Physics 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 …

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 …

A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov

Dissertations

Currently, all forecasts of currents, waves, and seafloor evolution are limited by a lack of fundamental knowledge and the parameterization of small-scale processes at the seafloor-ocean interface. Commonly used Euler-Lagrange models for sediment transport require parameterizations of the drag and lift forces acting on the particles. However, current parameterizations for these forces only work for spherical particles. In this dissertation we propose a new method for predicting the drag and lift forces on arbitrarily shaped objects at arbitrary orientations with respect to the direction of flow that will ultimately provide models for predicting the sediment sorting processes that lead to …

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 …

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 …

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 …

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 …

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 …

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 …

Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives, Maxsimo Salazar

Dissertations

Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of …

Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami

Dissertations

We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. …

Relativistic Studies Of The Charmonium And Bottomonium Systems Using The Sucher Equation, Charles Martin Werneth

Dissertations

In this dissertation, bound states of quarks and anti-quarks (mesons) are studied with a relativistic equation known as the Sucher equation. Prior to the work in this dissertation, the Sucher equation had never been used for meson mass spectra. Furthermore, a full angular momentum analysis of the Sucher equation has never been studied. The Sucher equation is a relativistic equation with positive energy projectors imposed on the interaction. Since spin is inherent to the equation, the Sucher equation is equivalent to a relativistic Schrödinger equation with a spin-dependent effective potential. Through a complete general angular momentum analysis of the equation, …

Studies Of Meson Mass Spectra In The Context Of Quark-Antiquark Bound States, Mallika Dhar

Dissertations

This dissertation deals with the computation of meson mass spectra in the context of quarkantiquark (q ¯ q) bound-state. Traditionally the q ¯ q bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is necessary. It is well known that relativistic kinematics cannot be treated properly in position representation, but it can easily be handled in momentum representation. On the other hand, the linear potential and Coulomb-like potential have singularities in momentum-space and complicated subtraction procedure is necessary to treat the …