Physics Commons^™

Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa

Doctoral Dissertations

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms.

This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A …

Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias

Doctoral Dissertations

In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ⁴ Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …

A Framework Of Multi-Dimensional And Multi-Scale Modeling With Applications, Zilong Li

Doctoral Dissertations

In this dissertation, a framework for multi-dimensional and multi-scale modeling is proposed. The essential idea is based on oriented space curves, which can be represented as a 3D slender object or 1D step parameters. SMILES and Masks provide functionalities that extend slender objects into branched and other objects. We treat the conversion between 1D, 2D, 3D, and 4D representations as data unification. A mathematical analysis of different methods applied to helices (a special type of space curves) is also provided. Computational implementation utilizes Model-ViewController design principles to integrate data unification with graphical visualizations to create a dashboard. Applications of multi-dimensional …

Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack

Doctoral Dissertations

We develop a nonequilibrium statistical mechanical description of the evolution of point vortex systems governed by either the Euler, single-layer quasigeostrophic or two-layer quasigeostrophic equations. Our approach is based on a recently proposed optimal closure procedure for deriving reduced models of Hamiltonian systems. In this theory the statistical evolution is kept within a parametric family of distributions based on the resolved variables chosen to describe the macrostate of the system. The approximate evolution is matched as closely as possible to the true evolution by minimizing the mean-squared residual in the Liouville equation, a metric which quantifies the information loss rate …

Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, Joel Anthony Mazer

Doctoral Dissertations

In relativistic heavy ion collisions at the Large Hadron Collider (LHC), a hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced. Quarks and gluons from incoming nuclei collide to produce partons at high momenta early in the collisions. By fragmenting into collimated sprays of hadrons, these partons form 'jets'. Within the framework of perturbative Quantum Chromodynamics (pQCD), jet production is well understood in pp collisions. We can use jets measured in pp interactions as a baseline reference for comparing to heavy ion collision systems to detect and study jet quenching. The jet quenching mechanism …

Surface Energy In Bond-Counting Models On Bravais And Non-Bravais Lattices, Tim Ryan Krumwiede

Doctoral Dissertations

Continuum models in computational material science require the choice of a surface energy function, based on properties of the material of interest. This work shows how to use atomistic bond-counting models and crystal geometry to inform this choice. We will examine some of the difficulties that arise in the comparison between these models due to differing types of truncation. New crystal geometry methods are required when considering materials with non-Bravais lattice structure, resulting in a multi-valued surface energy. These methods will then be presented in the context of the two-dimensional material graphene in a way that correctly predicts its equilibrium …

Numerical Solutions For Problems With Complex Physics In Complex Geometry, Yifan Wang

Doctoral Dissertations

In this dissertation, two high order accurate numerical methods, Spectral Element Method (SEM) and Discontinuous Galerkin method (DG), are discussed and investigated. The advantages of both methods and their applicable areas are studied. Particular problems in complex geometry with complex physics are investigated and their high order accurate numerical solutions obtained by using either SEM or DG are presented. Furthermore, the Smoothed Particle Hydrodynamics (SPH) (a mesh-free weighted interpolation method) is implemented on graphics processing unit (GPU). Some numerical simulations of the complex flow with a free surface are presented and discussed to show the advantages of SPH method in …

A Viscous Flow Analog To Prandtl’S Optimized Lifting Line Theory Utilizing Rotating Biquadratic Bodies Of Revolution, Mark Nathaniel Callender

Doctoral Dissertations

Prandtl’s lifting line theory expanded the Kutta-Joukowski theorem to calculate the lift and induced drag of finite wings. The circulation distribution about a real wing was represented by a superposition of infinitesimal vortex filaments. From this theory, the optimum distribution of circulation was determined to be elliptical. A consequence of this theory led to the prediction that the elliptical chord distribution on a real fixed wing would provide the elliptical circulation distribution. The author applied the same line of reasoning to lift-producing rotating cylinders in order to determine the cylindrical geometry that would theoretically produce an elliptical circulation distribution. The …

Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson

Doctoral Dissertations

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models …

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, …

Energy Functional For Nuclear Masses, Michael Giovanni Bertolli

Doctoral Dissertations

An energy functional is formulated for mass calculations of nuclei across the nuclear chart with major-shell occupations as the relevant degrees of freedom. The functional is based on Hohenberg-Kohn theory. Motivation for its form comes from both phenomenology and relevant microscopic systems, such as the three-level Lipkin Model. A global fit of the 17-parameter functional to nuclear masses yields a root- mean-square deviation of χ[chi] = 1.31 MeV, on the order of other mass models. The construction of the energy functional includes the development of a systematic method for selecting and testing possible functional terms. Nuclear radii are computed within …

Electronic Excitations In Ytio3 Using Tddft And Electronic Structure Using A Multiresolution Framework, William Scott Thornton

Doctoral Dissertations

We performed ab initio studies of the electronic excitation spectra of the ferro- magnetic, Mott-insulator YTiO3 using density functional theory (DFT) and time- dependent density functional theory (TDDFT). In the ground state description, we included a Hubbard U to account for the strong correlations present within the d states on the cation. The excitation spectra was calculated using TDDFT linear response formalism in both the optical limit and the limit of large wavevector transfer. In order to identify the local d-d transitions in the response, we also computed the density response of YTiO3 using a novel technique where the basis …

Theoretical Models For Wall Injected Duct Flows, Tony Saad

Doctoral Dissertations

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by …