Fast Method Of Particular Solutions For Solving Partial Differential Equations, 2016 University of Southern Mississippi

#### Fast Method Of Particular Solutions For Solving Partial Differential Equations, Anup Raja Lamichhane

*Dissertations*

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the large-scale problems are some of the challenges which need to overcome. In this dissertation, we have used several techniques to overcome such challenges.

The closed-form particular solutions for the Matérn and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matérn and Gaussian RBFs for the Laplace and biharmonic ...

Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, 2016 American University of the Middle East

#### Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, Unal Ufuktepe Prof

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Influence Of Preventive Measures To Eradicate The Spread Of The Zika Arbovirus, 2016 The Foxcroft School

#### Influence Of Preventive Measures To Eradicate The Spread Of The Zika Arbovirus, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, 2016 University of North Carolina at Chapel Hill

#### How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, Nicholas A. Battista

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A 2-D Compartmental Model For Multi-Capillary Supply, 2016 Georgia Gwinnett College

#### A 2-D Compartmental Model For Multi-Capillary Supply, Liang Sun, Junkoo Park, Alessandra L. Barrera

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Interdisciplinary Undergraduate Research In Biofluids, 2016 James Madison University

#### Interdisciplinary Undergraduate Research In Biofluids, Eva M. Strawbridge

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Mathematical Modeling, Analysis And Computation Of The Interaction Between Human Sub Populations And Vector-Borne Zika Transmission During The Summer 2016 Olympics, 2016 The Foxcroft School

#### Mathematical Modeling, Analysis And Computation Of The Interaction Between Human Sub Populations And Vector-Borne Zika Transmission During The Summer 2016 Olympics, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Multi-Dome Forming Of A Ti–Al–Mn Alloy, 2016 National Research University Higher School of Economics

#### Multi-Dome Forming Of A Ti–Al–Mn Alloy, Sergey Aksenov, Aleksey Kolesnikov, Ivan Zakhariev

*The 8th International Conference on Physical and Numerical Simulation of Materials Processing*

No abstract provided.

Numerical Simulation Of Residual Stress In Low-Temperature Colossal Carburized Layer On Austenitic Stainless Steel, 2016 Nanjing Tech University

#### Numerical Simulation Of Residual Stress In Low-Temperature Colossal Carburized Layer On Austenitic Stainless Steel, Dongsong Rong, Yong Jiang, Jianming Gong, Yawei Peng

*The 8th International Conference on Physical and Numerical Simulation of Materials Processing*

No abstract provided.

An Iterative Method To Solve A Nonlinear Matrix Equation, 2016 Hunan University, Changsha 410082, PR China

#### An Iterative Method To Solve A Nonlinear Matrix Equation, Peng Jingjing, Liao Anping, Peng Zhenyun

*Electronic Journal of Linear Algebra*

n this paper, an iterative method to solve one kind of nonlinear matrix equation is discussed. For each initial matrix with some conditions, the matrix sequences generated by the iterative method are shown to lie in a fixed open ball. The matrix sequences generated by the iterative method are shown to converge to the only solution of the nonlinear matrix equation in the fixed closed ball. In addition, the error estimate of the approximate solution in the fixed closed ball, and a numerical example to illustrate the convergence results are given.

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 ...

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 ...

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 ...

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 ...

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.

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.

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.].

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 ...