Mathematics Commons^™

Solutions For Fermi Questions, September 2021: Question 1: Cell Phone Gold, Question 2: Food For Thought, Larry Weinstein

Physics Faculty Publications

Answers to the questions: "How much gold is in a cell phone? Is it worth mining cell phones for gold?"

Solutions For Femi Questions, October 2021: Rising Water Level: Popping Many Pimples, Larry Weinstein

Physics Faculty Publications

[Introduction] How much would sea levels rise if everyone jumped in the ocean? (Thanks to Bob Friedhoffer for suggesting the problem.)

To estimate this, we need to know the number of people, the average volume of a person, and the area of the oceans. This is the kind of estimation problem where the inputs are relatively well known, and we are calculating the answer to see its order of magnitude.

There are about 7 X 10⁹ people in the world. If each person has a mass of 100 kg (in round numbers), then they each have a volume …

Question 1: Chess Moves; Question 2: Cat Litter, Larry Weinstein

Physics Faculty Publications

How many chess moves are made by Americans each year?

How much cat litter did Americans scoop last year?

Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen

Articles

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …

Numerical Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Method, Charles Armstrong, Yan Peng

Mathematics & Statistics Faculty Publications

In this work a quasisteady, dual time-stepping lattice Boltzmann method is proposed for simulation of capsule deformation. At each time step the steady-state lattice Boltzmann equation is solved using the full approximation storage multigrid scheme for nonlinear equations. The capsule membrane is modeled as an infinitely thin shell suspended in an ambient fluid domain with the fluid structure interaction computed using the immersed boundary method. A finite element method is used to compute the elastic forces exerted by the capsule membrane. Results for a wide range of parameters and initial configurations are presented. The proposed method is found to reduce …

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 …

Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians, Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar

Publications and Research

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J⁽ⁿ⁾ of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator …

Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study, Kevin Vehar

KGI Theses and Dissertations

The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation's physical resource demand. Specifically, …

Eureka Moment As Divine Spark In The Light Of Direct Experience With The Spirit And Nature, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the ancient world, the Greeks believed that all great insights came from one of nine muses, divine sisters who brought inspiration to mere mortals. In the modern world, few people still believe in the muses, but we all still love to hear stories of sudden inspiration. Like Newton and the apple, or Archimedes and the bathtub (both another type of myth), we’re eager to hear and to share stories about flashes of insight. But what does it take to be actually creative? How to have such a flash insight? Turns out, there is real science behind "aha moments." We …

Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.

An Update On The Computational Theory Of Hamiltonian Period Functions, Bradley Joseph Klee

Graduate Theses and Dissertations

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple …

Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans, Zachary Mobille, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov

Mathematics & Statistics ETDs

In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …

Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova

Mathematics & Statistics ETDs

The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …

Effective Number Theory: Counting The Identities Of A Quantum State, Ivan Horváth, Robert Mendris

Anesthesiology Faculty Publications

Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a “total” that takes into account their varied relevance. For example, such an effective count of position states available to a lattice electron could characterize its localization properties. Similarly, the effective total of outcomes in the measurement step of a quantum computation relates to the efficiency of the quantum algorithm. Despite a broad need for effective counting, a well-founded prescription has not …

Period Estimation And Noise In A Neutrally Stable Stochastic Oscillator, Kevin R. Sanft, Ben F. M. Intoy

Spora: A Journal of Biomathematics

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

Making Artificial Cips Data With A Generative Adversarial Neural Network, Austin Hedges

Fall Showcase for Research and Creative Inquiry

Polar mesospheric clouds (PMCs) have been studied for thirteen years by NASA's Aeronomy of Ice in the Mesosphere (AIM) satellite. The Cloud Imaging and Particle Size (CIPS) instrument onboard AIM has taken many images of PMCs over this time. Such a large number of images makes CIPS data ideal for training neural networks which require large datasets. CIPS images were used to train a Generative Adversarial Network (GAN) to train towards being able to generate purely artificial CIPS-like images.

Active Nonlocal Metasurfaces, Stephanie C. Malek, Adam C. Overvig, Sajan Shrestha, Nanfang Yu

Advanced Science Research Center

Actively tunable and reconfigurable wavefront shaping by optical metasurfaces poses a significant technical challenge often requiring unconventional materials engineering and nanofabrication. Most wavefront-shaping metasurfaces can be considered “local” in that their operation depends on the responses of individual meta-units. In contrast, “nonlocal” metasurfaces function based on the modes supported by many adjacent meta-units, resulting in sharp spectral features but typically no spatial control of the outgoing wavefront. Recently, nonlocal metasurfaces based on quasi-bound states in the continuum have been shown to produce designer wavefronts only across the narrow bandwidth of the supported Fano resonance. Here, we leverage the enhanced light-matter …

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T, I, F (truth, indeterminacy, falsehood) which can take a range of values. A previous paper in IJNS, 2020 shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. In any case, matter creation process in nature stays a major puzzle for physicists, scientists and other science analysts. To this issue neutrosophic logic offers an answer: "unmatter." This paper examines an extended model of unmatter, to incorporate issue soul solidarity. So, …

Spacetime Groups, Ian M. Anderson, Charles G. Torre

All Physics Faculty Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs, (g, n), with g being a 4-dimensional Lie algebra and n being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely …

Influence Of The Nature Of The Medium On The Conformational States Of Macromolecules Of Anionic Polyelectrolytes And Their Flocculating Effect, Mapruza Dzhumamuratova, Amanbay Pirniyazov, Oleg Dormeshkin, Akhmed Reymov, Tleumuratov Kuanish, Saparbay Kalbaev

Karakalpak Scientific Journal

The properties of surfactants of anionic polyelectrolytes are investigated depending on the nature of the medium, conformational states neutralized by organic bases, differing in the length of the hydrocarbon radical. The concept of the role of the state of macromolecules in solution in the indicated processes has been developed. The anionic carboxyl-containing polyelectrolytes synthesized on the basis of methacrylic acid differed not only in the length of the hydrocarbon radical of the organic base - counterion, but also in their branching. The relationship between the state of polyelectrolyte macromolecules in solution and their ability to regulate the properties of natural …

Optical Soliton Perturbation With Quadratic-Cubic Nonlinearity, Asma Mir

Student Works (2020-2029)

Solitons can be defined as wave packets that can travel undistorted across long distances even transcontinental and transoceanic. They serve as modern telecommunication means through cables and optical fibers for fast Internet activities. To maintain high-fidelity and time sensitive transmission, optical pulses manage the efficient flow of data. From the last few years, Nonlinear Schrödinger Equation (NLSE) has been a great attraction of research activities across the globe. The governing model is the Nonlinear Schrödinger Equation (NLSE). From a mathematical standpoint, NLSE is a nonlinear partial differential equation (PDE) that has been studied in a variety of other areas of …

Topics In Gravitational Wave Physics, Aaron David Johnson

Graduate Theses and Dissertations

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Features Of Heart Activity Of Cattle In The Conditions Of Southern Aral Sea Region, Svetlana Mambetullaeva, Khayratdin Seytkamalov

Karakalpak Scientific Journal

In this article, the results of comparative analysis of electrocardiogram are shown for the cows of different breeds in the Aral Sea region. It is set that the high temperature of the environment and sunny insolation render a negative influence on the functional parameters of the cardiac vascular system of animals. There are facts about the cows of different breeds at the influence of different temperatures that have unidirectional functional changes in the operation of the heart. At the same time, we will mark that these changes are less expressed for the cows of the improved zebu visible cattle, what …

Photoelectric Injection Amplification Of Al–Al2o3–P-Cdte–Mo Structures At Low Bias Voltages, A K. Uteniyazov

Karakalpak Scientific Journal

The results of studies of photoelectric injection enhancement of the Al–Al₂O₃–p-CdTe –Mo structure upon application of low bias voltages. It has been shown that the studied Al-Al₂O₃–p-CdTe-Mo structure under can be represented as a n⁺-p-R_ом structure with a long base. Conducted researches show that Al-Al₂O₃–p-CdTe-Mo structure has unique properties. It has very high photocurrent and photosensitivity at both direct and reverse dias voltage under even small bias voltage (up to 500mV).

Synthesis Of Supramolecular Complex L– (-) – Menthol, Ziyada Djumanova Dr, Lolaxan Ettibaeva, Ugilay Abduraxmonova, Zulfiya Khalmuratova

Karakalpak Scientific Journal

In this article glycyrrhizic acid content with menthol in several various proportions (2:1; 4:1; 9:1), information was given on synthesis and physical and chemical properties of new supermolecular complexes. Received supramolecular complexes concerning 4:1 it was chemically defined and also studied the structure of supramolecular complexes by physical methods on the basis of interaction of organic molecules with electromagnetic radiation, in particular their range IR – of spectroscopy. Our work of the near future will be turned to check its recent supramolecular complexes on the basis of GA: Menthol for growth of a plant and biotic elasticity of tension …

Spectrophotometric Characterization Of The Complexation Of Gossypol Acetic Acid With Cobalt Ion, Ugilay Abdurahmanova, Habibjon Kushiev, Maral Askarova, Dilafruz Allanazarova

Karakalpak Scientific Journal

The authors of the article suggest simple and express method of spectrophotometric determination of cobalt with the help of derivatives of gossypol. Optimal conditions of determining cobalt are found. Under optimal conditions there was created a graded graph, which is more linear in the range for cobalt concentration of 10.0 – 50.0 microgram/25 ml, contents and constants of cobalt complex with gossypol vinegar acid.

Fuzzy Synergetic Control Nonlinear Dynamic Objects, Isomiddin Sidikov, Noilakhon Yakubova, Komil Usmanov, Saparbay Kazakhbayev

Karakalpak Scientific Journal

The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a fuzzy synergistic controller for a class of indefinite nonlinear dynamic systems. A synergetic control scheme is proposed for solving the control problem for nonlinear systems. Non-linear systems with configurations and parameters that change over time require a completely non-linear model and adaptive control scheme for a practical operating environment. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ACAR). Fuzzy logic systems are used to evaluate the unknown nonlinear behavior of the system, and a new …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …