Physical Sciences and Mathematics Commons^™

A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, Keith Galvin

All Theses

This paper studies two artificial viscosity methods for approximating solutions to the Navier&ndashStokes Equations. Both methods that are introduced add stabilization, then remove it only on a coarse mesh. Both methods can be considered as conforming, mixed methods for 1) velocity and its gradient, and 2) velocity and vorticity. Herein we rigorously study the schemes both analytically and computationally, showing that both methods are unconditionally stable and optimally convergent. Numerical experiments show both methods provide improved results over the unstabilized Navier&ndashStokes Equations.

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

Neutrosophic Physics: More Problems, More Solutions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

When considering the laws of theoretical physics, one of the physicists says that these laws – the actual expressions of the laws of mathematics and logics being applied to physical phenomena – should be limited according to the physical meaning we attribute to the phenomena. In other word, there is an opinion that a theoretical physicist should put some limitations onto mathematics, in order to “reduce” it to the observed reality. No doubt, we can do it. However, if following this way, we would arrive at only mathematical models of already known physical phenomena. Of course, this might be useful …

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob

All Dissertations

The focus of this thesis is to formulate an optimal source problem for the medical imaging technique of optical tomography by maximizing certain distinguishability criteria. We extend the concept of distinguishability in electrical impedance tomography to the frequency-domain diffusion approximation model used in optical tomography.
We consider the dependence of the optimal source on the choice of appropriate function spaces, which can be chosen from certain Sobolev or Lp spaces. All of the spaces we consider are Hilbert spaces; we therefore exploit the inner product in several ways. First, we define and use throughout an inner product on the Sobolev …

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

Masters Theses & Specialist Projects

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …

Numerical Modelling Of A 10-Cm-Long Multi-Gev Laser Wakefield Accelerator Driven By A Self-Guided Petawatt Pulse, Serguei Y. Kalmykov, Sunghwan A. Yi, Arnaud Beck, Agustin F. Lifschitz, Xavier Davoine, Erik Lefebvre, Alexander Pukhov, Vladimir N. Khudik, Gennady Shvets, Steven A. Reed, Peng Dong, Xiaoming Wang, Dongsu Du, Stefan Bedacht, Rafal B. Zgadzaj, Watson Henderson, Aaron Bernstein, Gilliss Dyer, Mikael Martinez, Erhard Gaul, Todd Ditmire, Michael C. Downer

Serge Youri Kalmykov

Holographic Visualization Of Laser Wakefields, Peng Dong, Steven A. Reed, Sunghwan A. Yi, Serguei Y. Kalmykov, Zhengyan Y. Li, Gennady Shvets, Nicholas H. Matlis, Christopher Mcguffey, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Karl Krushelnick, Anatoly Maksimchuk, Takeshi Matsuoka, Alexander G. R. Thomas, Victor Yanovsky, Michael C. Downer

Serge Youri Kalmykov

We report ‘snapshots’ of laser-generated plasma accelerator structures acquired by frequency domain holography (FDH) and frequency domain shadowgraphy (FDS), techniques for visualizing quasi-static objects propagating near the speed of light. FDH captures images of sinusoidal wakes in mm-length plasmas of density 1 < n_{e} < 5 x 10^{18} cm^{−3} from phase modulations they imprint on co-propagating probe pulses. Changes in the wake structure (such as the curvature of the wavefront), caused by the laser and plasma parameter variations from shot to shot, were observed. FDS visualizes lasergenerated electron density bubbles in mm-length plasmas of density n_{e} > 10^{19} cm^{−3} using amplitude modulations they imprint on co-propagating probe pulses. Variations in the spatio-temporal structure of bubbles are inferred from corresponding variations in the shape of ‘bullets’ of probe light trapped inside them and correlated with mono-energetic electron generation. Both FDH and FDS average over structural variations that occur during propagation through the plasma medium. We explore …

The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

Undergraduate Theses and Capstone Projects

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of Long-Term Viabilities Of Annuals And Perennials, Anthony Delegge

Department of Mathematics: Dissertations, Theses, and Student Research

In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present …

Codes From Riemann-Roch Spaces For Y2 = Xp - X Over Gf(P), Darren B. Glass, David Joyner, Amy Ksir

Math Faculty Publications

Let Χ denote the hyperelliptic curve y2 = xp - x over a field F of characteristic p. The automorphism group of Χ is G = PSL(2, p). Let D be a G-invariant divisor on Χ(F). We compute explicit F-bases for the Riemann-Roch space of D in many cases as well as G-module decompositions. AG codes with good parameters and large automorphism group are constructed as a result. Numerical examples using GAP and SAGE are also given.

On Approximating Point Spread Distributions, Tamas Lengyel

Tamas Lengyel

We discuss some properties of the point spread distribution, defined as the distribution of the difference of two independent binomial random variables with the same parameter n in- cluding exact and approximate probabilities and related optimization issues. We use various approximation techniques for different distributions, special functions, and analytic, combi- natorial and symbolic methods, such as multi-summation techniques. We prove that in case of unequal success rates, if these rates change with their difference kept fix and small, and n is appropriately bounded, then the point spread distribution only slightly changes for small point differences. We also prove that for …

Medicen, Bahram Agheli

Bahram Agheli

No abstract provided.

Formation Of Optical Bullets In Laser-Driven Plasma Bubble Accelerators, Peng Dong, Steven A. Reed, Sunghwan A. Yi, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer, Nicholas H. Matlis, Wim P. Leemans, Christopher Mcguffey, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Karl Krushelnick, Anatoly Maksimchuk, Takeshi Matsuoka, Alexander G. R. Thomas, Victor Yanovsky

Serge Youri Kalmykov

Electron density bubbles—wake structures generated in plasma of density n_{e} ~ 10^{19} cm^{-3} by the light pressure of intense ultrashort laser pulses—are shown to reshape weak copropagating probe pulses into optical ‘‘bullets.’’ The bullets are reconstructed using frequency-domain interferometric techniques in order to visualize bubble formation. Bullets are confined in three dimensions to plasma-wavelength size, and exhibit higher intensity, broader spectrum and flatter temporal phase than surrounding probe light, evidence of their compression by the bubble. Bullets observed at 0.8 < n_{e} < 1.2 x 10^{19} cm^{-3} provide the first observation of bubble formation below the electron capture threshold. At higher n_{e}, bullets appear with high shot-to-shot stability together with relativistic electrons that vary widely in spectrum, and help relate bubble formation to fast electron generation.

Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina

Mathematics Research Reports

Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

Seducing The Single Ticket Buyer: Converting Single Ticket Buyers To Subscribers At The Binghamton Philharmonic, Lauren F. Elicks

MPA Capstone Projects 2006 - 2015

Declining interests in classical music have left many performances based organizations scrambling to maintain subscriptions rates, ticket revenue and attendance. The Binghamton Philharmonic has a substantial single ticket buyer base which if converted to subscribers, would secure revenue and attendance to each season. This study explores the motivations and attendance levels of Binghamton Philharmonic single ticket buyer population. Using frequency distribution charts, cross-tabular analysis and independent samples t-tests, variables of motivation were compared to the single ticket and subscriber population.This project discusses the factors affecting single ticket buyer motivations for attendance, effective methods for encouraging greater attendance, and provides an …

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Effect Of Node-Degree Correlation On Synchronization Of Identical Pulse-Coupled Oscillators, M. Drew Lamar, Gregory D. Smith

Arts & Sciences Articles

We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree …

Accurate And Stable Numerical Methods For Solving Micro Heat Transfer Models In An N-Carrier System In Spherical Coordinates, Di Zhao

Doctoral Dissertations

Energy exchange between electrons and phonons in metal provides the best example in describing non-equilibrium heating during the ultrafast transient. In times comparable to the thermalization and relaxation time of electrons and phonons, which are in the range of a few to several tens of picoseconds, heat continuously flows from hot electrons to cold phonons through mutual collisions. Consequently, electron temperature continuously decreases whereas phonon temperature continuously increases until thermal equilibrium is reached. Tien developed the well-known parabolic two-step model for describing the non-equilibrium heating in the electron-phonon system in 1992, and Tzou developed the parabolic model for the non-equilibrium …

Measuring Balkanization In Wikipedia, Colin Welch

Mathematics, Statistics, and Computer Science Honors Projects

Modern society has become increasingly balkanized, or ideologically polarized and socially fragmented. Political parties interact with each other over divisive issues by using polarizing rhetoric. Internet users create small, opinionated communities like dKosapedia and Conservapedia, Wikipedia-like websites written from positions of left-leaning and right-leaning bias. Even Wikipedia may not be immune to balkanization. As a free encyclopedia written by users from an unbiased point of view, it is in the interest of the general public to keep Wikipedia as free of balkanization and polarization as possible. If Wikipedia authors are free to express their conflicting points of view, the quality …

High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis

Master's Theses

A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence …

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mikhail Khenner

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational/Research presentation for senior physics majors

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational/Research presentation for senior physics majors

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational presentation for senior physics majors

Conference Proceedings 3rd International Scientific Conference On “Energy Systems With It” At Alvsjö Fair In Association With Energitinget March 16-17 2010, Dr. Erik Dahlquist, Dr. Jenny Palm

Dr. Erik Dahlquist

2010 “The Energiting” is performed for the 12th time. The International Scientific conference is arranged for the 3rd time. The organisers are Swedish Energy Agency, Mälardalen University and the Research School for Energy Systems with LiU, KTH, UU and CTH. The first topic will be “Energy systems” covering use of renewable energy sources, energy conversion and process efficiency improvement with new technologies, as well as societal aspects of the introduction of new technologies. The second topic is “Energy and IT”. This covers energy and load management, interaction between production, distribution and “consumption”, usage of data for decision support and control, …

Parametric Lp Analysis, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it is important since it highlights how a problem changes as what is often estimated data varies. We present what is a modern perspective on the classical analysis of the objective value's response to parametrizations in the right-hand side and cost vector. We also mention a few applications and provide citations for further study

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Bruce Kessler

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …

Maximizing Strike Planning Efficiency For A Given Class Of Targets, Necip Dirik

Theses and Dissertations

Strike planning is one of the fundamental tasks of the Turkish Air Force and involves assignment of strike aircraft to targets with a maximum level of efficiency. Therefore, planning an optimal strike plan based on the preferences of the decision maker is crucial. The efficiency of the strike plan in this research implies attacking the maximum number of targets while considering target priority and the desired level of damage on each target. Another objective is to minimize the cost of the plan. This research develops an exact model that maximizes the efficiency of the strike plan using LINGO with Excel …

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

The Uav Continuous Coverage Problem, Taegyun Ha

Theses and Dissertations

The purpose of this research is to develop a method to find an optimal UAV cyclic schedule to provide maximum coverage over a target area to support an ISR mission. The goal is to reach continuous coverage. UAV continuous coverage of a target area is crucial for the success of an ISR mission. Even the smallest coverage gap may jeopardize the success of the mission. Ideally it is desirable to obtain continuous coverage of a target area but the stochastic nature of the problem makes continuous coverage without gaps unlikely. However, it is still possible to obtain a high coverage …