Mathematics Commons^™

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

Senior Honors Projects

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the …

Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Toda flow is a generalization of a dynamical system describing the interaction of particles in a one-dimensional crystal. The concepts and energy and conservation are prominent in the study of dynamical systems, and quantities which remain the same over the evolution of a system provide valuable insights into the system’s behavior. In the realm of mathematics these quantities are called first integrals, or integrals of motion. This paper provides a background for study of the Toda flow, a verification of its integrability, and programming code for finding these quantities which remain unchanged over the evolution of the system.

Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating

Articles

Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …

Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, systems follow the pattern set by the second law of thermodynamics: they evolve from an organized inhomogeneous state into a homogeneous structure-free state. In many other practical situations, however, we observe the opposite emergence phenomenon: in an originally homogeneous structure-free state, an inhomogeneous structure spontaneously appears. In this paper, we show that the analysis of random metric spaces provides a possible explanation for this phenomenon. We also show that a similar analysis supports space-time models in which proper space is discrete.

Volume 07, Rachel C. Lombardi, Ben Osterhout, Lindsay Graybill, Rebecca E. Dey, Skyler T. Carpenter, Emma Beckett, Jason Ware, Mollie Andrews, James Bates, Landon Cooper, Tiffani Jeffries, Maria Wheaton, Dallas Price, Laura Kahler, Sarah Charlton, Anna Bultrowicz, Emily Spittle, Erin Godwin, Eamon Brokenbrough

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Spatial Analysis of Potential Risk Factors Associated with Addition of Atlantic Coast Pipeline Through Virginia by Rachel C. Lombardi

"Delicate Matters with No Speaking," "Hope and Nothing," "Mono Duality" by Ben Osterhout

"Connect" Graphic Design Senior Project by Lindsay Graybill

Phenolic Acids in Brassicaceae Plants: Ovipositional Stimulants or Deterrents for Cabbage White Butterfly, Pieris Rapae? by Rebecca E. Dey And Skyler T. Carpenter

"Abecedarian Cards" by Emma Beckett, Jason Ware, And Mollie Andrews

Helvetica: A Type Specimen Book by James Bates, Landon Cooper, Tiffani Jeffries, And Maria Wheaton

“Things Left Behind” by Dallas …

Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos

Presentations and Publications

Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and elec- tromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equa- tions are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Ge- ometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and for- mulas for constructing …

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

A Unified And Preserved Dirichlet Boundary Treatment For The Cell-Centered Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura A. Schaefer

Publications

A new boundary treatment is proposed for the finite volume discrete Boltzmann method (FVDBM) that can be used for accurate simulations of curved boundaries and complicated flow conditions. First, a brief review of different boundary treatments for the general Boltzmann simulations is made in order to primarily explain what type of boundary treatment will be developed in this paper for the cell-centered FVDBM. After that, the new boundary treatment along with the cell-centered FVDBM model is developed in detail. Next, the proposed boundary treatment is applied to a series of numerical tests with a detailed discussion of its qualitative and …

Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen

Philosophy Faculty Articles and Research

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …

Quantum And Post-Newtonian Effects In The Anomalistic Period And The Mean Motion Of Celestial Bodies, Ioannis Haranas, Omiros Ragos, Ioannis Gkigkitzis, Ilias S. Kotsireas

Physics and Computer Science Faculty Publications

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on the orbiting body. More specifically, two equations are derived to approximate the perigee/perihelion/periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the quantum as well as post-Newtonian accelerations. Numerical results have been obtained for the artificial Earth satellite Molnya, Mercury, and, finally, the …

2015 Oklahoma Research Day Full Program, Northeastern State University

Oklahoma Research Day Abstracts

This document contains all abstracts from the 2015 Oklahoma Research Day held at Northeastern State University.

Analytic Structure Of The S-Matrix For Singular Quantum Mechanics, Horacio E. Camblong, Luis N. Epele, Huner Fanchiotti, Carlos A. García Canal

Physics and Astronomy

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.

Vacuum Polarization On The Brane, Cormac Breen, Matthew Hewitt,, Elizabeth Winstanley, Adrian Ottewill

Articles

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD braneworld scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation …

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Bifurcation Analysis Of Mutually Coupled Laser Systems, Vincent Brennan

Theses

Coupled laser systems have application in everyday modern life, including for example, telecommunications and cryptography. Therefore it is important to gain insight into the dynamic processes at work and theoretical modeling can elucidate such processes. The work presented in this thesis is primarily concerned with aspects such as excitability and phase locking in mutually coupled oscillators. Phase-only delay-coupled oscillator models are introduced to demonstrate excitability and it is subsequently shown that similar processes can occur in a low-dimensional variation of these models. Further, delay differential rate equation models also exhibit excitability and these are explored and contrasted with another, similar, …

Non-Planar On-Shell Diagrams, Sebastían Franco, Daniele Galloni, Brenda Penante, Congkao Wen

Publications and Research

We initiate a systematic study of non-planar on-shell diagrams in N = 4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the d log form of the on-shell form explicit. We make significant progress towards a general classification of arbitrary on-shell diagrams by means of two classes of combinatorial objects: generalized matching and matroid polytopes. We propose a boundary measurement that connects general on-shell diagrams to the Grassmannian. Our proposal exhibits two important and non-trivial properties: positivity in the planar case and it matches the combinatorial description of the diagrams in …

Differentiability Of Correlations In Realistic Quantum Mechanics, Alejandro Cabrera, Edson De Faria, Enrique Pujals, Charles Tresser

Publications and Research

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed …

Robust Fast Direct Integral Equation Solver For Quasi-Periodic Scattering Problems With A Large Number Of Layers, Min Hyung Cho, Alex H. Barnett

Dartmouth Scholarship

We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust at all scattering parameters, unlike the conventional quasi-periodic Green’s function method which fails whenever any of the layers approaches a Wood anomaly. We achieve this by a decomposition into near- and far-field contributions. The former uses the free-space Green’s function in a second-kind integral equation on one period of the material interfaces and their immediate left and right neighbors; the latter uses proxy point sources and small …

Question 1: Shaving Time; Question 2: Half-Filling The Gas Tank, Larry Weinstein

Physics Faculty Publications

How much total time does a typical American spend shaving during his or her life? How much total time per year do Americans spend shaving?

How much money can you save by only half-filling your car's gas tank to reduce weight?

Question 1: "Up" — A Fermi Question About Buoyancy; Question 2: Traffic Jams, Larry Weinstein

Physics Faculty Publications

Is it possible for a house to fly by the uplift of balloons, like in the movie "Up"? (written by R. Allart, A. Cazenave, and A. Müller, University of Geneva)

How much total time do Americans spend waiting in traffic each year? What is the total cost of this time?

Question 1: Kill The K-Cup; Question 2: Water Cooling, Larry Weinstein

Physics Faculty Publications

According to KillTheKCup.org, single-use non-recyclable Keurig K-cups “are killing our planet.” How large is the environmental impact of K-Cups?

How much more cooling do you get from drinking cold rather than room-temperature water on a hot day? How much do you sweat per day when the ambient temperature is about 35 °C (95 °F)?

Hamiltonian Approach To Internal Wave-Current Interactions In A Two-Media Fluid With A Rigid Lid, Alan Compelli, Rossen Ivanov

Articles

We examine a two-media 2-dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface with wind generated surface waves but considered bounded above by a lid by an assumption that surface waves have negligible amplitude. An internal wave driven by gravity which propagates in the positive x-direction acts as a free common interface between the media. The current is such that it is zero at the flatbed but a negative constant, due to an assumption that surface winds blow in the negative x-direction, at the lid. We are concerned …

Fundamental Mathematics Of Consciousness, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

A Potential Foundation For Emergent Space-Time, Kevin H. Knuth, Newshaw Bahreyni

Physics Faculty Scholarship

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an …

Physics: Rethinking The Foundations, Kevin H. Knuth

Physics Faculty Scholarship

Physics is traditionally conceived of as a set of laws that universally governs the behavior of physical systems. These laws, however they are decreed, are believed to govern the behavior of not only everything in the universe, but the form of the universe itself. However, this traditional concept of physics as a universal governance is at odds with our modern theories of quantum mechanics and relativity, which place the observer and information in a central role. In this talk, I aim to rethink the foundations and attempt to build physics from the bottom up based on a very simple foundational …

Casimir Energies In Spherically Symmetric Background Potentials Revisited, Matthew Beauregard, Michael Bordag, Klaus Kirsten

Faculty Publications

In this paper we reconsider the formulation for the computation of the Casimir energy in spherically symmetric background potentials. Compared to the previous analysis, the technicalities are much easier to handle and final answers are surprisingly simple.

Fractal Growth On The Surface Of A Planet And In Orbit Around It, Ioannis Haranas, Ioannis Gkigkitzis, Athanasios Alexiou

Physics and Computer Science Faculty Publications

Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This property is also called self-similarity with several applications including nano-pharmacology and drug nanocarriers. We are interested in the study of the properties of fractal aggregates in a microgravity environment above an orbiting spacecraft. To model the effect we use a complete expression for the gravitational acceleration. In particular on the surface of the Earth the acceleration is …

The Mass Of Graviton And Its Relation To The Number Of Information According To The Holographic Principle, Ioannis Haranas, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

We investigate the relation of the mass of the graviton to the number of information 𝑁 in a flat universe. As a result we find that the mass of the graviton scales as 𝑚_gr ∝ 1/√𝑁. Furthermore, we find that the number of gravitons contained inside the observable horizon is directly proportional to the number of information 𝑁; that is, 𝑁_gr ∝ 𝑁. Similarly, the total mass of gravitons that exist in the universe is proportional to the number of information 𝑁; that is, 𝑀_gr ∝ √𝑁. In an effort to establish a relation between the graviton …