Other Mathematics Commons^™

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

An Alternative Approach To Non-Relativistic Quantum Mechanics In Curved Space, Robert A. Hulsey

Dissertations

In the research presented in this dissertation, we propose an alternative formulation of non-relativistic quantum mechanics in curved spaces (Riemannian manifolds). Some toy quantum models (2D quantum harmonic oscillator in Poincaré half-plane model and the flat chart model of hyperbolic 2-space) are studied to understand the physical implications of this alternative formulation.

A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte

Dissertations

Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.

Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, Svetlana Nikic

Dissertations

Teachers’ effectiveness is associated with their instructional practices and is ultimately linked to students’ learning outcomes. In order to impact teachers’ effectiveness, schools focus substantial effort and resources on professional development led by an assumption that teachers’ classroom practices can be improved through targeted interventions. Even if this premise is correct, little information is available about how much a teacher’s practice may change through interventions, or which aspects of instructional practice are more receptive to improving teacher effectiveness (Garret et al., 2019).

This study took place at an urban middle school and examined teachers’ responsiveness to targeted engagement intervention in …

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 …

Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson

Dissertations

As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval …

Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, Balaram Khatri Ghimire

Dissertations

In the numerical solution of partial differential equations (PDEs), it is common to find situations where the best choice is to use more than one method to arrive at an accurate solution. In this dissertation, hybrid Chebyshev polynomial scheme (HCPS) is proposed which is applied in two-step approach and one-step approach. In the two-step approach, first, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then, the resulting homogeneous equation is solved by boundary type methods including …

Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica

Dissertations

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …