Other Mathematics Commons^™

Measuring The Lengths Of Sperm Whales Of The Northern Gulf Of Mexico By Wavelet Analysis Of Their Usual Clicks, George Drouant

University of New Orleans Theses and Dissertations

Abstract

Acoustic recordings of underwater sounds produced by marine mammals present an attractive alternative to costly and logistically complex ship based visual surveys for collecting population data for various species.

The first reported use of underwater acoustic recordings in the long-term monitoring of sperm whale populations was by Ackleh et al. (Ackleh et al., 2012). The paper describes counting sperm whale clicks at different locations to track population changes over time.

Analysis of sperm whale clicks offers additional insight into sperm whale populations. The echo location clicks (usual clicks) of sperm whales can be used to give an estimate of …

General Covariance With Stacks And The Batalin-Vilkovisky Formalism, Filip Dul

Doctoral Dissertations

In this thesis we develop a formulation of general covariance, an essential property for many field theories on curved spacetimes, using the language of stacks and the Batalin-Vilkovisky formalism. We survey the theory of stacks, both from a global and formal perspective, and consider the key example in our work: the moduli stack of metrics modulo diffeomorphism. This is then coupled to the Batalin-Vilkovisky formalism–a formulation of field theory motivated by developments in derived geometry–to describe the associated equivariant observables of a theory and to recover and generalize results regarding current conservation.

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …

Dimentia: Footnotes Of Time, Zachary Hait

Senior Projects Spring 2021

Time from the physicist's perspective is not inclusive of our lived experience of time; time from the philosopher's perspective is not mathematically engaged, in fact Henri Bergson asserted explicitly that time could not be mathematically engaged whatsoever. What follows is a mathematical engagement of time that is inclusive of our lived experiences, requiring the tools of storytelling.

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

At The Interface Of Algebra And Statistics, Tai-Danae Bradley

Dissertations, Theses, and Capstone Projects

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals …

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 …

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

Nonlinear Coupled Effects In Nanomaterials, Sia Bhowmick

Theses and Dissertations (Comprehensive)

Materials at the nanoscale have different chemical, structural, and optoelectrical properties compared to their bulk counterparts. As a result, such materials, called nanomaterials, exhibit observable differences in certain physical phenomena. One such resulting phenomenon called the piezoelectric effect has played a crucial role in miniature self-powering electronic devices called nanogenerators which are fabricated by using nanostructures, such as nanowires, nanorods, and nanofilms. These devices are capable of harvesting electrical energy by inducing mechanical strain on the individual nanostructures. Electrical energy created in this manner does not have environmental limitations. In this thesis, important coupled effects, such as the nonlinear piezoelectric …

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne

Mathematics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

Invisibility: A Mathematical Perspective, Austin G. Gomez

CMC Senior Theses

The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. …

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett

Theses and Dissertations

This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. The three level system consists of an alkali metal vapor, typically Rb or Cs, pumped by a diode from the ²S_1/2 state to the ²P_3/2 , a collisional relaxation from ²P_3/2 to ²P_{1/ 2} , and then lasing from ²P_1/2 to ²S_1/2 . The hyperfine absorption and emission cross sections for these transitions are developed in detail. Differential equations for intra-gain pump attenuation …