscaling known fine-scale drag coefficient data to a coarser grid resolution for a model. For the tested conditions, it appears that a simple area-weighted linear average is simple to apply and creates a flow field very similar to the best results achieved by calibration. As a secondary issue, the present work examines grid-dependent behaviors when using model calibration. Although recalibration of models for different grid scales is a common practice among modelers, we could find relatively little documentation or analysis. In our work, we examine both single-cell calibration (i.e. changing roughness in only the cell containing the rough patch) and multiple-grid cell calibration involving neighbor cells. With either method, improving calibration required multiple model simulations and comparative analysis for each tested grid size and was inefficient compared to the upscaling approach. As expected, the calibration at a given grid size was always inappropriate for a different grid size. / text

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

A novel cell culture system was designed to serve as a model of neuroinflammation. Neurons, astrocytes, and microglia derived from embryonic and perinatal rat cortical tissue were combined in a three-dimensional hydrogel utilizing a method that facilitated cell maturation and viability. Chemical challenge of the cultures with a broad pro-inflammatory stimulus resulted in the production of inflammatory cytokines and other associated molecules commensurate with the response observed in vivo and in other in vitro systems. It was hypothesized that mechanical deformation of the multitypic neural cell cultures would produce a similar response and thus validate the system as an in vitro model of traumatic brain injury-induced neuroinflammation. Mechanical injury delivered using custom-manufactured culture chambers and injury devices successfully imparted a moderate level of cell death to the cultures. It was determined that a mechanically-induced inflammatory response required chemical stimulation prior to the injury. The research presented here describes the generation and characterization of a novel in vitro culture system and its implementation in experiments designed to model secondary injury mechanisms associated with injury-induced neuroinflammation. The findings of these studies, applications of the culture system, and future research avenues are discussed.

No description available.

Background: The applications for rapid prototyping have expanded dramatically over the last 20 years. In recent years, additive manufacturing has been intensely investigated for surgical implants, tissue scaffolds, and organs. There is, however, scant literature to date that has investigated the viability of 3D printing of surgical instruments. Materials and Methods: Using a fused deposition manufacturing (FDM) printer, an army/ navy surgical retractor was replicated from polylactic acid (PLA) filament. The retractor was sterilized using standard FDA approved glutaraldehyde protocols, tested for bacteria by PCR, and stressed until fracture in order to determine if the printed instrument could tolerate force beyond the demands of an operating room. Results: Printing required roughly 90 minutes. The instrument tolerated 13.6 kg of tangential force before failure, both before and after exposure to the sterilant. Freshly extruded PLA from the printer was sterile and produced no PCR product. Each instrument weighed 16g and required only $0.46 of PLA. Conclusions: Our estimates place the cost per unit of a 3D printed retractor to be roughly 1/10th the cost of a stainless steel instrument. The PLA Army/ Navy is strong enough for the demands of the operating room. Freshly extruded PLA in a clean environment, such as an OR, would produce a sterile, ready to use instrument. Due to the unprecedented accessibility of 3D printing technology world wide, and the cost efficiency of these instruments, there are far reaching implications for surgery in some underserved and less developed parts of the world.

Core-collapse supernovae are some of the most energetic events in the Universe, they herald the birth of neutron stars and black holes, are a major site for nucleosynthesis, influence galactic hydrodynamics, and trigger further star formation. As such, it is important to understand the mechanism of explosion. Moreover, observations imply that asymmetries are, in the least, a feature of the mechanism, and theory suggests that multi-dimensional hydrodynamics may be crucial for successful explosions. In this dissertation, we present theoretical investigations into the multi-dimensional nature of the supernova mechanism. It had been suggested that nuclear reactions might excite non-radial g-modes (the ε-mechanism) in the cores of progenitors, leading to asymmetric explosions. We calculate the eigenmodes for a large suite of progenitors including excitation by nuclear reactions and damping by neutrino and acoustic losses. Without exception, we find unstable g-modes for each progenitor. However, the timescales for growth are at least an order of magnitude longer than the time until collapse. Thus, the ε-mechanism does not provide appreciable amplification of non-radial modes before the core undergoes collapse. Regardless, neutrino-driven convection, the standing accretion shock instability, and other instabilities during the explosion provide ample asymmetry. To adequately simulate these, we have developed a new hydrodynamics code, BETHE-hydro that uses the Arbitrary Lagrangian-Eulerian (ALE) approach, includes rotational terms, solves Poisson’s equation for gravity on arbitrary grids, and conserves energy and momentum in its basic implementation. By using time dependent arbitrary grids that can adapt to the numerical challenges of the problem, this code offers unique flexibility in simulating astrophysical phenomena. Finally, we use BETHE-hydro to investigate the conditions and criteria for supernova explosions by the neutrino mechanism. We find that a critical luminosity/ mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic 1D and 2D simulations. Importantly, the critical luminosity for 2D simulations is found to be ∼70% of the critical luminosity for 1D simulations. We identify the specifics ofmulti-dimensional hydrodynamic simulations that enable explosions at lower neutrino luminosities in 2D and discuss how these results might foreshadow successful explosions by eventual 3D radiation-hydrodynamic simulations.

The objective of this research is to identify the circulation patterns of the water and sediment fluxes in coastal and estuarine zones, where the shoaling processes correlate with tide generating flow patterns. The research provides a better understanding of the characteristics of spatial and temporal variability of currents. An important deviation from previous research is the inclusion of the baroclinic term, which becomes very important in density driven flows. The understanding of this process provides a basis for determining how the water circulation three-dimensionally controls the hydrodynamics of the system and ultimately transports the suspended and soluble materials due to combined currents and waves. A three-dimensional circulation model is used to calculate the water circulation. The model is based on the three-dimensional (3D) version of Advanced Circulation (AD-CIRC) Hydrodynamic Model with extending the Sediment Transport module. The model is based on the finite element method on unstructured grids. The output of the hydrody-namic model is used to estimate spatial and temporal advections, dispersions and bottom shear stress for the erosion, suspension, deposition and transport of sediment. The model development includes extending the existing three-dimensional (3D) ADCIRC Model with (1) baroclinic forcing term and (2) transport module of suspended and soluble materials. The transport module covers the erosion, material suspension and deposition processes for both cohesive and non-cohesive type sediments. The inclusion of the baroclinic demonstrates the potential of over or underpredicting the total net transport of suspended cohesive sediment under influence of currents. The model provides less than 6% error of theoretical mass conservation for eroded, suspended and deposited sediment material. The inclusion of the baroclinic term in stratified water demonstrates the prevailing longshore sediment transport. It is shown that the model has an application to the transport of the cohesive sediments from the mouth of the Mississippi River along the north shore of the Gulf of Mexico towards and along the Texas coast. The model is also applicable to determine the design erosion thickness of a cap for isolating contaminated dredged material and to evaluate the appro-priate grain size of cap sediments to minimize the erosion.

In order to predict the behavior of bubbly flows, it is necessary to know the three dimensional profiles of the bubbles present in the flow. With advancements in the field of flow visualization, accurate reconstruction of the bubble shape has become necessary. The PIV and the SIV techniques, used to acquire images of particles and bubbles, have been found to be extremely useful in this regard. The study, development, implementation, applications and limitations of a unique reconstruction technique applied to various regular and irregular bubble shapes, using the two orthogonal projections of the three-dimensional bubble profiles as captured by the SIV cameras are presented here. The technique is a blend of neural networks, combinatorial optimization and advanced computer aided design methods. The technique involves the robustness and ruggedness of the neural network approach and the flexibility and reliability of advanced computer aided design methods. The technique uses a well-known problem in neural networks and combinatorial optimization known as the Traveling Salesman Problem approach to identify the bubble boundaries on the images. An optimization solution technique known as the Simulated Annealing technique is employed to solve the Traveling Salesman Problem and obtain the bubble profiles. These results are employed to reconstruct bubble shapes using NURBS computer aided design software. Two main applications of this technique are demonstrated and the results are found to be promising. The first application included the calculation of the void fraction at a particular depth of the channel/ pipe and at a particular radius of the channel. The second application was Lagrangian tracking of bubbles, wherein the centroids of the bubbles were tracked between image frames to determine the linear and transverse velocities of the bubbles. This technique has shown scope for development including the development as integrated bubble surface reconstruction software and advanced modifications at various levels for efficient and accurate reconstruction.