Physical Sciences and Mathematics Commons^™

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

Explicit Synchronized Solitary Waves For Some Models For The Interaction Of Long And Short Waves In Dispersive Media., Bruce Brewer

Fall Student Research Symposium 2021

Four systems have recently been proposed for the study of the interaction of long and short waves in dispersive media. This poster establishes the synchronized solitary wave solutions for one of these systems.

Tractor Connections For Killing Tensors And Their Generalizations, Benjamin D. Shaw

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We create new symbolic software tools for the analysis of Killing tensors. Central to our work is the construction of the tractor connection defined on the tractor bundle, which allows one to obtain information about the space of Killing tensors without solving the Killing equations–an approach termed the tractor approach. We give a new application of the tractor approach which allows one to more easily check explicitly for linear independence of a given set of Killing tensors. We develop software to implement such methods in the case of rank 2 Killing tensors; similarly, we develop software to implement analogous methods …

On The Geometry Of The Moduli Space Of Certain Lattice Polarized K3 Surfaces And Their Picard-Fuchs Operators, Michael T. Schultz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

K3 surfaces have a long and rich study in mathematics, and more recently in physics via string theory. Often, K3 surfaces come in multiparameter families - the parameters describing these surfaces fit together to form their own geometric space, a so-called moduli space. In particular, the moduli spaces of K3 surfaces equipped with a lattice polarization can sometimes be constructed explicitly, which subsequently reveals important information about the original K3 surface.

In this work, we construct such families explicitly from certain rational elliptic surfaces via the so-called mixed-twist construction of Doran & Malmendier, which in turn produces the moduli …

Transformation Groups And The Method Of Darboux, Brandon P. Ashley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In the study of partial differential equations (PDE), one is often concerned as to whether or not explicit solutions can be obtained via various integration techniques. One such technique, known as the method of Darboux, has had particular success in solving nonlinear problems as demonstrated by the classical works of Goursat. Recently, Anderson, Fels, and Vassiliou provided a far-reaching generalization of Vessiot’s group-theoretic interpretation of the method of Darboux. This generalization allows for the characterization of Darboux integrable systems in terms of fundamental geometric invariants as well as the construction of Darboux integrable systems in general.

In this work, we …

Physics-Informed Structure-Preserving Numerical Approximations Of Thermodynamically Consistent Models For Non-Equilibrium Phenomena, Jia Zhao

Funded Research Records

No abstract provided.

Mathematical Models And Homogenization Of Deer Dispersal, Environmental Hazard, And Direct/Indirect Transmission To Predict Spread Of Chronic Wasting Disease, James A. Powell

Funded Research Records

No abstract provided.

Regionalized Models With Spatially Continuous Predictions At The Borders, Jadon S. Wagstaff

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Creating maps of continuous variables involves estimating values between measurement locations scattered throughout a geographic region. These maps often leverage observed similarities between geographically close measurements, but may also make predictions using other geographic information such as elevation. The relationship between the available geographic information and the variable of interest can vary with location, especially when mapping large areas like a continent. A simple way to account for the changing relationship is to divide the space into different sub-regions and model the relationship at each region. The naive implementation of this approach has the side effect of making sudden changes …

Studies Of Classical Analysis After Whittaker And Watson, Ting-Yao Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The goal of this thesis is to solve problems from the first four chapters of the book, titled A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions with an Account of the Principal Transcendental Functions by E.T. Whittaker and G.N. Watson. The titles of the first four chapters are “Complex Numbers,” “The Theory of Convergence,” “Continuous Functions and Uniform Convergence,” and “The Theory of Riemann Integration,” respectively. This book is a classic mathematical analysis textbook that contains some challenging end-of-chapter exercises and some details within each chapter are often left to …

Ground Snow Loads For Asce 7-22 – What Has Changed And Why?, Marc Maguire, Brennan L. Bean, James Harris, Abbie Liel, Scott Russell

Mathematics and Statistics Faculty Publications

The changes to the ASCE 7 ground snow load maps proposed for the 2022 edition target a uniform reliability rather than a uniform hazard – an important distinction – and are the first of their kind in ASCE 7. Previously, the ASCE 7 snow loads used a uniform-hazard 50-year mean recurrence interval (MRI) with a 1.6 load factor. The newly proposed loads directly target the safety levels stipulated in Chapter 1 of ASCE 7, resulting in a strength design level load that is to be used with a load factor of 1.0. This paper describes changes in design provisions that …

The 2020 National Snow Load Study, Brennan L. Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers

Mathematics and Statistics Faculty Publications

The United States has a rich history of snow load studies at the state and national level. The current ASCE 7 snow loads are based on studies performed at the Cold Regions Research and Engineering Laboratory (CRREL) ca. 1980 and updated ca. 1993. The map includes large regions where a site-specific case study is required to establish the load. Many state reports attempt to address the "case-study regions" designated in the current ASCE 7 design snow load requirements. The independently developed state-specific requirements vary in approach, which can lead to discrepancies in requirements at state boundaries. In addition, there has …