Breakdown Of Itcz-Like Pv Patterns, 2016 Embry-Riddle Aeronautical University - Daytona Beach

#### Breakdown Of Itcz-Like Pv Patterns, Ajay Raghavendra, Thomas A. Guinn

*Beyond: Undergraduate Research Journal*

The Inter-Tropical Convergence Zone (ITCZ) is a zonal belt of intense convection, responsible for the genesis of over 80% of all tropical cyclones. This region of intense diabatic heating and shear results in a maximum of Ertel's potential vorticity (PV) meeting Rayleigh's necessary condition for barotropic instability. A fundamental issue is understanding the necessary precursor events leading to the breakdown of the ITCZ and subsequent formation of tropical cyclones. Our research examines the non-linear PV dynamics of the breakdown of both finite-length and infinite-length vorticity strips of varying widths and shapes, simulating the ITCZ found near the tropical ...

A Comparison Of Solution Methods For Mandelbrot-Like Polynomials, 2016 The University of Western Ontario

#### A Comparison Of Solution Methods For Mandelbrot-Like Polynomials, Eunice Y. S. Chan

*Electronic Thesis and Dissertation Repository*

We compare two different root-finding methods, eigenvalue methods and homotopy methods, using three test problems: Mandelbrot polynomials, Fibonacci-Mandelbrot polynomials, and Narayana-Mandelbrot polynomials. For the eigenvalue methods, using both MATLAB and Maple, we computed the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix, inspired by Piers Lawrence's original construction for the Mandelbrot polynomials, for all three families of polynomials. This led us to prove that this construction works in general. Therefore, this construction is genuinely a new kind of companion matrix. For the homotopy methods, we used a special-purpose homotopy, in which we used an equivalent differential equation to ...

Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, 2016 Universidad de Los Andes - Colombia

#### Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, Juan Sebastian Martinez, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

*The Summer Undergraduate Research Fellowship (SURF) Symposium*

Multi-objective optimization (MOO) problems arise frequently in science and engineering situations. In an optimization problem, we want to find the set of input parameters that generate the set of optimal outputs, mathematically known as the Pareto frontier (PF). Solving the MOO problem is a challenge since expensive experiments can be performed only a constrained number of times and there is a limited set of data to work with, e.g. a roll-to-roll microwave plasma chemical vapor deposition (MPCVD) reactor for manufacturing high quality graphene. State-of-the-art techniques, e.g. evolutionary algorithms; particle swarm optimization, require a large amount of observations and ...

A Fast Model For The Simulation Of External Gear Pumps, 2016 Purdue University

#### A Fast Model For The Simulation Of External Gear Pumps, Zechao Lu, Xinran Zhao, Andrea Vacca

*The Summer Undergraduate Research Fellowship (SURF) Symposium*

External gear pump is an important category of positive displacement fluid machines used to perform the mechanical–hydraulic energy conversions in many fluid power applications. An efficient numerical simulation program is needed to simulate the system in order to provide a direction for design purpose. The model consists of a lumped parameter fluid dynamic model and a model that simulates the radial micro-motions of the gear’s axes of rotation. The system consists of a set of ordinary differential equations related to the conservation on mass of the internal control volumes of the pump, which are given by the tooth ...

Multi-Objective Optimization Under Uncertainty Using The Hyper-Volume Expected Improvement, 2016 South Carolina State University

#### Multi-Objective Optimization Under Uncertainty Using The Hyper-Volume Expected Improvement, Martin Figura, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

*The Summer Undergraduate Research Fellowship (SURF) Symposium*

The design of real engineering systems requires the optimization of multiple quantities of interest. In the electric motor design, one wants to maximize the average torque and minimize the torque variation. A study has shown that these attributes vary for different geometries of the rotor teeth. However, simulations of a large number of designs cannot be performed due to their high cost. In many problems, design optimization of multi-objective functions is a very challenging task due to the difficulty to evaluate the expectation of the objectives. Current multi-objective optimization (MOO) techniques, e.g., evolutionary algorithms cannot solve such problems because ...

Numerical Computing With Functions On The Sphere And Disk, 2016 Boise State University

#### Numerical Computing With Functions On The Sphere And Disk, Heather Denise Wilber

*Boise State University Theses and Dissertations*

A new low rank approximation method for computing with functions in polar and spherical geometries is developed. By synthesizing a classic procedure known as the double Fourier sphere (DFS) method with a structure-preserving variant of Gaussian elimination, approximants to functions on the sphere and disk can be constructed that (1) preserve the bi-periodicity of the sphere, (2) are smooth over the poles of the sphere (and origin of the disk), (3) allow for the use of FFT-based algorithms, and (4) are near-optimal in their underlying discretizations. This method is used to develop a suite of fast, scalable algorithms that exploit ...

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.

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.

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.].

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.