Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 55-56).

Thesis (M.S.)--University of Tennessee, Knoxville, 2002. / Title from title page screen (viewed Sept. 6, 2002). Thesis advisor: Michael Langston. Document formatted into pages (vi, 119 pages). Vita. Includes bibliographical references (p. 43-46).

Thesis (Ph. D.)--State University of New York at Buffalo, 2001. / "August 2001." Includes bibliographical references (p. 80-87). Also available in print.

Thesis (M.S.)--California Polytechnic State University, 2010. / Title from PDF title page; viewed on February 22, 2010. Major professor: Xiao-Hua (Helen) Yu, Ph.D. "Presented to the faculty of California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree [of] Master of Science in Electrical Engineering." "February, 2010." Includes bibliographical references (p. 90-91).

Thesis--Auburn University, 2010. / Abstract. Includes bibliographic references (p.28).

An efficient FAS muldgrid solution strategy is presented for the accurate and economic simulation of convection dominated flows. The use of a high-order approximation to the convective transport terms found in the governing equations of motion has been investigated in conjunction with an unsegregated smoothing technique. Results are presented for a sequence of problems of increasing complexity requiring that careful attention be directed toward; the proper treatment of different types of boundary condition. The classical two-dimensional problem of flow in a lid-driven cavity is investigated in depth for flows at Reynolds numbers of 100,400 and 1000. This gives an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, and to the flow over a step discontinuity in the case of an abruptly expanding channel. Although, at first sight, these problems appear to require only minor extensions to the existing approach, it is found that they are rather more idiosyncratic. Finally, the governing equations and numerical algorithm are extended to encompass the treatment of thermally driven flows. Ile solution to two such problems is presented and compared with corresponding results obtained by traditional methods.

Understanding flow processes of sea and fresh water through complex coastal regions is of utmost importance for a number of applications of interest to the scientific and engineering community, including wetland health and restoration, inland flooding due to tropical storms and hurricanes, and navigation through coastal waters. In such regions, the existence of vegetation increases flow resistance, which is a major factor in determining velocity and water level distribution in wetlands and inland. Commonly, the momentum loss due to vegetation is included in a bottom friction term in the model equations; however, such models may oversimplify the complex resistance characteristics of such a system. With recent increases in computational capabilities, it is now feasible to develop and implement more intricate resistance models that more accurately capture these characteristics. We present two methods for modeling flow through vegetated regions. With the first method, we employ mathematical and computational upscaling techniques from the study of subsurface flow to parametrize drag in a complex heterogeneous region. These parameterizations vary greatly depending on Reynolds number. For the coastal flows in which we are interested the Reynolds number at different locations in the domain may vary from order 1 to order 1000, so we must consider laminar and fully turbulent flows. Large eddy simulation (LES) is used to model the effects of turbulence. The geometry of a periodic cell of vegetative obstacles is completely resolved in the fluid mesh with a standard no-slip boundary condition imposed on the fluid-vegetation boundaries. The corresponding drag coefficient is calculated and upscaling laws from the study of inertial flow through porous media are used to parametrize the drag coefficient over a large range of Reynolds numbers. Simulations are performed using a locally conservative, stabilized continuous Galerkin finite element method on highly-resolved, unstructured 2D and 3D meshes. The second method we present is an immersed structure approach. In this method, separate meshes are used for the fluid domain and vegetative obstacles. Taking techniques from immersed boundary finite element methods, the effects of the fluid on the vegetative structures and vice versa are calculated using integral transforms. This method allows us to model flow over much larger scales and containing much more complicated obstacle geometry. Using a simple elastic structure model we can incorporate bending and moving obstacles which would be extremely computationally expensive for the first method. We model flexible vegetation as thin, elastic, inextensible cantilever beams. We present two numerical methods for modeling the beam motion and analyze their computational expense, stability, and accuracy. Using the immersed structure approach, a fully coupled steady-state fluid-vegetation interaction model is developed as well as a dynamic interaction model assuming dynamic fluid flow and quasi-static beam bending. This method is verified using channel flow and wave tank test problems. We calculate the bulk drag coefficient in these flow scenarios and analyze their trends with changing model parameters including stem population density and flow Reynolds number. These results are compared to well-respected experimental results. We model real-life beds of Spartina alterniflora grass with representative beds of flexible beams and perform similar comparisons. / text

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Biological systems are complex in that they comprise large number of interacting entities, and their dynamics follow mechanic regulations for movement and biological function organization. Established computational modeling deals with studying and manipulating biologically relevant systems as a powerful approach. Inner structure and behavior of complex biological systems can be analyzed and understood by computable biological networks. In this thesis, models and computation methods are proposed for biological networks. The study of Genetic Regulatory Networks (GRNs) is an important research topic in genomic research. Several promising techniques have been proposed for capturing the behavior of gene regulations in biological systems. One of the promising models for GRNs, Boolean Network (BN) has gained a lot of attention. However, little light has been shed on the analysis of internal connection between the dynamics of biological molecules and network systems. Inference and completion problems of a BN from a given set of singleton attractors are considered to be important in understanding the relationship between dynamics of biological molecules and network systems. Discrete dynamic systems model has been recently proposed to model time-course microarray measurements of genes, but delay effect may be modeled as a realistic factor in studying GRNs. A delay discrete dynamic systems model is developed to model GRNs. Inference and analysis of networks is one of the grand challenges in modern statistical biology. Machine learning method, in particular, Support Vector Machine (SVM), has been successfully applied in predictions of internal connections embedded in networks. Kernels in conjunction with SVM demonstrate strong ability in performing various tasks such as biomedical diagnosis, function prediction and motif extractions. In biomedical diagnosis, data sets are always high dimensional which provide a challenging research problem in machine learning area. Novel kernels using distance-metric that are not common in machine learning framework are proposed for possible tumor differentiation discrimination problem. Protein function prediction problem is a hot topic in bioinformatics. The K-spectrum Kernel is among the top popular models in description of protein sequences. Taking into consideration of positive-semi-definiteness in kernel construction, Eigen-matrix translation technique is introduced in novel kernel formulation to give better prediction result. In a further step, power of Eigen-matrix translation technique in feature selection is demonstrated through mathematical formulation. Due to structure complexity of carbohydrates, the study of carbohydrate sugar chains has lagged behind compared to that of DNA and proteins. A weighted q-gram kernel is constructed in classifying glycan structures with limitations in feature extractions. A biochemically-weighted tree kernel is then proposed to enhance the ability in both classification as well as motif extractions. Finally the problem of metabolite biomarker discovery is researched. Human diseases, in particular metabolic diseases, can be directly caused by the lack of essential metabolites. Identification of metabolite biomarkers has significant importance in the study of biochemical reaction and signaling networks. A promising computational approach is proposed to identify metabolic biomarkers through integrating biomedical data and disease-specific gene expression data. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy