Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, 2016 Western Kentucky University

#### Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner

*Mikhail Khenner*

Introduction To Classical Field Theory, 2016 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

*Charles G. Torre*

Creating Art Patterns With Math And Code, 2016 CUNY New York City College of Technology

#### Creating Art Patterns With Math And Code, Boyan Kostadinov

*Publications and Research*

The goal of this talk is to showcase some visualization projects that we developed for a 3-day **Code in R** summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing **calculus level math and code** to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for ...

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.

Newsvendor Models With Monte Carlo Sampling, 2016 East Tennessee State University

#### Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

*Electronic Theses and Dissertations*

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected proﬁt. Finally, this method will be used ...

Delay-Independent Stability Analysis Of Linear Time-Delay Systems Based On Frequency, 2016 Harbin Institute of Technology

#### Delay-Independent Stability Analysis Of Linear Time-Delay Systems Based On Frequency, Xianwei Li, Huijun Gao, Keqin Gu

*SIUE Faculty Research, Scholarship, and Creative Activity*

This paper studies strong delay-independent stability of linear time-invariant systems. It is known that delay-independent stability of time-delay systems is equivalent to some *frequency-dependent *linear matrix inequalities. To reduce or eliminate conservatism of stability criteria, the frequency domain is discretized into several sub-intervals, and *piecewise constant *Lyapunov matrices are employed to analyze the frequency-dependent stability condition. Applying the generalized Kalman–Yakubovich–Popov lemma, new necessary and sufficient criteria are then obtained for strong delay-independent stability of systems with a single delay. The effectiveness of the proposed method is illustrated by a numerical example.

How To Determine The Stiffness Of The Pavement's Upper Layer (Base) Based On The Overall Stiffness And The Stiffness Of The Lower Layer (Subgrade), 2016 El Paso Community College

#### How To Determine The Stiffness Of The Pavement's Upper Layer (Base) Based On The Overall Stiffness And The Stiffness Of The Lower Layer (Subgrade), Christian Servin, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In road construction, it is important to estimate difficult-measure stiffness of the pavement's upper layer based the easier-to-measure overall stiffness and the stiffness of the lower layer. In situations when the overall stiffness is not yet sufficient, it is also important to estimate how much more we need to add to the upper layer to reach the desired overall stiffness. In this paper, for the cases when a linear approximation is sufficient, we provide analytical formulas for the desired estimations.

On Approximately Controlled Systems, 2016 Eastern Mediterranean University - Turkey

#### On Approximately Controlled Systems, Nazim I. Mahmudov, Mark A. Mckibben

*Mathematics*

No abstract provided.

Introduction To Classical Field Theory, 2016 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

*All Complete Monographs*

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

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.

The Survival Probability Of Beneficial De Novo Mutations In Budding Viruses, With An Emphasis On Influenza A Viral Dynamics, 2016 The University of Western Ontario

#### The Survival Probability Of Beneficial De Novo Mutations In Budding Viruses, With An Emphasis On Influenza A Viral Dynamics, Jennifer Ns Reid

*Electronic Thesis and Dissertation Repository*

A deterministic model is developed of the within-host dynamics of a budding virus, and coupled with a detailed life-history model using a branching process approach to follow the fate of *de novo* beneficial mutations affecting five life-history traits: clearance, attachment, eclipse, budding, and cell death. Although the model can be generalized for any given budding virus, our work was done with a major emphasis on the early stages of infection with influenza A virus in human populations. The branching process was then interleaved with a stochastic process describing the disease transmission of this virus. These techniques allowed us to predict ...

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.].

Optimization Of Takeoffs On Unbalanced Fields Using Takeoff Performance Tool, 2016 AAR Aerospace Consulting, LLC

#### Optimization Of Takeoffs On Unbalanced Fields Using Takeoff Performance Tool, Nihad E. Daidzic

*International Journal of Aviation, Aeronautics, and Aerospace*

Unbalanced field length exists when ASDA and TODA are not equal. Airport authority may add less expensive substitutes to runway full-strength pavement in the form of stopways and/or clearways to basic TORA to increase operational takeoff weights. Here developed Takeoff Performance Tool is a physics-based total-energy model used to simulate FAR/CS 25 regulated airplane takeoffs. Any aircraft, runway, and environmental conditions can be simulated, while complying with the applicable regulations and maximizing performance takeoff weights. The mathematical model was translated into Matlab, Fortran 95/2003/2008, Basic, and MS Excel computer codes. All existing FAR/CS 25 takeoff ...

Model For Computing Kinetics Of The Graphene Edge Epitaxial Growth On Copper, 2016 Western Kentucky University

#### Model For Computing Kinetics Of The Graphene Edge Epitaxial Growth On Copper, Mikhail Khenner

*Mikhail Khenner*

Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems, 2016 University of Minnesota - Twin Cities

#### Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov

*Jay Gopalakrishnan*

We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continu- ous Galerkin, non-conforming and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric and positive definite, these methods can be efficiently implemented. Moreover, the ...

The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, 2016 University of Minnesota - Twin Cities

#### The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan

*Jay Gopalakrishnan*

In this paper, we introduce a new class of discontinuous Galerkin methods for the Stokes equations. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to certain approximations on the element boundaries. We present four ways of hybridizing the methods, which differ by the choice of the globally coupled unknowns. Classical methods for the Stokes equations can be thought of as limiting cases of these new methods.

The Convergence Of V-Cycle Multigrid Algorithms For Axisymmetric Laplace And Maxwell Equations, 2016 Portland State University

#### The Convergence Of V-Cycle Multigrid Algorithms For Axisymmetric Laplace And Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak

*Jay Gopalakrishnan*

We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknowns. This is contrary to suggestions in the existing literature that line relaxations and semicoarsening are needed in multigrid algorithms to overcome difficulties caused by the singularities in the axisymmetric Maxwell problems. Our multigrid analysis proceeds by applying the well known regularity ...

Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, 2016 Portland State University

#### Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak

*Jay Gopalakrishnan*

The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory ...

Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, 2016 Portland State University

#### Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh

*Jay Gopalakrishnan*

Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that if the original three-dimensional domain is convex then the multigrid Vcycle applied to the inner product in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for ...

Multigrid For The Mortar Finite Element Method, 2016 Portland State University

#### Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak

*Jay Gopalakrishnan*

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulations (which need not align across subdomain interfaces) are in general not nested. Suitable grid transfer operators and smoothers are developed which lead to a variable Vcycle preconditioner resulting in a uniformly preconditioned algebraic system. Computational results illustrating the theory are also presented.