An Algorithm For The Machine Calculation Of Minimal Paths, 2016 East Tennessee State University

#### An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

*Electronic Theses and Dissertations*

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R^{3}, but also to the general case of finding minimal functionals on hypersurfaces in R^{n} associated with an arbitrary metric.

Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, 2016 The University of Southern Mississippi

#### Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, Haley Renee Dozier

*Master's Theses*

Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.

This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.

A New Error Bound For Linear Complementarity Problems For B-Matrices, 2016 Yunnan University

#### A New Error Bound For Linear Complementarity Problems For B-Matrices, Chaoqian Li, Mengting Gan, Shaorong Yang

*Electronic Journal of Linear Algebra*

A new error bound for the linear complementarity problem is given when the involved matrix is a $B$-matrix. It is shown that this bound improves the corresponding result in [M. Garc\'{i}a-Esnaola and J.M. Pe\~{n}a. Error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 22:1071--1075, 2009.] in some cases, and that it is sharper than that in [C.Q. Li and Y.T. Li. Note on error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 57:108--113, 2016.].

A Tent Pitching Scheme Motivated By Friedrichs Theory, 2016 Portland State University

#### A Tent Pitching Scheme Motivated By Friedrichs Theory, Jay Gopalakrishnan, Peter Monk, Paulina Sepúlveda

*Jay Gopalakrishnan*

Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.

Polynomial Extension Operators. Part Ii, 2016 University of Texas at Austin

#### Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

*Jay Gopalakrishnan*

Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.

A Tent Pitching Scheme Motivated By Friedrichs Theory, 2016 Portland State University

#### A Tent Pitching Scheme Motivated By Friedrichs Theory, Jay Gopalakrishnan, Peter Monk, Paulina Sepúlveda

*Jay Gopalakrishnan*

Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.

Optimizing The Mix Of Games And Their Locations On The Casino Floor, 2016 nQube Technical Computing Corp.

#### Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

*International Conference on Gambling and Risk Taking*

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor ...

Signal Processing Based On Stable Radix-2 Dct I-Iv Algorithms Having Orthogonal Factors, 2016 Embry-Riddle Aeronautical University - Daytona Beach

#### Signal Processing Based On Stable Radix-2 Dct I-Iv Algorithms Having Orthogonal Factors, Sirani K. M. Perera

*Electronic Journal of Linear Algebra*

This paper presents stable, radix-2, completely recursive discrete cosine transform algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having sparse and orthogonal factors are addressed. Signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors. Finally image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size 512 by 512 pixels with transfer block sizes 8 by 8, 16 by 16, and 32 ...

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, 2016 nQube Technical Computing Corp.

#### Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

*International Conference on Gambling and Risk Taking*

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single ...

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, 2016 AAR Aerospace Consulting, LLC

#### Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

*Journal of Aviation Technology and Engineering*

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model ...

Black Holes Modeled As Fluid Droplets On Membranes, 2016 California Polytechnic State University, San Luis Obispo

#### Black Holes Modeled As Fluid Droplets On Membranes, Anthony Bardessono

*Physics*

No abstract provided.

Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, 2016 Virginia Tech

#### Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, Steven Poelzing, Amara Greer-Short, Seth H. Weinberg

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Explicitly Separating Growth And Motility In A Glioblastoma Tumor Model, 2016 Arizona State University

#### Explicitly Separating Growth And Motility In A Glioblastoma Tumor Model, Tracy Stepien, Erica Rutter, Meng Fan, Yang Kuang

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Lubricated Immersed Boundary Method In Two Dimensions, 2016 Harvard University

#### A Lubricated Immersed Boundary Method In Two Dimensions, Thomas G. Fai

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Maximally Informative Next Experiments For Nonlinear Models, 2016 Mathematical Biosciences Institute

#### Maximally Informative Next Experiments For Nonlinear Models, Reginald Mcgee

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Statistics In League Of Legends: Analyzing Runes For Last-Hitting, 2016 Augustana College, Rock Island Illinois

#### Statistics In League Of Legends: Analyzing Runes For Last-Hitting, Brian M. Hook

*Mathematics: Student Scholarship & Creative Works*

While other sports have statisticians to evaluate players and their stats, in electronic sports there is a need for statisticians to evaluate different parts of the game. League of Legends is the most popular of ESports and is the focus of this discussion. The mechanic of focus here is runes which give boosts to the players stats in-game like being able to do extra damage. We will be finding the effectiveness of these runes by looking at gold efficiency, help with last hitting, and extra damage dealt through the use of Python.

Teaching Numerical Methods In The Context Of Galaxy Mergers, 2016 California Polytechnic State University, San Luis Obispo

#### Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia

*Physics*

Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating ...

Cfd Model For Ventilation In Broiler Holding Sheds, 2016 University of Arkansas, Fayetteville

#### Cfd Model For Ventilation In Broiler Holding Sheds, Christian Heymsfield

*Biological and Agricultural Engineering Undergraduate Honors Theses*

Broiler production in Arkansas was valued at over $3.6 billion in 2013 (University of Arkansas Extension of Agriculture). Consequently, improvement in any phase of the production process can have significant economic impact and animal welfare implications. From the time poultry leave the farm and until they are slaughtered, they can be exposed to harsh environmental conditions, both in winter and in summer. After road transportation, birds are left to wait in holding sheds once they arrive at the processing plant, for periods of approximately 30 minutes to two hours. This project was interested in this holding shed waiting time ...

Using Poincaré And Coefficient Analyses To Assess Changes In Variability In Respiration As A Function Of Leptin Status, Sex, And Buprenorphine In Mice, 2016 University of Tennessee, Knoxville

#### Using Poincaré And Coefficient Analyses To Assess Changes In Variability In Respiration As A Function Of Leptin Status, Sex, And Buprenorphine In Mice, Wateen Hussein Alami

*University of Tennessee Honors Thesis Projects*

No abstract provided.

Kinetic Monte Carlo Models For Crystal Defects, 2016 University of Tennessee - Knoxville

#### Kinetic Monte Carlo Models For Crystal Defects, Kyle Louis Golenbiewski

*Doctoral Dissertations*

Kinetic Monte Carlo algorithms have become an increasingly popular means to simulate stochastic processes since their inception in the 1960's. One area of particular interest is their use in simulations of crystal growth and evolution in which atoms are deposited on, or hop between, predefined lattice locations with rates depending on a crystal's configuration. Two such applications are heteroepitaxial thin films and grain boundary migration. Heteroepitaxial growth involves depositing one material onto another with a different lattice spacing. This misfit leads to long-range elastic stresses that affect the behavior of the film. Grain boundary migration, on the other ...