Physical Sciences and Mathematics Commons^™

Investigation Of Student Understanding Of Representations Of Probability Concepts In Quantum Mechanics, William D. Riihiluoma

Electronic Theses and Dissertations

The ability to relate physical concepts and phenomena to multiple mathematical representations—and to move fluidly between these representations—is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered. Thus, developing the ability to generate and translate expressions in these notations is of great importance, and the extent to which students can relate these expressions to physical quantities and phenomena is crucial to understand.

To investigate student understanding of the expressions used in these notations and the ways they relate, clinical think-aloud interviews were conducted …

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi

Undergraduate Research Posters

We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.

Aps March Meeting 2021 (Online) Updates On Scientific Research During Pandemic Times, Vianney Gimenez-Pinto

Title III Professional Development Reports

While the ongoing global pandemic continues to affect our everyday lives, researchers in Science, Technology, Engineering and Math found a way to come together at the American Physical Society (APS) March Meeting 2021. The conference was online-only and had more than 11,000 registered attendants who actively participated in the program during March 14- 19, 2021.

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 …

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

Modelling Potential Fluctuations In Double Layer Graphene Systems As A Periodic Oscillation In Electron Density & Its Effect On Coulomb Drag, Ryan Bogucki

Williams Honors College, Honors Research Projects

An expression for the drag transresistivity in a graphene double layer system exhibiting potential fluctuations modelled as a periodic oscillation in electron density is derived. Our model starts from the Coulombic interaction and we derive the correlation between a sinusoidal fluctuation in electron density in the first layer and the induced electron density in the second layer. Previous models in the literature have employed an arbitrary correlation between each layer’s electron density, and the model presented is the first attempt in the literature to explicitly derive this correlation. Recent experiments have found that the drag transresistivity in graphene double layers …

Four Derivations Of Schrödinger’S Time Dependent Equation, Sydney Swanson

Essential Studies UNDergraduate Showcase

Physics and the natural world have been studied by humans since the first person wondered ‘Why?’ The Schrödinger equation is important because it attempts to describe a relatively new (to us) and unfamiliar part of our universe, behavior of subatomic particles, and helps modern scientists uncover secrets that have proven useful in technology and explaining our origins. The time dependent Schrödinger equation can be derived from various starting points in Classical such as the equation of a wave, the time independent Schrödinger equation, and Hamilton-Jacobi equations. Why Quantum mechanics exists, useful applications, and cases when it fails or is inaccurate …

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …

Math And Physics Activities, Maureen Miller, Hope Bragg, Christy Keefer

Integrated Math & Social Studies Lessons

Mathematics is at the core of the Hidden Figures story. These women were united by their passion for the field of mathematics. Society often portrays that there are “bad” math students, those that struggle with calculations and applications. The structure of these activities, pairing of students, permits students to support each other in working through the problems. The video clip allows students to establish connections between mathematical calculations and scientific concepts. The physics problems that students complete are motion problems that beginning rocket engineers would have solved to determine how high their rocket flew.

Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova

Physics Faculty Publications

This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

All At One Point: The New Physics Of Italo Calvino And Jorge Luis Borges, Mark Thomas Rinaldi

Dissertations, Theses, and Capstone Projects

This work of comparative literary criticism focuses on the presence of mathematical and scientific concepts and imagery in the works of Italo Calvino and Jorge Luis Borges, beginning with an historical overview of scientific philosophy and an introduction to the most significant scientific concepts of the last several centuries, before shifting to deep, scientifically-driven analyses of numerous individual fictions, and finally concluding with a meditation on the unexpectedly fictive aspects of science and mathematics. The close readings of these authors' fictions are contextualized with thorough explanations of the potential literary implications of theories from physics, mathematics, neuroscience and chaos theory. …

Structure Of Lipid Bilayers, John Nagle, Stephanie Tristram-Nagle

Prof. Stephanie Tristram-Nagle Ph.D.

The quantitative experimental uncertainty in the structure of fully hydrated, biologically relevant, fluid (L(alpha)) phase lipid bilayers has been too large to provide a firm base for applications or for comparison with simulations. Many structural methods are reviewed including modern liquid crystallography of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the L(alpha) phase. These fluctuations degrade the higher order diffraction data in a way that, if unrecognized, leads to erroneous conclusions regarding bilayer structure. Diffraction measurements at high instrumental resolution provide a measure of these fluctuations. In addition to providing better structural determination, this …

Student Application Of The Fundamental Theorem Of Calculus With Graphical Representations In Mathematics And Physics, Rabindra R. Bajracharya

Electronic Theses and Dissertations

One mathematical concept frequently applied in physics is the Fundamental Theorem of Calculus (FTC). Mathematics education research on student understanding of the FTC indicates student difficulties with the FTC. Similarly, a few studies in physics education have implicitly indicated student difficulties with various facets of the FTC, such as with the definite integral and the area under the curve representation, in physics contexts. There has been no research on how students apply the FTC in graphically-based physics questions.

This study investigated student understanding of the FTC and its application to graphically-based problems. Our interest spans several aspects of the FTC: …

Re-Analysis Of The World Data On The Emc Effect And Extrapolation To Nuclear Matter, Stacy E. Karthas

Honors Theses and Capstones

The EMC effect has been investigated by physicists over the past 30 years since it was discovered at CERN. This effect shows that the internal nucleon structure varies when in the nuclear medium. Data from SLAC E139 and JLab E03 103 were studied with the Coulomb correction and directly compared. The Coulomb distortion had a greater impact on the JLab data due to slightly lower energies and different kinematics. The EMC ratio was found to have a dependence on a kinematic variable, which was removed when Coulomb corrections were applied. The methodology was developed to apply Coulomb corrections, which had …

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 …

Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright

John B. Geddes

We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.

Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola

Dartmouth Scholarship

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

Objectivity, Information, And Maxwell's Demon, Steven Weinstein

Dartmouth Scholarship

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.