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Visualization And Analysis Of A Numerical Simulation Of Gw150914, Nicole Rosato

Theses

We present a visualization and analysis of a supercomputer simulation displaying the apparent horizons' curvature and radiation emitted from a binary black hole system modeling the LIGO observed signal GW150914. The simulation follows the system from seven orbits prior to merger down to the resultant final Kerr black hole. Apparent horizons are calculated during the simulation with mean curvature data displayed on them. Radiation data was visualized via the real part of the $\Psi_4$ component of the Weyl scalars, which were determined using a numerical quasi-Kinnersley method. We also present a comparative study of the differences in using the quasi-Kinnersley …

Hopf Hypersurfaces In Spaces Of Oriented Geodesics., Nikos Georgiou, Brendan Guilfoyle

Publications

A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the normal vector. We consider particular Hopf hypersurfaces in the space of oriented geodesics of a non-flat space form of dimension greater than 2. For spherical and hyperbolic space forms, the space of oriented geodesics admits a canonical Kaehler–Einstein and para-Kaehler–Einstein structure, respectively, so that a natural notion of a Hopf hypersurface exists. The particular hypersurfaces considered are formed by the oriented geodesics that are tangent to a given convex hypersurface in …

Forest Understory Trees Can Be Segmented Accurately Within Sufficiently Dense Airborne Laser Scanning Point Clouds, Hamid Hamraz, Marco A. Contreras, Jun Zhang

Computer Science Faculty Publications

Airborne laser scanning (LiDAR) point clouds over large forested areas can be processed to segment individual trees and subsequently extract tree-level information. Existing segmentation procedures typically detect more than 90% of overstory trees, yet they barely detect 60% of understory trees because of the occlusion effect of higher canopy layers. Although understory trees provide limited financial value, they are an essential component of ecosystem functioning by offering habitat for numerous wildlife species and influencing stand development. Here we model the occlusion effect in terms of point density. We estimate the fractions of points representing different canopy layers (one overstory and …

Coordination Of Leader-Follower Multi-Agent System With Time-Varying Objective Function, Zalan Mark Fabian

Master's Theses and Capstones

This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the …

A Converging Lagrangian Flow In The Space Of Oriented Lines, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

Under mean radius of curvature flow, a closed convex surface in Euclidean space is known to expand exponentially to infinity. In the three-dimensional case we prove that the oriented normals to the flowing surface converge to the oriented normals of a round sphere whose centre is the Steiner point of the initial surface, which remains constant under the flow.
To prove this we show that the oriented normal lines, considered as a surface in the space of all oriented lines, evolve by a parabolic flow which preserves the Lagrangian condition.Moreover, this flow converges to a holomorphic Lagrangian section, which forms …

Infinite Color Urn Models., Debleena Thacker Dr.

Doctoral Theses

In recent years, there has been a wide variety of work on random reinforcement models of various kinds. Urn models form an important class of random reinforcement models, with numerous applications in engineering and informatics and bioscience. In recent years there have been several works on different kinds of urn models and their generalizations. For occupancy urn models, where one considers recursive addition of balls into finite or infinite number of boxes, there are some works which introduce models with infinitely many colors, typically represented by the boxes.As observed in [51], the earliest mentions of urn models are in the …

Essays On Strategy-Proofness And Implementation., Sonal Yadav Dr.

Doctoral Theses

This thesis comprises of three chapters relating to strategy-proofness and implementation. We provide a brief description of each chapter below.1.1 A Hurwicz Type Result in a Model with Public Good Production We consider a two-good model with an arbitrary number of agents. One of the goods is a public good and the other is a private good. Each agent has an endowment of the private good and the private good can be converted into the public good using a well-behaved production function. A Social Choice Function (SCF) associates an allocation with each admissible preference profile. We impose the following requirements …

"Smoking-Gun" Observables Of Magnetic Reconnection: Spatiotemporal Evolution Of Electron Characteristics Throughout The Diffusion Region, Jason Shuster

Doctoral Dissertations

How does magnetic reconnection happen in a collisionless plasma? Knowledge of electron-scale dynamics is necessary to answer this outstanding question of plasma physics. Based on fully kinetic particle-in-cell (PIC) simulations of symmetric reconnection, the spatiotemporal evolution of velocity distribution functions in and around the electron diffusion region (EDR) elucidates how electrons are accelerated and heated by the cooperating reconnection electric and normal magnetic fields. The discrete, triangular structures characteristic of EDR distributions rotate and gyrotropize in velocity space as electrons remagnetize, forming multicomponent arc and ring structures. Further downstream, exhaust electrons are found to exhibit highly structured, time-dependent anisotropies that …

Design And Evaluation Of A Force Platform-Type Instrument To Measure Rate Change In Mass And Centroid Of An Ablating Body, Travis Paul Trottier

Master's Theses and Capstones

This study pertains to the design and evaluation of a force-platform type instrument comprised of three strain gauge load cells, intended to measure the rate of change in mass and centroid position of an object undergoing rapid ablation by heated flow of air. The strain gauges are affixed to a steel frame, oriented in a triangle beneath a 25 X 20 cm rectangular platform, into which is machined a 9 X 9 regular grid for the purpose of static calibration. An algorithm derived from first principles is used to convert the distribution of the applied load among the strain gauges …

The Minimum And Other Free Energies For Non-Linear Materials With Memory., John Murrough Golden

Articles

Expressions are obtained for free energies of materials with a certain type of non-linear constitutive relation. In particular, the minimum and related free energies are considered in some detail. Minimal states are defined for these materials, and it is shown that any free energy yielding a linear constitutive equation that is a functional of the minimal state has a counterpart in the non-linear case which is also a minimal state functional in this more general context. These results are explored for simple examples, including discrete spectrum materials.

Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman

FIU Electronic Theses and Dissertations

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to …

Methods For The Direct Simulation Of Nanoscale Film Breakup And Contact Angles, Kyle Mahady

Dissertations

This thesis investigates direct simulation of fluids with free surfaces and contact lines, with a focus on capturing nanoscale physics in a continuum based computational framework. Free surfaces and contact lines have long presented some of the most challenging problems in computational fluid dynamics. Extensive progress has been made in recent years, and a wide variety of different methods are currently employed for direct simulation in these contexts. The complexity of the full governing equations for such flows poses significant challenges in terms of analytical techniques, and leads to lengthy computational times for direct simulations. For these reasons, reduced models …

Nonlinear Waves On A String With Inhomogeneous Properties, Robert Arredondo

Doctoral Dissertations

Nonlinear waves on an infinite string with a rapid change in properties at one location are treated. The string is an idealized version of more complex configurations in both fluids and solids. This idealized version treats the property change as an interface with a discontinuity in properties. Packets of waves are then considered with a reduced model, here a set of nonlinear Schr¨odinger (NLS) equations. The stress and the displacement must both be matched at the interface, resulting in dynamic and kinematic interfacial conditions. The dynamic condition produces an inhomogeneous effect that cannot be treated successfully with separation-of-variables. This inhomogeneity …

A Supercell, Bloch Wave Method For Calculating Low-Energy Electron Reflectivity With Applications To Free-Standing Graphene And Molybdenum Disulfide, John Francis Mcclain

Doctoral Dissertations

This dissertation reports on a novel theoretical and computational framework for calculating low-energy electron reflectivities from crystalline surfaces and its application to two layered systems of two-dimensional materials, graphene and molybdenum disulfide. The framework provides a simple and efficient approach through the matching of a small set of Fourier components of Bloch wave solutions to the Schrodinger Equation in a slab-in-supercell geometry to incoming and outgoing plane waves on both sides of the supercell. The implementation of this method is described in detail for the calculation of reflectivities in the lowest energy range, for which only specular reflection is allowed. …

Porous Medium Convection At Large Rayleigh Number: Studies Of Coherent Structure, Transport, And Reduced Dynamics, Baole Wen

Doctoral Dissertations

Buoyancy-driven convection in fluid-saturated porous media is a key environmental and technological process, with applications ranging from carbon dioxide storage in terrestrial aquifers to the design of compact heat exchangers. Porous medium convection is also a paradigm for forced-dissipative infinite-dimensional dynamical systems, exhibiting spatiotemporally chaotic dynamics if not ``true" turbulence. The objective of this dissertation research is to quantitatively characterize the dynamics and heat transport in two-dimensional horizontal and inclined porous medium convection between isothermal plane parallel boundaries at asymptotically large values of the Rayleigh number $Ra$ by investigating the emergent, quasi-coherent flow. This investigation employs a complement of direct …

Mathematical Analysis Of Energy Harvester Model, Oleksandr Vdovyn

Master's Theses and Capstones

Energy Harvesting from ambient waste energy for the purpose of running low-powered electronics has emerged during last decades. The goal of energy harvesting devices is to provide remote sources of electrical power and/or recharge storage devices such as batteries and capacitors.

The evolution of low-power-consuming electronics have led to and active academic research in energy harvesting. One of the most studied areas is the use of the piezoelectric effect to convert ambient vibration into useful electrical energy. The focus of this study on placed on detailed mathematical analysis of electromechanical models of piezoelectric energy harvester. The area of vibration-based energy …

An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

Theses and Dissertations

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a …

A Contagion Model Of Emergency Airplane Evacuations, Junyuan Lin

Seaver College Research And Scholarly Achievement Symposium

Motivated by the Asiana Flight 214 crash in San Francisco this summer, this project focuses on modeling an emergency airplane evacuation. Our models are based on the Particle Swarm Optimization (PSO) algorithm, where each agent's position is compared to a fitness function that describes the current environment. Each agent moves according to its knowledge of its own previous best position and the group's current best position. The static environment is modeled by a potential function that describes the layout of the airplane that includes the exits and physical barriers such as the seats. We model the interactions within the swarm …

An Investigation Of Traveling-Wave Electrophoresis Using A Trigonometric Potential, James Vopal

Graduate Theses, Dissertations, and Problem Reports

Traveling-wave electrophoresis, a technique for microfluidic separations in lab-on-achip devices, is investigated using a trigonometric model that naturally incorporates the spatial periodicity of the device. Traveling-wave electrophoresis can be used to separate high-mobility ions from low-mobility ions in forensic and medical applications, with a separation threshold that can be tuned for specific applications by simply choosing the traveling wave frequency. Our simulations predict plateaus in the average ion velocity verses the mobility, plateaus that correspond to Farey fractions and yield Devil's staircases for non-zero discreteness values. The plateaus indicate that ions with different mobilities can travel with the same average …

Discrete Time Dynamic Traffic Assignment Models With Lane Reversals For Evacuation Planning, Yeh-Ern Poh

Graduate Theses, Dissertations, and Problem Reports

In an event of a natural or man-made disaster, an evacuation is likely to be called for to move residents away from potentially hazardous areas. Road congestion and traffic stalling is a common occurrence as residents evacuate towns and cities for safe refuges. Lane reversal, or contra-flow, is a remedy to increase outbound flow capacities from disaster areas which in turn will reduce evacuation time of evacuees during emergency situations. This thesis presents a discrete-time traffic assignment system with lane reversals which incorporates multiple sources and multiple destinations to predict optimal traffic flow at various times throughout the entire planning …

Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore

Dartmouth Scholarship

In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example …

Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings

Doctoral Dissertations

An in-depth understanding of a wide range of physical, chemical, atmospheric and biological processes can only be achieved after the structure and dynamics of interfaces and the interfacial behavior of aqueous species, such as ions, are thoroughly studied and understood. This dissertation describes computational studies conducted to gain a more comprehensive understanding of such interfaces and the behavior of ions in the bulk and interfacial regions of the (1) air/water interface, and (2) alkane/water interfaces.

At the air/water interface the effect of counterion (sodium cations) charge and the influence of ion pairing on anion (chloride) propensity for the air/water interface …

Circuits, Perfect Matchings And Paths In Graphs, Wenliang Tang

Graduate Theses, Dissertations, and Problem Reports

We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this topic.;In Chapter two, we shall pay our attention to the Strong Circuit Double Cover Conjecture (SCDC Conjecture). This conjecture was verified for some graphs with special structure. As the complement of two factor in cubic graph, the Berge-Fulkersen Conjecture was introduced right after SCDC Conjecture. …

Affine Invariant Signed-Rank Multivariate Exponentially Weighted Moving Average Control Chart For Process Location Monitoring, Jamil H. Zeinab

Dissertations

Multivariate statistical process control (SPC) charts for detecting possible shifts in mean vectors assume that data observation vectors follow a multivariate normal distribution. This assumption is ideal and seldom met. Nonparametric SPC charts have increasingly become viable alternatives to parametric counterparts in detecting process shifts when the underlying process output distribution is unknown, specifically when the process measurement is multivariate. This study examined a new nonparametric signed-rank multivariate exponentially weighted moving average type (SRMEWMA) control chart for monitoring location parameters. The control chart was based on adapting a multivariate spatial signed-rank test. The test was affine-invariant and the weighted version …

Connectivity And Spanning Trees Of Graphs, Xiaofeng Gu

Graduate Theses, Dissertations, and Problem Reports

This dissertation focuses on connectivity, edge connectivity and edge-disjoint spanning trees in graphs and hypergraphs from the following aspects.;1. Eigenvalue aspect. Let lambda2(G) and tau( G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of tau(G), Cioaba and Wong conjectured that for any integers d, k ≥ 2 and a d-regular graph G, if lambda 2(G)) < d -- 2k-1d+1 , then tau(G) ≥ k. They proved the conjecture for k = 2, 3, and presented evidence for the cases when k ≥ 4. We propose a more general conjecture that for a graph G with minimum degree delta ≥ 2 k ≥ 4, if lambda2(G) < delta -- 2k-1d+1 then tau(G) ≥ k. We prove the conjecture for k = 2, 3 and provide partial results for k ≥ 4. We also prove that for a graph G with minimum degree delta ≥ k ≥ 2, if lambda2( G) < delta -- 2k-1d +1 , then the edge connectivity is at least k. As corollaries, we investigate the Laplacian and signless Laplacian eigenvalue conditions on tau(G) and edge connectivity.;2. Network reliability aspect. With graphs considered as natural models for many network design problems, edge connectivity kappa'(G) and maximum number of edge-disjoint spanning trees tau(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G. Let kappa'(G) = max{lcub}kappa'(H) : H is a subgraph of G{rcub}. We present: (i) For each integer k > 0, a characterization for graphs G with the property that kappa'(G) ≤ k but for any additional …

Analysis And Implementation Of A High-Order Reconstruction Algorithm For An Unstructured Finite Volume Flow Solver, Shane Edmond Sawyer

Masters Theses and Doctoral Dissertations

A high-order scheme is examined an implemented in an unstructured solver. The motivation for this researcher is driven by research goals to simulate field equations, particularly those of fluid dynamics, with high fidelity. High-order schemes overcome computational limitations by computing comparable solutions on grids that are coarser than grids required by a second-order flow solver. The scheme was chosen based on two criteria. The first being that it is well documented in the literature for two-dimensional flow solvers. The second is that the scheme is extendable to the framework used in the Tenasi flow solver developed at the University of …

Fundamentals Of Arabic Cryptology And Covert Communication Networks, Adam Miles

Applied Mathematics Master's Theses

The need for accurate intelligence concerning possible terrorist attacks, spies, and other hostile military type actions, whether it be at home or abroad, remains of critical importance to the U.S. Intelligence Community. In this context, this paper focuses directly on the foundational aspects of covert communication networks and how they may be formed by groups or organizations such as al-Qaeda, jihadists, insurgents, etc. using spy tradecraft, cryptography and the language of Modern Standard Arabic. The paper itself is divided into two parts, one that focuses upon communicating covertly through methods without the use of electronics, and the other with electronics. …

Nanocapillary Membrane Devices: A Study In Electrokinetic Transport Phenomena, Jarrod Schiffbauer

Graduate Theses, Dissertations, and Problem Reports

There is considerable interest in developing micro-total analysis systems, also known as lab-on-a-chip devices, for applications in chemical and biological analysis. These devices often employ electrokinetic transport phenomena to move, mix, concentrate and separate dissolved species. The details of these phenomena in micro- and nanometer scale geometries are not fully understood; consequently, the basic principles of device operation are often unclear. For example, nanocapillary membranes (NCM) and other nanometer-sized passages can exhibit charge-selectivity and rectification effects similar to those observed in biological membranes. This dissertation addresses several issues related to ion transport in these membranes. Leading-order 1D steady-state models for …

Mathematical Modeling And Analysis Of Epidemiological And Chemical Systems, Calistus N. Ngonghala

Graduate Theses, Dissertations, and Problem Reports

This dissertation focuses on three interdisciplinary areas of applied mathematics, mathematical biology/epidemiology, economic epidemiology and mathematical physics, interconnected by the concepts and applications of dynamical systems.;In mathematical biology/epidemiology, a new deterministic SIS modeling framework for the dynamics of malaria transmission in which the malaria vector population is accounted for at each of its developmental stages is proposed. Rigorous qualitative and quantitative techniques are applied to acquire insights into the dynamics of the model and to identify and study two epidemiological threshold parameters reals* and R0 that characterize disease transmission and prevalence, and that can be used for disease control. It …

Group Colorability And Hamiltonian Properties Of Graphs, Hao Li

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-edge-connected, essentially 4-edge-connected graph G has a spanning eulerian subgraph, if for every pair of adjacent vertices u and v, dG(u) + dG(v) ≥ 9. A straight forward corollary is that every 4-connected, essentially 6-connected line graph with minimum degree at least 7 is hamiltonian.;We also investigate graphs G such that the line graph L(G) is …