MATH Theses and Dissertationshttps://hdl.handle.net/10057/1842024-04-16T20:23:31Z2024-04-16T20:23:31Z1111A brief treatise on the Joukowski transformationHolmes, Wayne B.https://hdl.handle.net/10057/250132023-02-16T20:54:18Z1954-06-01T00:00:00Zdc.title: A brief treatise on the Joukowski transformation
dc.contributor.author: Holmes, Wayne B.
dc.description.abstract: The problem of predicting the flight characteristics of an arbitrary airfoil is very complicated, and does not readily lend itself to exact mathematical methods. However if certain simplifying assumptions are made the problem may be solved in certain cases, by the methods of conformal mapping of a complex variable. This solution is based upon the fact that the dynamics of fluid flow past a circular cross-section have been rather completely solved. Thus the problem reduces to one of finding a conformal transformation which will map the given airfoil into a circle. Unfortunately a general solution of this problem for any arbitrary shape airfoil has not been published. For certain special cases the problem has been solved by numerous writers, and the theoretical results have been checked by experimental data to a reasonable degree of accuracy.
This paper will discuss primarily the transformation of a symmetrical airfoil into a circle by the Kutta-Joukowski transformation. The stream function for the airfoil will be transformed from that of a circle by the Joukowski transformation. The lift and moment for the airfoil will be discussed. Brief mention of other more complicated transformation will also be made.
dc.description: Thesis (M.A.)-- University of Wichita, Dept. of mathematics
1954-06-01T00:00:00ZA capillary surface with no radial limitsMitchell, Colm Patrichttps://hdl.handle.net/10057/145042020-06-14T14:46:31Z2017-05-01T00:00:00Zdc.title: A capillary surface with no radial limits
dc.contributor.author: Mitchell, Colm Patric
dc.description.abstract: We begin by discussing the circumstances of capillary surfaces in regions with a corner, both
concave and convex. These circumstances led to the (since proved) Concus-Finn Conjecture,
which gives the requirements for a continuous solution to the capillary problem. We include
the requirements for the existence of radial limits and fans of radial limits in these corner
regions. We outline the method for which conformal mapping of the Gauss map of these
surfaces can be computed to allow the analytic extension of many related theorems. Finally,
we introduce a broadening of the existing research by taking an example done with Dirichlet
conditions in 1996 by Kirk Lancaster and David Siegel and recreating the example with
contact angle data instead.
With the use of contact angle data we find that where in the
original example γ could not be bounded away from zero or π, we were able to find a capillary
surface such that γ is bounded away from 0 and π.
dc.description: Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics
2017-05-01T00:00:00ZA comparative study of electroweak Higgs boson production at future Hadron CollidersChen, Tinghuahttps://hdl.handle.net/10057/155242019-07-25T06:48:14Z2018-07-01T00:00:00Zdc.title: A comparative study of electroweak Higgs boson production at future Hadron Colliders
dc.contributor.author: Chen, Tinghua
dc.description.abstract: The discovery of the Higgs boson has opened the door to the next phase of exploration in particle physics. Since the Higgs boson was found in July 2012 at CERN's
Large Hadron Collider (LHC), many researches and experiments tried to measure its
properties, making processes involving Higgs production interesting and important in many different ways.
Monte Carlo simulations play an important role in studies of particle physics. They
generate theoretical predictions and can be compared with experimental data to test our
understanding of physics. With the arithmetic speed of super-computers increasing, we can
use computer programs to simulate combinations of next-to-leading order (NLO) matrix
elements and parton showers in Higgs production processes.
In this thesis, by using a Monte Carlo event generator named Herwig 7, Higgs plus two jet production processes have been simulated with two different matrix elements, HJets++ and VBFNLO. Higgs plus two jet production was analyzed at 14 TeV, 33 TeV, and 100 TeV. This project also computed the differential cross section at the leading order and next-to-leading order with matched parton showers. This research provides a comparative study of the electroweak Higgs boson at future colliders.
dc.description: Thesis (M.S.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
2018-07-01T00:00:00ZA comparison of some numerical conformal mapping methods for simply and multiply connected domainsBadreddine, Mohamedhttps://hdl.handle.net/10057/128502019-07-25T06:38:16Z2016-05-01T00:00:00Zdc.title: A comparison of some numerical conformal mapping methods for simply and multiply connected domains
dc.contributor.author: Badreddine, Mohamed
dc.description.abstract: This dissertation compares several methods for computing conformal maps from sim-ply and multiply connected domains bounded by circles to target domains bounded by smooth curves and curves with corners. We discuss the use of explicit preliminary maps, including the osculation method of Grassmann to conformally map the target domain to a more nearly circular domain. The Fourier series method due to Fornberg and its generalizations to multiply connected domains are then applied to compute the maps to the nearly circular domains. The ?nal map is represented as a composition of the Fourier/Laurent series with the inverted explicit preliminary maps. A novel method for systematically re-moving corners with power maps is also implemented and composed with the Fornberg maps (which require smooth boundaries) and the level of error that can be expected when using Fourier series to treat domains with corners is illustrated. Some comparison to Wegmann's alternating projection method, which does not require smooth boundaries, is included. We also combine the Fornberg-like method with Karman-Tre?tz method for removing trailing edge corners in multi-element airfoils.
The use of explicit maps has been suggested often in the past, but has rarely been carefully studied especially for the multiply connected case. A key contribution of this dissertation is the development of Matlab code for testing existing and new combinations of these various methods, in order to provide a tool for future applications, such as solving potential theory problems in general, multiply connected domains in the plane.
dc.description: Thesis (Ph.D.)-- Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics
2016-05-01T00:00:00ZA computing method for multivariate isotonic regressionTraore, Ye Emmahttps://hdl.handle.net/10057/37532019-07-25T06:42:30Z2010-12-01T00:00:00Zdc.title: A computing method for multivariate isotonic regression
dc.contributor.author: Traore, Ye Emma
dc.description: Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
2010-12-01T00:00:00ZA exploratory study to create an anti-neutrino directional and ranging sensitive detector (NUDAR)Novak, Jarred C.https://hdl.handle.net/10057/257192024-02-01T15:43:21Z2023-07-01T00:00:00Zdc.title: A exploratory study to create an anti-neutrino directional and ranging sensitive detector (NUDAR)
dc.contributor.author: Novak, Jarred C.
dc.description.abstract: This research project set out to do an exploratory study to find a novel way to detect $\bar{\nu }$ for
small reactor powered vessels and to analyze the potential capabilities within the realm of
nuclear defense. A comprehensive study of the energy spectrum of $\bar{\nu }$ particles produced as
byproducts of nuclear fission processes was performed. The study combines theoretical
calculations and experimental observations from other experiments, to understand the
complex dynamics of $\bar{\nu }$ interactions.
In addition, this research explores the selection of isotopes with favorable __
cross-sections for detection purposes. The GENIE platform is used to analyze hundreds of
isotopes, leading to the identification of $^{137}$Ba, $^{152}$Gd, and $^{183}$W as potential candidates. These isotopes exhibit suitable cross-sections and threshold energies for detecting $\bar{\nu }$ particles. Scintillator materials, such as $BaF_2, GAGG,$ and $NaPGaW$ are assessed for their performance in detecting $\bar{\nu }$ particles. As well, a comprehensive study was carried out to determine the total ranging capabilities of the detector, with the results indicating detection is possible at great lengths. Along with this a possible new $\bar{\nu }$ detecton method was modeled with a double pulse indicator based off of the excitation state of Tantalum.
Furthermore, detector construction and simulations are conducted to study particle
tracking mechanisms. Crystal structures and segmented scintillator plates are evaluated for
their ability to track particles effectively. A proposed detector design involves assembling
scintillator structures using optical glue and utilizing fiber-optic lines for light collection.
Monte Carlo simulations using Geant4 provide insights into energy deposition, timing, and
the potential for detecting low-energy gamma rays.
This research paves the way for advancements in understanding of low energy $\bar{\nu }$ physics and offers insights into the development of next-generation detectors. The findings contribute to fundamental physics and have implications for nuclear deterrence,
non-proliferation, and defense.
dc.description: Thesis (M.S.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
2023-07-01T00:00:00ZA Fornberg-like method for the numerical conformal mapping of bounded multiply connected domainsKropf, Everetthttps://hdl.handle.net/10057/24252019-07-25T06:46:57Z2009-05-01T00:00:00Zdc.title: A Fornberg-like method for the numerical conformal mapping of bounded multiply connected domains
dc.contributor.author: Kropf, Everett
dc.description.abstract: A new Fornberg-like method is presented for computing conformal maps from the
interior of the unit disk with m-1 circular holes to the interior of a smooth closed curve with
m-1 holes bounded by smooth curves. The method is a Newton-like method for computing
the boundary correspondences and the conformal moduli (centers and radii of the circles).
The inner linear systems are derived from conditions for analytic extension of functions
de ned on the circles to the interior domain. These systems are N-point trigonometric
discretizations of the identity plus a compact operator and are solved efficiently with the
conjugate gradient method at a cost of O(N²)per step. Two formulations of the map are
given: the rst uses a disk with circular holes, and the second uses an annulus with circular
holes. Some numerical examples are given.
dc.description: Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics
2009-05-01T00:00:00ZA general legendre transformationDamaskos, Nickander J.https://hdl.handle.net/10057/259602023-10-18T00:05:44Z1958-06-01T00:00:00Zdc.title: A general legendre transformation
dc.contributor.author: Damaskos, Nickander J.
dc.description: Thesis (M.A.)-- University of Wichita, College of Liberal Arts and Sciences, Dept. of Mathematics
1958-06-01T00:00:00ZA historical overview of connections in geometryFreeman, Kamiellehttps://hdl.handle.net/10057/39532019-07-25T06:49:01Z2011-05-01T00:00:00Zdc.title: A historical overview of connections in geometry
dc.contributor.author: Freeman, Kamielle
dc.description.abstract: This thesis is an attempt to untangle/clarify the modern theory of connections in
Geometry. Towards this end a historical approach was taken and original as well as secondary
sources were used. An overview of the most important historical developments is given as
well as a modern look at how the various de nitions of connection are related.
dc.description: Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
2011-05-01T00:00:00ZA linearised inverse conductivity problem for the Maxwell system at a high frequencyIsakov, VictorLu, ShuaiXu, Boxihttps://hdl.handle.net/10057/230282022-05-08T18:24:31Z2022-04-15T00:00:00Zdc.title: A linearised inverse conductivity problem for the Maxwell system at a high frequency
dc.contributor.author: Isakov, Victor; Lu, Shuai; Xu, Boxi
dc.description.abstract: We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded
domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell
system and in a simplified transverse electric mode are derived. These bounds contain a Lipschitz term with a factor growing
polynomially in terms of the frequency, a H¨older term, and a logarithmic term which decays with respect to the frequency
as a power. To validate this increasing stability numerically, we propose a reconstruction algorithm aiming at the recovery of
sufficiently many Fourier modes of the conductivity. A numerical evidence sheds light on the influence of the growing frequency
and confirms the improved resolution at higher frequencies.
dc.description: Preprint version available. Also available from the publisher at DOI (may not be free).
2022-04-15T00:00:00Z