Physical Sciences and Mathematics Commons^™

Direct Computations Of Marangoni Driven Flows Using A Volume Of Fluid Method, Ivana Seric

Dissertations

The volume of fluid (VoF) interface tracking methods have been used for simulating a wide range of interfacial flows. An improved accuracy of the surface tension force computation has enabled the VoF method to become widely used for simulating flows driven by the surface tension force. A general methodology for the inclusion of variable surface tension coefficient into a VoF based Navier-Stokes solver is developed. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation applies to both temperature and concentration …

Efficient Coarse-Grained Brownian Dynamics Simulations For Dna And Lipid Bilayer Membrane With Hydrodynamic Interactions, Szu-Pei Fu

Dissertations

The coarse-grained molecular dynamics (CGMD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). From simple biological systems such as a single DNA macromolecule to large and complicated systems, for instances, vesicles and red blood cells (RBCs), the numerical results have shown outstanding agreements with experiments and continuum modeling by adopting Stokesian dynamics and explicit solvent model. Finally, when combined with fast algorithms such as the fast multipole method (FMM) which has nearly optimal complexity in …

Boundary Integral Equation Based Numerical Solutions Of Helmholtz Transmission Problems For Composite Scatters, Haiyang Qi

Dissertations

In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite two-dimensional media is presented. Composite media are characterized by piece-wise constant material properties (i.e., index of refraction) and thus, they exhibit interfaces of material discontinuity and multiple junctions. Whenever possible to use, boundary integral methods for solution of Helmholtz boundary value problems are computationally advantageous. Indeed, in addition to the dimensional reduction and straightforward enforcement of the radiation conditions that these methods enjoy, they do not suffer from the pollution effect present in volumetric discretization. The …

Mathematical Modeling Of Membrane Filtration, Pejman Sanaei

Dissertations

The purpose of this thesis is to formulate and investigate new mathematical models for membrane filtration. The work presented is divided into six chapters. In the first chapter the problem is introduced and motivated. In the second chapter, a new mathematical model for flow and fouling in a pleated membrane filter is presented. Pleated membrane filters are widely used in many applications, and offer significantly better surface area to volume ratios than equal area unpleated membrane filters. However, their filtration characteristics are markedly inferior to those of equivalent unpleated membrane filters in dead-end filtration. While several hypotheses have been advanced …

Qualitative Modeling Of Chaotic Logical Circuits And Walking Droplets: A Dynamical Systems Approach, Aminur Rahman

Dissertations

Logical circuits and wave-particle duality have been studied for most of the 20th century. During the current century scientists have been thinking differently about these well-studied systems. Specifically, there has been great interest in chaotic logical circuits and hydrodynamic quantum analogs.

Traditional logical circuits are designed with minimal uncertainty. While this is straightforward to achieve with electronic logic, other logic families such as fluidic, chemical, and biological, naturally exhibit uncertainties due to their inherent nonlinearity. In recent years, engineers have been designing electronic logical systems via chaotic circuits. While traditional boolean circuits have easily determined outputs, which renders dynamical models …

Hamiltonian Bifurcations In Schrodinger Trimers, Casayndra H. Basarab

Dissertations

The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic orbits whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of periodic orbits are discussed as a conserved …

Structural Exploration And Inference Of The Network, Ruihua Cheng

Dissertations

This dissertation consists of two parts. In the first part, a learning-based method for classification of online reviews that achieves better classification accuracy is extended. Automatic sentiment classification is becoming a popular and effective way to help online users or companies to process and make sense of customer reviews. The method combines two recent developments. First, valence shifters and individual opinion words are combined as bigrams to use in an ordinal margin classifier. Second, relational information between unigrams expressed in the form of a graph is used to constrain the parameters of the classifier. By combining these two components, it …

Efficient High-Order Integral Equation Methods For The Heat Equation, Shaobo Wang

Dissertations

Efficient high-order integral equation methods have been developed for solving the boundary value problems of the heat equation with complex geometries in two and three dimensions. First of all, the classical heat potential theory is applied to convert such problems to Volterra integral equations of the second kind via the heat layer potentials. Some advantages of the integral formulation as compared with standard finite difference and finite element methods include reduction of the dimension of the problem by one, high order accuracy, unconditional stability, insensitivity to different geometries, and elimination of truncating the computational domain and the need of artificial …

Numerical Simulations Of Dense Granular Systems With And Without Cohesive Effects, Lenka Kovalcinova

Dissertations

Granular materials are collections of objects ranging from sand grains that form sand piles or even sand castles to collections of large objects such as a group of meteors in outer space. The considered range of sizes of granular particles is such that the effect of thermal fluctuations is not relevant. However, the interaction between the particles may be very complex, involving inelasticity and friction, in addition to repulsive and possibly attractive interaction forces. These interactions that may be history dependent, make the systems that consist of a large number of particles complex to analyze and difficult to understand using …

Methods For The Direct Simulation Of Nanoscale Film Breakup And Contact Angles, Kyle Mahady

Dissertations

This thesis investigates direct simulation of fluids with free surfaces and contact lines, with a focus on capturing nanoscale physics in a continuum based computational framework. Free surfaces and contact lines have long presented some of the most challenging problems in computational fluid dynamics. Extensive progress has been made in recent years, and a wide variety of different methods are currently employed for direct simulation in these contexts. The complexity of the full governing equations for such flows poses significant challenges in terms of analytical techniques, and leads to lengthy computational times for direct simulations. For these reasons, reduced models …

Investigation Of Infinite-Dimensional Dynamical System Models Applicable To Granular Flows, Hao Wu

Dissertations

Recently Blackmore, Samulyak and Rosato developed a class of infinite-dimensional dynamical systems in the form of integro-partial differential equations, which have been called the BSR models. The BSR models were originally derived to model granular flows, but they actually have many additional applications in a variety of fields. BSR models have already been proven to be completely integrable infinite-dimensional Hamiltonian dynamical systems for perfectly elastic interactions in the case of one space dimension, but the well-posedness question of these systems is at least partially answered for the first time here. In particular, dynamical systems of the BSR type are proven …

Methods For Two-Sample Comparisons From Censored Time-To-Event Data, Nubyra Ahmed

Dissertations

In the analysis of censored survival data, it is frequently of interest to determine the efficacy of a treatment or new method over a control or existing method. For this purpose, one may report estimates of the two survival functions or, more specifically, their difference, accompanied by simultaneous confidence bands (SCBs). Alternatively, or in addition, one may conduct hypothesis testing for the difference of the two survival functions.

The first project exploits two bootstrap methods to develop new Wald-type SCBs for the difference of survival functions. The censored data bootstrap is employed to obtain nonparametric SCBs for the difference of …

Multiple Testing Procedures For Complex Structured Hypotheses And Directional Decisions, Anjana Grandhi

Dissertations

Several multiple testing procedures are developed based on the inherent structure of the tested hypotheses and specific needs of data analysis. Incorporating the inherent structure of the hypotheses results in development of more powerful and situation-specific multiple testing procedures than existing ones. The focus of this dissertation is on developing multiple testing procedures that utilize the information on this structure of the hypotheses and aims at answering research questions while controlling appropriate error rates.

In the first part of the thesis, a mixed directional false discovery rate (mdFDR) controlling procedure is developed in the context of uterine fibroid gene expression …

Confidence Bands For Survival Curves Using Model Assisted Cox Regression, Shoubhik Mondal

Dissertations

The goal of this dissertation is to develop informative subject-specific simultaneous confidence bands (SCBs) for survival functions from right censored data. The approach is based on an extension of semiparametric random censorship models (SRCMs) to Cox regression, which produces reliable and more informative SCBs. SRCMs derive their rationale from their ability to utilize parametric ideas within the random censorship environment. Incorporating SRCMs into the existing framework produces more powerful procedures to analyze right censored data. The first part of the project focuses on proposing new estimators of Cox regression parameters and the cumulative baseline hazard function, and deriving their large …

Efficient Domain Decomposition Algorithms For The Solution Of The Helmholtz Equation, Dawid Midura

Dissertations

The purpose of this thesis is to formulate and investigate new iterative methods for the solution of scattering problems based on the domain decomposition approach. This work is divided into three parts. In the first part, a new domain decomposition method for the perfectly matched layer system of equations is presented. Analysis of a simple model problem shows that the convergence of the new algorithm is guaranteed provided that a non-local, square-root transmission operator is used. For efficiency, in practical simulations such operators need to be localized. Current, state of the art domain decomposition algorithms use the localization technique based …

The Control Of The False Discovery Rate Under Structured Hypotheses, Gavin Lynch

Dissertations

The hypotheses in many multiple testing problems often have some inherent structure based on prior information such as Gene Ontology in gene expression data. However, few false discovery rate (FDR) controlling procedures take advantage of this inherent structure. In this dissertation, we develop FDR controlling methods which exploit the structural information of the hypotheses.

First, we study the fixed sequence structure where the testing order of the hypotheses has been pre-specified. We are motivated to study this structure since it is the most basic of structures, yet, it has been largely ignored in the literature on large scale multiple testing. …

Electro-Deformation Of A Moving Boundary: A Drop Interface And A Lipid Bilayer Membrane, Herve Nganguia

Dissertations

This dissertation focuses on the deformation of a viscous drop and a vesicle immersed in a (leaky) dielectric fluid under an electric field. A number of mathematical tools, both analytical and numerical, are developed for these investigations. The dissertation is divided into three parts. First, a large-deformation model is developed to capture the equilibrium deformation of a viscous spheroidal drop covered with non-diffusing insoluble surfactant under a uniform direct current (DC) electric field. The large- deformation model predicts the dependence of equilibrium spheroidal drop shape on the permittivity ratio, conductivity ratio, surfactant coverage, and the elasticity number. Results from the …

Data Analysis And Simulation For Warranties And Golf Handicaps, Sonia Bandha

Dissertations

In this dissertation, we discuss the application of data analysis and numerical simulation in order to gain insight into problems related to warranty cost management and the effectiveness of the golf handicap system. Despite the commonalities of the approaches, we will discuss these problems in turn.

For many moderately high value items with a substantial sales volume (such as automobiles), a warranty is used as an important element of marketing products as a better warranty typically signals higher product quality to customers. Much recent research on modeling and optimization of servicing costs for Non-Renewing Free Replacement Warranties (NR-FRW) assumes that …

Fwer Controlling Procedures For Testing Multiple Hypotheses With Hierarchical Structure And Applications In Clinical Trials, Zhiying Qiu

Dissertations

In applications of clinical trials, the hypotheses to be tested often exhibit a hierarchical structure, and are usually hierarchically ordered based on their importance, clinical relevance, or dose concentration, etc. Thus, they are tested in a pre-defined fixed sequence. In some more complex cases, the hypotheses to be tested are hierarchically grouped into several families, and thus the families are tested in a sequential order. Although such problems of structured multiple testing have received much attention and several popular FWER controlling procedures, such as conventional fixed sequence procedure, fallback procedure and gatekeeping procedure have been introduced, not much progress has …

Inverse Methods For Sound Speed Estimation In The Ocean, Tao Lin

Dissertations

This dissertation presents theoretical and computational approaches for estimating sound-speed in the ocean under different conditions. The first part of the dissertation discusses a fast approach for solving the inverse problem of estimating sediment sound-speed based on the Deift-Trubowitz trace formula. Under certain assumptions, this algorithm can recover the sound speed profile in the seabed using pressure field measurements in the water column at low frequencies. The inversion algorithm requires solving a non-linear integral equation. In the past, Stickler and Zhou employed a first order Born approximation for solving the integral equation. This work introduces two new methods. The first …

Dynamics Of Phase Locking In Neuronal Networks In The Presence Of Synaptic Plasticity, Zeynep Akcay

Dissertations

The behavior generated by neuronal networks depends on the phase relationships of its individual neurons. Observed phases result from the combined effects of individual cells and synaptic connections whose properties change dynamically. The properties of individual cells and synapses can often be characterized by driving the cell or synapse with inputs that arrive at different phases or frequencies, thus producing a feed-forward description of these properties. In this study, a recurrent network of two oscillatory neurons that are coupled with reciprocal synapses is considered. Feed-forward descriptions of the phase response curves of the neurons and the short-term synaptic plasticity properties …

A Modeling Study Of The History-Dependence Of Conduction Delay In Unmyelinated Axons, Yang Zhang

Dissertations

Conduction delay in an axon is the time required for an action potential to propagate between two positions. It is a function of the axon’s passive membrane properties, voltage-gated ion channels and the Na+/K+ pump, and can be substantially affected by neuromodulators. The conduction delay of action potential, generated by the pyloric dilator (PD) neuron unmyel i nated motor axon in the stomatogastric nervous system, shows significant variability with ongoing bursting or Poisson stimulation. When the axon is stimulated, the mean value (Dmean) and coefficient variation of conduction delay (CV-D) slowly increase with time (slow timescale effect), and the relationship …

Particle Filtering For Frequency Estimation From Acoustic Time-Series In Dispersive Media, Nattapol Aunsri

Dissertations

Acoustic signals propagating in the ocean carry information about geometry and environmental parameters within the propagation medium. Accurately retrieving this information leads us to effectively estimate parameters that are of utmost importance in environmental studies, climate monitoring, and defense. This dissertation focuses on the development of sequential Bayesian filtering methods to obtain accurate estimates of instantaneous frequencies using Short Term Fourier Transforms within the acoustic field measured at an array of hydrophones, which can be used in a subsequent step for the estimation of propagation related parameters. We develop a particle filter to estimate these frequencies along with modal amplitudes, …

The Application Of Bayesian Adaptive Design And Markov Model In Clinical Trials, Xiaoyu Lu

Dissertations

In this research, two new designs in clinical trials are proposed. The first problem is a new Bayesian adaptive dose-finding design and its application in an oncology clinical trial. This design is used for phase IB studies with the biomarker as the endpoint and with the fewer patients. The second problem is another new Bayesian adaptive dose-finding design with longitudinal analysis and its application in phase II depression clinical trial. This design is best fit for phase II dosing-finding clinical trials with clinical endpoints. MTD information has been obtained before the trials.

In adaptive dose-finding clinical trials, the strategy is …

Mathematical Models For Bistable Nematic Liquid Crystal Displays, Chenjing Cai

Dissertations

Bistable Liquid Crystal Displays (LCDs) offer the potential for considerable power savings, compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically-distinct means that contrast can be maintained in a display without an externally-applied electric field. An applied field is required only to switch the device from one state to the other, as needed. This dissertation focuses on theoretical models of a possible bistable nematic device, whose operating principle relies on controlling surface anchoring conditions. Switching between the two stable steady states is achieved by application of a transient electric field. A 1D …

A Numerical Method For Electro-Kinetic Flow With Deformable Interfaces, Manman Ma

Dissertations

We consider two-phase flow of ionic fluids whose motion is driven by an imposed electric field. At a fluid-fluid interface, a screening cloud of ions develops and forms an electro-chemical double layer or ‘Debye layer’. The applied electric field acts on the ionic cloud it induces, resulting in a strong slip flow near the interface. This is known as ‘induced-charge electro-kinetic flow’, and is an important phenomenon in microfluidic applications and in the manipulation of biological cells. The models with two different cases including the fast or slow charging time scales are studied both analytically and numerically. We address a …

Modeling Cell Proliferation In A Perfusion Tissue Engineering Bioreactor, Jeffrey Vincent Pohlmeyer

Dissertations

In this dissertation we develop a comprehensive model to simulate a tissue engineering experiment. The experiment takes place in a bioreactor in which a cell seeded porous scaffold is placed, and the scaffold experiences a perfused flow of a nutrient-rich culture medium. The goal of the model is to assist experimentalists in evaluation of different parameter scenarios as the time needed to simulate an experiment is significantly less than the time needed for the experiment itself. We provide the full two-dimensional model development, as well as investigation into possible variations of specific model choices, and we demonstrate the robustness and …

The Goodness-Of-Fit Tests For Geometric Models, Feiyan Chen

Dissertations

We propose two types of goodness-of-fit tests for geometric distribution and for a bivariate geometric distribution called BGD(B&D), based on their probability generating function (PGF). The first type is a special-case application of the general testing procedure for discrete distributions proposed by Kocherlakota and Kocherlakota (1986). The second type utilizes the supremum of the absolute value of the standardized difference between the PGF’s maximum likelihood estimator (MLE) and its empirical counterpart as the test statistic. We verify the asymptotic properties of the test statistics for the first type of test and explore the asymptotic behaviors of the test statistics for …

Fast Algorithms For Brownian Dynamics Simulation With Hydrodynamic Interactions, Zhi Liang

Dissertations

In the Brownian dynamics simulation with hydrodynamic interactions, one needs to generate the total displacement vectors of Brownian particles consisting of two parts: a deterministic part which is proportional to the product of the Rotne-Prager-Yamakawa (RPY) tensor D [1, 2] and the given external forces F; and a hydrodynamically correlated random part whose covariance is proportional to the RPY tensor. To be more precise, one needs to calculate Du for a given vector u and compute √Dv for a normally distributed random vector v. For an arbitrary N-particle configuration, D is a 3N x 3N matrix and u, v are …

Analytical And Computational Methods For The Study Of Rare Event Probabilities In Dispersive And Dissipative Waves, Daniel S. Cargill

Dissertations

The main focus of this dissertation is the application of importance sampling (IS) to calculate the probabilities associated with rare events in nonlinear, large-dimensional lightwave systems that are driven by noise, including models for fiber-based optical communication system and mode-locked lasers. Throughout the last decade, IS has emerged as a valuable tool for improving the efficiency of simulating rare events in such systems. In particular, it has shown great success in simulating various sources of transmission impairments found in optical communication systems, with examples ranging from large polarization fluctuations resulting from randomly varying fiber birefringence to large pulse-width fluctuations resulting …