Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, 2018 Illinois State University

#### Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

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

No abstract provided.

Modeling The Impact Of The Latent Period On The Spatial Spread Of Dengue Fever, 2018 Illinois State University

#### Modeling The Impact Of The Latent Period On The Spatial Spread Of Dengue Fever, Juan Melendez-Alvarez

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

No abstract provided.

On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, 2018 University of Nebraska - Lincoln

#### On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson

*Dissertations, Theses, and Student Research Papers in Mathematics*

The theory of beams and plates has been long established due to works spanning many fields, and has been explored through many investigations of beam and plate mechanics, controls, stability, and the well-posedness of systems of equations governing the motions of plates and beams. Additionally, recent investigations of flutter phenomena by Dowell, Webster et al. have reignited interest into the mechanics and stability of nonlinear beams. In this thesis, we wish to revisit the seminal well-posedness results of Lagnese and Leugering for the one dimensional, nonlinear beam from their 1991 paper, "Uniform stabilization of a nonlinear beam by nonlinear boundary ...

Adaptive Meshfree Methods For Partial Differential Equations, 2018 The University of Southern Mississippi

#### Adaptive Meshfree Methods For Partial Differential Equations, Jaeyoun Oh

*Dissertations*

There are many types of adaptive methods that have been developed with different algorithm schemes and definitions for solving Partial Differential Equations (PDE). Adaptive methods have been developed in mesh-based methods, and in recent years, they have been extended by using meshfree methods, such as the Radial Basis Function (RBF) collocation method and the Method of Fundamental Solutions (MFS). The purpose of this dissertation is to introduce an adaptive algorithm with a residual type of error estimator which has not been found in the literature for the adaptive MFS. Some modifications have been made in developing the algorithm schemes depending ...

Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, 2018 Tallinn University of Technology

#### Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek

*Publications*

In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a one-dimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and ...

Spectra Of Quantum Trees And Orthogonal Polynomials, 2018 Louisiana State University and Agricultural and Mechanical College

#### Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang

*LSU Doctoral Dissertations*

We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive ...

Transport Phenomena In Field Effect Transistors, 2018 National Institute of Standards and Technology

#### Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Spatial Spread Of Defective Interfering Particles And Its Role In Suppressing Viral Load, 2018 North Carolina State University at Raleigh

#### Spatial Spread Of Defective Interfering Particles And Its Role In Suppressing Viral Load, Qasim Ali Qa, Ruian Ke

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Properties And Convergence Of State-Based Laplacians, 2018 University of Nebraska - Lincoln

#### Properties And Convergence Of State-Based Laplacians, Kelsey Wells

*Dissertations, Theses, and Student Research Papers in Mathematics*

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different ...

Harmonic Functions And Harmonic Measure, 2018 University of Connecticut

#### Harmonic Functions And Harmonic Measure, David Mcdonald

*Honors Scholar Theses*

The purpose of this thesis is to give a brief introduction to the field of harmonic measure. In order to do this we first introduce a few important properties of harmonic functions and show how to find a Green’s function for a given domain. Following this we calculate the harmonic measure for some easy cases and end by examining the connection between harmonic measure and Brownian motion.

Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, 2018 The University of Southern Mississippi

#### Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Montiforte

*Master's Theses*

Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.

Energy Calculations And Wave Equations, 2018 Missouri State University

#### Energy Calculations And Wave Equations, Ellen R. Hunter

*MSU Graduate Theses*

The focus of this thesis is to show how methods of Fourier analysis, in particular Parseval’s equality, can be used to provide explicit energy calculations for solutions of wave equations in one dimension. These calculations are discussed for simple examples and then extended to ﬁt the general wave equation with Robin boundary conditions. Ideas from Sobolev space theory are used to provide justiﬁcation of the method.

The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, 2018 The Graduate Center, City University of New York

#### The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

*All Dissertations, Theses, and Capstone Projects*

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices representing ...

Physical Applications Of The Geometric Minimum Action Method, 2018 The Graduate Center, City University of New York

#### Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

*All Dissertations, Theses, and Capstone Projects*

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...

Homogenization In Perforated Domains And With Soft Inclusions, 2018 University of Kentucky

#### Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

*Brandon Russell*

The Pope's Rhinoceros And Quantum Mechanics, 2018 Bowling Green State University

#### The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

*Honors Projects*

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time ...

Swelling As A Stabilizing Mechanism During Ion Bombardment Of Thin Films: An Analytical And Numerical Study, 2018 Southern Methodist University

#### Swelling As A Stabilizing Mechanism During Ion Bombardment Of Thin Films: An Analytical And Numerical Study, Jennifer M. Swenson

*Mathematics Theses and Dissertations*

Irradiation of semiconductor surfaces often leads to the spontaneous formation of rippled structures at certain irradiation angles. However, at high enough energies, these structures are observed to vanish for all angles, despite the absence of any identified, universally-stabilizing physical mechanisms in operation. Here, we examine the effect on pattern formation of radiation-induced swelling, which has been excluded from prior treatments of stress in irradiated films. After developing a suitable continuum model, we perform a linear stability analysis to determine its effect on stability. Under appropriate simplifying assumptions, we find swelling indeed to be stabilizing at wavenumbers typical of experimental observations ...

Numerical Simulation Of Energy Localization In Dynamic Materials, 2018 Tallinn University of Technology

#### Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

*Publications*

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also ...

Screening Algorithm Based On The Color Halftone Fluorescent Printing And Its Application In Packaging Design, 2018 Hunan University of Technology

#### Screening Algorithm Based On The Color Halftone Fluorescent Printing And Its Application In Packaging Design, Hu Yaojian, Liu Juan, Wang Ruojing, Zhong Yunfei

*Journal of Applied Packaging Research*

**Abstract：**This paper analyzed the characteristics of colorless fluorescent ink and the existing color separation theory, so that colored additive method should be used in printing color pattern with colorless fluorescent ink as well as three-color screening separation type (red, green and blue). Considering the exhibition of the tone, this paper selected dot parallel screening method. At the same time, through comparing the properties of different dots, this paper adopted a special method of AM screening, using regular triangle as the basic dot model to a threshold matrix of AM screening. Finally, designing a screening algorithm which best suit the ...

Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, 2018 University of Massachusetts Amherst

#### Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack

*Doctoral Dissertations*

We develop a nonequilibrium statistical mechanical description of the evolution of point vortex systems governed by either the Euler, single-layer quasigeostrophic or two-layer quasigeostrophic equations. Our approach is based on a recently proposed optimal closure procedure for deriving reduced models of Hamiltonian systems. In this theory the statistical evolution is kept within a parametric family of distributions based on the resolved variables chosen to describe the macrostate of the system. The approximate evolution is matched as closely as possible to the true evolution by minimizing the mean-squared residual in the Liouville equation, a metric which quantifies the information loss rate ...