Physical Sciences and Mathematics Commons^™

The Multilevel Structures Of Nurbs And Nurblets On Intervals, Weiwei Zhu

Dissertations

This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs", and such biorthogonal wavelets ``NURBlets". Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout …

Reduced Order Models For Fluid-Structure Interaction Systems By Mixed Finite Element Formulation, Ye Yang

Dissertations

In this work, mixed finite element formulations are introduced for acoustoelastic fluid- structure interaction (FSI) systems. For acoustic fluid, in addition to displacement- pressure (u/p) mixed formulation, a three-field formulation, namely, displacement-pressure-vorticity moment formulation (u - p -Λ) is employed to eliminate some zero frequencies. This formulation is introduced in order to compute the coupled frequencies without the contamination of nonphysical spurious non-zero frequencies. Furthermore, gravitational forces are introduced to include the coupled sloshing mode. In addition, u/p mixed formulation is the first time employed in solid. The numerical examples will demonstrate that the mixed formulations are capable of predicted …

Self Similar Flows In Finite Or Infinite Two Dimensional Geometries, Leonardo Xavier Espin Estevez

Dissertations

This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order …

Discreet Dynamical Population Models : Higher Dimensional Pioneer-Climax Models, Yogesh Joshi

Dissertations

There are many population models in the literature for both continuous and discrete systems. This investigation begins with a general discrete model that subsumes almost all of the discrete population models currently in use. Some results related to the existence of fixed points are proved. Before launching into a mathematical analysis of the primary discrete dynamical model investigated in this dissertation, the basic elements of the model - pioneer and climax species - are described and discussed from an ecological as well as a dynamical systems perspective. An attempt is made to explain why the chosen hierarchical form of the …

Numerical Detection Of Complex Singularities In Two And Three Dimensions, Kamyar Malakuti

Dissertations

Singularities often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. …

Loss Of Synchrony In An Inhibitory Network Of Type-I Oscillators, Myongkeun Oh

Dissertations

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris-Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation …

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …