Physical Sciences and Mathematics Commons^™

Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan

Dissertations

Despite an extensive history of oceanic observation, researchers have only begun to build a complete picture of oceanic currents. Sparsity of instrumentation has created the need to maximize the information extracted from every source of data in building this picture. Within the last few decades, autonomous vehicles, or AVs, have been employed as tools to aid in this research initiative. Unmanned and self-propelled, AVs are capable of spending weeks, if not months, exploring and monitoring the oceans. However, the quality of data acquired by these vehicles is highly dependent on the paths along which they collect their observational data. The …

Rare Event Sampling In Applied Stochastic Dynamical Systems, Yiming Yu

Dissertations

Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser …

Dynamical Systems Associated With Particle Flow Models : Theory And Numerical Methods, Roman V. Samulyak

Dissertations

A new class of integro - partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and …

Microwave Heating Of Fluid/Solid Layers : A Study Of Hydrodynamic Stability And Melting Front Propagation, John Gilchrist

Dissertations

In this work we study the effects of externally induced heating on the dynamics of fluid layers, and materials composed of two phases separated by a thermally driven moving front. One novel aspect of our study is in the nature of the external source, which is provided by the action of microwaves acting on dielectric materials. The main challenge is to model and solve systems of differential equations, which couple fluid dynamical motions (the Navie- Stokes equations for nonisothermal flows) and electromagnetic wave propagation (governed by Maxwell's equations).

When an electromagnetic wave impinges on a material, energy is generated within …

Bootstrapping Tsmars Models, Liangzhong Chen

Theses

We investigate bootstrap inference methods for nonlinear time series models obtained using Multivariate Adaptive Regression Splines for Time Series (TSMARS), for which theoretical properties are not currently known. We use two different methods of bootstrapping to obtain confidence intervals for the underlying nonlinear function and prediction intervals for future values, based on estimated TSMARS models for the bootstrapped data. We also explore the method of Bootstrap AGGregatING (Bagging), due to Breiman (1996), to investigate whether the residual and prediction mean squared errors from a fitted TSMARS model can be reduced by averaging across the values obtained from each of the …

Diffusive And Wavelike Phenomena In Thermal Processing Of Materials, John A. Pelesko

Dissertations

Contemporary materials science abounds with novel processing methods. Devices such as lasers, microwave sources, and electron beam guns, provide unprecedented control over the deposition of energy within a material. The modern materials scientist has the ability to deposit energy volumetrically, to precisely control the location of energy deposition within a material, and to deposit energy in extremely short intervals of time. While making possible numerous thermal processing methods, these devices also push the limits of our understanding of the response of materials to energy deposition. In order to optimize and control these processing methods, it becomes necessary to further our …

Applications Of Binary Sequence Of Order K, Xulun Jiang

Theses

The cumulative distribution of the finite sum of the binary sequence of order k is studied and some of its applications discussed. Certain properties of this sequence are studied and uniformly superior bounds for the cumulative distribution under minimal information on the "success" probabilities are derived.

As an application, an optimal randomized response model to collect sensitive information with dependence in the sample is proposed. This dependence is caused by untruthful response to stigmatizing questions and has been ignored in the past procedures.

The proposed method is useful in collecting reliable information in situations where the response is difficult to …

Finite-Element Ray Tracing, Yong-Chun Liu

Theses

The interesting acoustic modeling problems often push the practical limits of full-wave models. For instance, in acoustic tomography one needs to be able to predict the propagation of an acoustic pulse for successive realizations of 31) environments. For these types of problems ray methods continue to be attractive because of their speed. Unfortunately, existing codes are prone to a number of implementation difficulties which often degrade their accuracy.

As a result most ray models are actually incapable of producing the ray theoretic result. We discuss a. new method for implementing ray theory that uses a. finite-clement formulation. This method is …

Bayesian Methods In Preoperative Risk Assessment For Cardiac Surgery, Huey-Chung Teng

Theses

Many strides have been made in the last decade to improve the accuracy of preoperative risk estimation, particular for cardiovascular surgery. It is our goal to estimate the preoperative risk associated with cardiac bypass surgery for patients in different risk categories. These risk categories are determined by the Parsonett model.

The Parsonett model assigns a risk value to a range of risk factors consisting of patient attributes and disease parameters. Logistic modeling is applied to generate a comprehensive risk function. The database being utilized contains over 3,000 patients who have had cardiovascular surgery within the last 5 years.

This thesis …

The Flow Approach To Swept Volume, Haitao Jiang

Theses

In this thesis, a method for representing swept volume based on the sweep differential equation and sweep vector field flow is developed. This method can be used to determine the boundary representation of a swept volume generated by any polygonal object undergoing a general smooth 2-D sweep. For any given sweep and object, a. set of candidate boundary points is computed using a selection criterion based on vector field behavior. The set of candidate boundary points is then trimmed in order to obtain the true boundary of the swept volume. This trimming procedure is based on some simple topological principles …

Deconvolution Techniques With Applications In Cardiovascular Systems Analysis, Lakshminarayan Rajaram

Theses

System characterization by means of Impulse and Frequency Response Functions are well known in classical linear systems analysis. Impulse Response Function is a time domain description of a linear system where as the Frequency Response Function represents the frequency domain counterpart. Linear systems are often characterized in frequency domain. In many biological research applications, it becomes necessary to examine the impulse response function in order to understand the behavior of the system under investigation. One such application is the arterial system in cardiovascular dynamics. It has been shown that although both representations are identical, some aspects of the arterial system …

Random Genetic Drift Diffusion Model And Deterministic And Stochastic Models Of Epidemics, Norman W. Loney

Theses

In the Random Genetic Drift Diffusion model two approaches are taken. First we examined a discrete model that represent a relatively idealised version of the phenomena. Hefurther make the assumption that the Population reproduces itself and then dies, thus maintaining a finite population size at all times. If at a given locus there are two possible allels A and B and if X(t) is the number of A type in the genetic pool of size 2N, then 2N-X(t) is the number of B type. We then proceed to obtain a probability density function of X( t) by an Exact method …