Physical Sciences and Mathematics Commons^™

Exploring Topological Phonons In Different Length Scales: Microtubules And Acoustic Metamaterials, Ssu-Ying Chen

Dissertations

The topological concepts of electronic states have been extended to phononic systems, leading to the prediction of topological phonons in a variety of materials. These phonons play a crucial role in determining material properties such as thermal conductivity, thermoelectricity, superconductivity, and specific heat. The objective of this dissertation is to investigate the role of topological phonons at different length scales.

Firstly, the acoustic resonator properties of tubulin proteins, which form microtubules, will be explored The microtubule has been proposed as an analog of a topological phononic insulator due to its unique properties. One key characteristic of topological materials is the …

Computation Of Risk Measures In Finance And Parallel Real-Time Scheduling, Yajuan Li

Dissertations

Many application areas employ various risk measures, such as a quantile, to assess risks. For example, in finance, risk managers employ a quantile to help determine appropriate levels of capital needed to be able to absorb (with high probability) large unexpected losses in credit portfolios comprising loans, bonds, and other financial instruments subject to default. This dissertation discusses the computation of risk measures in finance and parallel real-time scheduling.

Firstly, two estimation approaches are compared for one risk measure, a quantile, via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large, but …

Low-Reynolds-Number Locomotion Via Reinforcement Learning, Yuexin Liu

Dissertations

This dissertation summarizes computational results from applying reinforcement learning and deep neural network to the designs of artificial microswimmers in the inertialess regime, where the viscous dissipation in the surrounding fluid environment dominates and the swimmer’s inertia is completely negligible. In particular, works in this dissertation consist of four interrelated studies of the design of microswimmers for different tasks: (1) a one-dimensional microswimmer in free-space that moves towards the target via translation, (2) a one-dimensional microswimmer in a periodic domain that rotates to reach the target, (3) a two-dimensional microswimmer that switches gaits to navigate to the designated targets in …

Nystrom Methods For High-Order Cq Solutions Of The Wave Equation In Two Dimensions, Erli Wind-Andersen

Dissertations

An investigation of high order Convolution Quadratures (CQ) methods for the solution of the wave equation in unbounded domains in two dimensions is presented. These rely on Nystrom discretizations for the solution of the ensemble of associated Laplace domain modified Helmholtz problems. Two classes of CQ discretizations are considered: one based on linear multistep methods and the other based on Runge-Kutta methods. Both are used in conjunction with Nystrom discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. CQ in conjunction with BIE is an excellent candidate …

Type I Error Rate Controlling Procedures For Multiple Hypotheses Testing, Beibei Li

Dissertations

This dissertation addresses several different but related topics arising in the field of multiple testing, including weighted procedures and graphical approaches for controlling the familywise error rate (FWER), and stepwise procedures with control of the false discovery rate (FDR) for discrete data. It consists of three major parts.

The first part investigates weighted procedures for controlling the FWER. In many statistical applications, hypotheses may be differentially weighted according to their different importance. Many weighted multiple testing procedures (wMTPs) have been developed for controlling the FWER. Among these procedures, two weighted Holm procedures are commonly used in practice: one is based …

Model Checks For Two-Sample Location-Scale, Atefeh Javidialsaadi

Dissertations

Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X₁ and X₂ are two random variables with means µ₁ and µ₂ and standard deviations ?₁ and ?₂, then (X₁ - µ₁)/?₁ and (X₂ - µ₂)/?₂ have some common unspecified standard or base distribution F₀. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale …

Dependent Censoring In Survival Analysis, Zhongcheng Lin

Dissertations

This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is …

On Non-Linear Network Embedding Methods, Huong Yen Le

Dissertations

As a linear method, spectral clustering is the only network embedding algorithm that offers both a provably fast computation and an advanced theoretical understanding. The accuracy of spectral clustering depends on the Cheeger ratio defined as the ratio between the graph conductance and the 2nd smallest eigenvalue of its normalizedLaplacian. In several graph families whose Cheeger ratio reaches its upper bound of Theta(n), the approximation power of spectral clustering is proven to perform poorly. Moreover, recent non-linear network embedding methods have surpassed spectral clustering by state-of-the-art performance with little to no theoretical understanding to back them.

The dissertation includes work …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

Asymmetric Multivariate Archimedean Copula Models And Semi-Competing Risks Data Analysis, Ziyan Guo

Dissertations

Many multivariate models have been proposed and developed to model high dimensional data when the dimension of a data set is greater than 2 (d ≥ 3). The existing multivariate models often force the “exchangeable” structure for part or the whole model, are not very flexible which tends to be of limited use in practice. There is a demand for developing and studying multivariate models with any pre-specified bivariate margins.

Suppose there exists such a class of flexible models with any pre-specified bivariate margins. Given a multivariate data, what is the distribution function and how to easily estimate the parameters …

Mechanisms Of Oscillations And Polyglot Entrainment In Neuronal And Circadian Models, Emel Khan

Dissertations

Entrainment is a type of synchronization in which the period of an endogenous oscillator matches the period of an external forcing signal and a stable phase relationship is maintained between them. Entrainment patterns are described in terms of the number of input oscillations (N) that are phase-locked to a number of output oscillations (M), referred to as N:M patterns. Arnold tongue diagrams are used to depict the regions of N:M entrainment patterns in the input period-amplitude parameter space. Although the entrainment of self-sustained oscillators by periodic forcing are well investigated is a well-studied problem, entrainment of damped oscillators has been …

Semantic, Integrated Keyword Search Over Structured And Loosely Structured Databases, Xinge Lu

Dissertations

Keyword search has been seen in recent years as an attractive way for querying data with some form of structure. Indeed, it allows simple users to extract information from databases without mastering a complex structured query language and without having knowledge of the schema of the data. It also allows for integrated search of heterogeneous data sources. However, as keyword queries are ambiguous and not expressive enough, keyword search cannot scale satisfactorily on big datasets and the answers are, in general, of low accuracy. Therefore, flat keyword search alone cannot efficiently return high quality results on large data with structure. …

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

Hybrid Deep Neural Networks For Mining Heterogeneous Data, Xiurui Hou

Dissertations

In the era of big data, the rapidly growing flood of data represents an immense opportunity. New computational methods are desired to fully leverage the potential that exists within massive structured and unstructured data. However, decision-makers are often confronted with multiple diverse heterogeneous data sources. The heterogeneity includes different data types, different granularities, and different dimensions, posing a fundamental challenge in many applications. This dissertation focuses on designing hybrid deep neural networks for modeling various kinds of data heterogeneity.

The first part of this dissertation concerns modeling diverse data types, the first kind of data heterogeneity. Specifically, image data and …

Resonant Triad Interactions In One And Two-Layer Systems, Malik Chabane

Dissertations

This dissertation is a study of the weakly nonlinear resonant interactions of a triad of gravity-capillary waves in systems of one and two fluid layers of arbitrary depth, in one and two-dimentions. For one-layer systems, resonant triad interactions of gravity-capillary waves are considered and a region where resonant triads can be always found is identified, in the two-dimensional wavevector angles-space. Then a description of the variations of resonant wavenumbers and wave frequencies over the resonance region is given. The amplitude equations correct to second order in wave slope are used to investigate special resonant triads that, providing their initial amplitude …

Data Assimilation For Conductance-Based Neuronal Models, Matthew Moye

Dissertations

This dissertation illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. Throughout this work, twin experiments, where the data is synthetically generated from output of the model, are used to validate use of these techniques for conductance-based models observing only the voltage trace. In Chapter 1, these techniques are described in detail and the …

Convex Relaxations Of A Continuum Aggregation Model, And Their Efficient Numerical Solution, Mahdi Bandegi

Dissertations

In this dissertation, the global minimization of a large deviations rate function (the Helmholtz free energy functional) for the Boltzmann distribution is discussed. The Helmholtz functional arises in large systems of interacting particles — which are widely used as models in computational chemistry and molecular dynamics. Global minimizers of the rate function (Helmholtz functional) characterize the asymptotics of the partition function and thereby determine many important physical properties such as self-assembly, or phase transitions. Finding and verifying local minima to the Helmholtz free energy functional is relatively straightforward. However, finding and verifying global minima is much more difficult since the …

Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

Dissertations

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between …

Domain Decomposition Methods For The Solution Of Multiple Scattering Problems, Michael Pedneault

Dissertations

This presents a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods,(1) the ensemble of scatterers is enclosed in a domain bounded by an artificial boundary, (2) this domain is subdivided into a collection of nonoverlapping subdomains so that the boundaries of the subdomains do not intersect any of the scatterers, and (3) the solutions of the subproblems are connected via Robin boundary conditions matching on the common interfaces between subdomains. Subdomain Robin-to-Robin maps are used to recast the DD problem as a sparse linear system whose …

Fwer Controlling Procedures In Simultaneous And Selective Inference, Li Yu

Dissertations

With increasing complexity of research objectives in clinical trials, a variety of relatively complex and less intuitive multiple testing procedures (MTPs) have been developed and applied in clinical data analysis. In order to make testing strategies more explicit and intuitive to communicate with non-statisticians, several flexible and powerful graphical approaches have recently been introduced in the literature for developing and visualizing newer MTPs. Nevertheless, some theoretical as well as methodological issues still remain to be fully addressed. This dissertation addresses several important issues arising in graphical approaches and related selective inference problems. It consists of three parts.

In the first …

Survival Analysis Using Archimedean Copulas, Xieyang Jia

Dissertations

This dissertation has three independent parts. The first part studies a variation of the competing risks problem, known as the semi-competing risks problem, in which a terminal event censors a non-terminal event, but not vice versa, in the presence of a censoring event which is independent of these two events. The joint distribution of the two dependent events is formulated under Archimedean copula. An estimator for the association parameter of the copula is proposed, which is shown to be consistent. Simulation shows that the method works well with most common Archimedean copula models.

The second part studies the properties of …

Numerical Simulations Of Thin Viscoelastic Films, Valeria Barra

Dissertations

This dissertation is developed in the field of Computational Fluid Dynamics (CFD) and it focuses on numerical simulations of the dynamics of thin viscoelastic films in different settings. The first part of this dissertation presents a novel computational investigation of thin viscoelastic films and drops, that are subject to the van der Waals interaction force, in two spatial dimensions. The liquid films are deposited on a flat solid substrate, that can have a zero or nonzero inclination with respect to the base. The equation that governs the interfacial dynamics of the thin films and drops is obtained within the long-wave …

Instabilities In Nematic Liquid Crystal Films And Droplets, Michael-Angelo Y.-H. Lam

Dissertations

The dynamics of thin films of nematic liquid crystal (NLC) are studied. Nematic liquid crystals are a type of non-Newtonian fluid with anisotropic viscous effects (due to the shape of the molecules) and elasticity effects (due to interacting electrical dipole moments). Exploiting the small aspect ratio in the geometry of interest, a fourth-order non-linear partial differential equation is used to model the free surface of the thin films. Particular attention is paid to the interplay between the bulk elasticity and the preferred orientation (boundary condition) of NLC molecules at the two interfaces: the substrate and the free surface. This work …

Mathematical Models For Polymer-Nematic Interactions, Ensela Mema

Dissertations

This dissertation considers a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field may be applied. Particular attention is paid to the effect of an applied field on the layer as well as the interaction between the liquid crystal molecules and the molecules of the substrate. The system studied may be considered as a simple model of a Liquid Crystal Display (LCD) device, and the results obtained are discussed and interpreted within this context.

The first part of this dissertation considers a study that investigates how the number …

Topics On Multiple Hypotheses Testing And Generalized Linear Model, Yalin Zhu

Dissertations

In applications such as studying drug adverse events (AE) in clinical trials and identifying differentially expressed genes in microarray experiments, the data of the experiments usually consists of frequency counts. In the analysis of such data, researchers often face multiple hypotheses testing based on discrete test statistics. Incorporating this discrete property of the data, several stepwise procedures, which allow to use the CDF of p-values to determine the testing threshold, are proposed for controlling familiwise error rate (FWER). It is shown that the proposed procedures strongly control the FWER and are more powerful than the existing ones for discrete data. …

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 …