Physical Sciences and Mathematics Commons^™

Bacterial Motion And Spread In Porous Environments, Yasser Almoteri

Dissertations

Micro-swimmers are ubiquitous in nature from soil and water to mammalian bodies and even many technological processes. Common known examples are microbes such as bacteria, micro-algae and micro-plankton, cells such as spermatozoa and organisms such as nematodes. These swimmers live and have evolved in multiplex environments and complex flows in the presence of other swimmers and types, inert particles and fibers, interfaces and non-trivial confinements and more. Understanding the locomotion and interactions of these individual micro-swimmers in such impure viscous fluids is crucial to understanding the emergent dynamics of such complex systems, and to further enabling us to control and …

Fluid Dynamics Of Interacting Particles: Bouncing Droplets And Colloid-Polymer Mixtures, Lauren Barnes

Dissertations

Interacting particles are a common theme across various physical systems, particularly on the atomic and sub-atomic scales. While these particles cannot be seen with the human eye, insight into such systems can be gained by observing macroscopic systems whose physical behavior is similar. This dissertation consists of three different chapters, each presenting a different problem related to interacting particles, as follows:

Chapter 1 explores chaotic trajectories of a droplet bouncing on the surface of a vertically vibrating fluid bath, with a simple harmonic force acting on the droplet. The bouncing droplet system has attracted recent interest because it exhibits behaviors …

Boundary Integral Equation Methods For Superhydrophobic Flow And Integrated Photonics, Kosuke Sugita

Dissertations

This dissertation presents fast integral equation methods (FIEMs) for solving two important problems encountered in practical engineering applications.

The first problem involves the mixed boundary value problem in two-dimensional Stokes flow, which appears commonly in computational fluid mechanics. This problem is particularly relevant to the design of microfluidic devices, especially those involving superhydrophobic (SH) flows over surfaces made of composite solid materials with alternating solid portions, grooves, or air pockets, leading to enhanced slip.

The second problem addresses waveguide devices in two dimensions, governed by the Helmholtz equation with Dirichlet conditions imposed on the boundary. This problem serves as a …

Continuum Modeling Of Active Nematics Via Data-Driven Equation Discovery, Connor Robertson

Dissertations

Data-driven modeling seeks to extract a parsimonious model for a physical system directly from measurement data. One of the most interpretable of these methods is Sparse Identification of Nonlinear Dynamics (SINDy), which selects a relatively sparse linear combination of model terms from a large set of (possibly nonlinear) candidates via optimization. This technique has shown promise for synthetic data generated by numerical simulations but the application of the techniques to real data is less developed. This dissertation applies SINDy to video data from a bio-inspired system of mictrotubule-motor protein assemblies, an example of nonequilibrium dynamics that has posed a significant …

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

Bright Light Therapy And Depression: Assessing Suitability Using Entrainment Maps, Charles A. Mainwaring

Theses

Bright Light Therapy has been shown to be efficacious to mood disorders including Major Depression. Researchers use the Jewett-Forger-Kronauer model of the circadian rhythm with the Unified Model of melatonin including a mathematical term implementing feedback from the melatonin system into the circadian system to quantify the effects of bright light. Early investigations into intrinsic period, light sensitivity, and the circadian pacemaker's sensitivity to blood melatonin concentration may be indicators of subsets of patients with long intrinsic periods exhibiting symptoms of depression.

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

Numerical Methods For Optimal Transport And Optimal Information Transport On The Sphere, Axel G. R. Turnquist

Dissertations

The primary contribution of this dissertation is in developing and analyzing efficient, provably convergent numerical schemes for solving fully nonlinear elliptic partial differential equation arising from Optimal Transport on the sphere, and then applying and adapting the methods to two specific engineering applications: the reflector antenna problem and the moving mesh methods problem. For these types of nonlinear partial differential equations, many numerical studies have been done in recent years, the vast majority in subsets of Euclidean space. In this dissertation, the first major goal is to develop convergent schemes for the sphere. However, another goal of this dissertation is …

Optimization Opportunities In Human In The Loop Computational Paradigm, Dong Wei

Dissertations

An emerging trend is to leverage human capabilities in the computational loop at different capacities, ranging from tapping knowledge from a richly heterogeneous pool of knowledge resident in the general population to soliciting expert opinions. These practices are, in general, termed human-in-the-loop (HITL) computations.

A HITL process requires holistic treatment and optimization from multiple standpoints considering all stakeholders: a. applications, b. platforms, c. humans. In application-centric optimization, the factors of interest usually are latency (how long it takes for a set of tasks to finish), cost (the monetary or computational expenses incurred in the process), and quality of the completed …

Periodic Fast Multipole Method, Ruqi Pei

Dissertations

Applications in electrostatics, magnetostatics, fluid mechanics, and elasticity often involve sources contained in a unit cell C, centered at the origin, on which periodic boundary condition are imposed. The free-space Green’s functions for many classical partial differential equations (PDE), such as the modified Helmholtz equation, are well-known. Among the existing schemes for imposing the periodicity, three common approaches are: direct discretization of the governing PDE including boundary conditions to yield a large sparse linear system of equations, spectral methods which solve the governing PDE using Fourier analysis, and the method of images based on tiling the plane with copies of …

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 …

Coherent Control Of Dispersive Waves, Jimmie Adriazola

Dissertations

This dissertation addresses some of the various issues which can arise when posing and solving optimization problems constrained by dispersive physics. Considered here are four technologically relevant experiments, each having their own unique challenges and physical settings including ultra-cold quantum fluids trapped by an external field, paraxial light propagation through a gradient index of refraction, light propagation in periodic photonic crystals, and surface gravity water waves over shallow and variable seabeds. In each of these settings, the physics can be modeled by dispersive wave equations, and the technological objective is to design the external trapping fields or propagation media such …

Advances In Modeling Gas Adsorption In Porous Materials For The Characterization Applications, Max A. Maximov

Dissertations

The dissertation studies methods for mesoporous materials characterization using adsorption at various levels of scale and complexity. It starts with the topic introduction, necessary notations and definitions, recognized standards, and a literature review.

Synthesis of novel materials requires tailoring of the characterization methods and their thorough testing. The second chapter presents a nitrogen adsorption characterization study for silica colloidal crystals (synthetic opals). These materials have cage-like pores in the range of tens of nanometers. The adsorption model can be described within a macroscopic approach, based on the Derjaguin-Broekhoff-de Boer (DBdB) theory of capillary condensation. A kernel of theoretical isotherms is …

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 …

Intermittent Dynamics Of Dense Particulate Matter, Chao Cheng

Dissertations

Granular particle systems are scattered around the universe, and they can behave like solids when there exist strong force-bearing networks, so that the granular system can resist certain stress without deformation. When such a network is not present, particles yield to small stress and behave like a fluid. A wide range of systems exhibit intermittent dynamics as they are slowly loaded, with different dynamical regimes governing many industrial and natural phenomena. While a significant amount of research on exploring intermittent dynamics of granular systems has been carried out, not much is known about the connection between particle-scale response and the …

Eigenvalue Problems For Fully Nonlinear Elliptic Partial Differential Equations With Transport Boundary Conditions, Jacob Lesniewski

Dissertations

Fully nonlinear elliptic partial differential equations (PDEs) arise in a number of applications. From mathematical finance to astrophysics, there is a great deal of interest in solving them. Eigenvalue problems for fully nonlinear PDEs with transport boundary conditions are of particular interest as alternative formulations of PDEs that require data to satisfy a solvability condition, which may not be known explicitly or may be polluted by noisy data. Nevertheless, these have not yet been well-explored in the literature. In this dissertation, a convergence framework for numerically solving eigenvalue problems for fully nonlinear PDEs is introduced. In addition, existing two-dimensional methods …

Finite Element Modeling Of Underwater Acoustic Environments And Domain Decomposition Methods, General Ozochiawaeze

Theses

Underwater acoustic scattering problems have several important applications ranging from sonar imaging in target detection to providing information for sediment classification and geoacoustic inversion. This work presents numerical methods for time-harmonic acoustic scattering problems, specifically, finite element methods for the Helmholtz equation. Furthermore, an iterative domain decomposition formulation is introduced for acoustic scattering problems where the physical domain consists of multiple layers of different materials.

Dances And Escape Of The Vortex Quartet, Brandon Behring

Dissertations

This dissertation considers the linear stability of a one-parameter family of periodic solutions of the four-vortex problem known as 'leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W. Gröbli (1877) and A. E. H. Love (1883) and can be parameterized by a dimensionless parameter related to the geometry of the initial configuration. Simulations by Acheson and numerical Floquet analysis by Tophøj and Aref both indicate, to many digits, that the bifurcation occurs at a value related to the inverse square of the golen ratio. Acheson observed that, after an initial period …

Convergence Of The Boundary Integral Method For Interfacial Stokes Flow, Keyang Zhang

Dissertations

Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no analysis of the convergence of these methods for interfacial Stokes flow. In practice, the stability of discretizations of the boundary integral formulation can depend sensitively on details of the discretization and on the application of numerical filters. A convergence analysis of the boundary integral method for Stokes flow …

Mathematical Models And Tools To Understand Coupled Circadian Oscillations And Limit Cycling Systems, Guangyuan Liao

Dissertations

The circadian rhythm refers to an internal body process that regulates many body processes including the sleep-wake cycle, digestion and hormone release. The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of the most important properties. There are several scenarios in which circadian oscillators do not directly receive light-dark forcing. Instead they are part of hierarchical systems in which, as \peripheral" oscillators, they are periodically forced by other \central" circadian oscillators that do directly receive light input. Such dynamics are modeled as hierarchical coupled limit cycle systems. Those models usually have a large population, …

Efficient Approximations For Stationary Single-Channel Calcium Nanodomains, Yinbo Chen

Dissertations

Mathematical and computational modeling plays an important role in the study of local Ca2+ signals underlying many fundamental physiological processes such as synaptic neurotransmitter release and myocyte contraction. Closed-form approximations describing steady-state distribution of Ca2+ in the vicinity of an open Ca2+ channel have proved particularly useful for the qualitative modeling of local Ca2+ signals. This dissertation presents several simple and efficient approximants for the equilibrium Ca2+ concentration near a point source in the presence of a mobile Ca2+ buffer, which achieve great accuracy over a wide range of model parameters. Such approximations provide an efficient method for estimating Ca2+ …

Global Optimization Algorithms For Image Registration And Clustering, Cuicui Zheng

Dissertations

Global optimization is a classical problem of finding the minimum or maximum value of an objective function. It has applications in many areas, such as biological image analysis, chemistry, mechanical engineering, financial analysis, deep learning and image processing. For practical applications, it is important to understand the efficiency of global optimization algorithms. This dissertation develops and analyzes some new global optimization algorithms and applies them to practical problems, mainly for image registration and data clustering.

First, the dissertation presents a new global optimization algorithm which approximates the optimum using only function values. The basic idea is to use the points …

Towards Practical Homomorphic Encryption And Efficient Implementation, Gyana R. Sahu

Dissertations

Cloud computing has gained significant traction over the past few years and its application continues to soar as evident from its rapid adoption in various industries. One of the major challenges involved in cloud computing services is the security of sensitive information as cloud servers have been often found to be vulnerable to snooping by malicious adversaries. Such data privacy concerns can be addressed to a greater extent by enforcing cryptographic measures. Fully homomorphic encryption (FHE), a special form of public key encryption has emerged as a primary tool in deploying such cryptographic security assurances without sacrificing many of the …

Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater

Dissertations

Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity

In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this …

Coding Against Stragglers In Distributed Computation Scenarios, Malihe Aliasgari

Dissertations

Data and analytics capabilities have made a leap forward in recent years. The volume of available data has grown exponentially. The huge amount of data needs to be transferred and stored with extremely high reliability. The concept of "coded computing", or a distributed computing paradigm that utilizes coding theory to smartly inject and leverage data/computation redundancy into distributed computing systems, mitigates the fundamental performance bottlenecks for running large-scale data analytics.

In this dissertation, a distributed computing framework, first for input files distributedly stored on the uplink of a cloud radio access network architecture, is studied. It focuses on that decoding …

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 …

Topics On High Dimensional Selective Inference, Yan Zhang

Dissertations

In such applications as identifying differentially expressed genes in micro-array experiments or assessing safety and efficacy of drugs in clinical trials, researchers often report confidence intervals (CIs) and p-values only for the selected parameters, which is called selective inference. While constructing multiple CIs for the selected parameters, it is common practice to ignore issue of selection and multiplicity. Although protection against the effect of selection is sufficient in some cases, simultaneous coverage should be also needed in real applications. For example, in clinical trials, multiple endpoints are considered to assess effects of a drug and the ultimate decision often depends …