Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, 2018 The University of Akron

#### Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans

*Honors Research Projects*

The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and ...

Random Walks On Simple Two-Dimensional Manifolds, 2018 Hamline University

#### Random Walks On Simple Two-Dimensional Manifolds, Tom Eichlersmith

*Departmental Honors Projects*

A C++ implementation of random walks is constructed with examples for the plane, sphere, and torus included. This package is available publicly, and can be expanded to different situations on the included surfaces as well as other surfaces. The random walks are studied by measuring how long they take to reach a pre-defined escape region on the surface. These escape regions and their interaction with the surface are what affect the behavior of the random walks the most.

High-Order Integral Equation Methods For Quasi-Magnetostatic And Corrosion-Related Field Analysis With Maritime Applications, 2018 University of Kentucky

#### High-Order Integral Equation Methods For Quasi-Magnetostatic And Corrosion-Related Field Analysis With Maritime Applications, Robert Pfeiffer

*Theses and Dissertations--Electrical and Computer Engineering*

This dissertation presents techniques for high-order simulation of electromagnetic fields, particularly for problems involving ships with ferromagnetic hulls and active corrosion-protection systems.

A set of numerically constrained hexahedral basis functions for volume integral equation discretization is presented in a method-of-moments context. Test simulations demonstrate the accuracy achievable with these functions as well as the improvement brought about in system conditioning when compared to other basis sets.

A general method for converting between a locally-corrected Nyström discretization of an integral equation and a method-of-moments discretization is presented next. Several problems involving conducting and magnetic-conducting materials are solved to verify the accuracy ...

Decoding Book Barcode Images, 2018 Claremont McKenna College

#### Decoding Book Barcode Images, Yizhou Tao

*CMC Senior Theses*

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises ...

Pseudo-Companion Matrices For Polynomial Systems, 2018 Michigan Technological University

#### Pseudo-Companion Matrices For Polynomial Systems, Melinda Kleczynski

*Dissertations, Master's Theses and Master's Reports*

Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, 2018 Michigan Technological University

#### A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

*Dissertations, Master's Theses and Master's Reports*

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty ...

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2017 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, 2017 Scuola Normale Superiore, Pisa, Italy

#### From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, Giovanni Barbarino, Carlo Garoni

*Electronic Journal of Linear Algebra*

Sequences of matrices with increasing size naturally arise in several areas of science, such as, for example, the numerical discretization of differential and integral equations. An approximation theory for sequences of this kind has recently been developed, with the aim of providing tools for computing their asymptotic singular value and eigenvalue distributions. The cornerstone of this theory is the notion of approximating classes of sequences (a.c.s.), which is also fundamental to the theory of generalized locally Toeplitz (GLT) sequences, and hence to the spectral analysis of PDE discretization matrices. Drawing inspiration from measure theory, here it is introduced ...

Feasible Computation In Symbolic And Numeric Integration, 2017 The University of Western Ontario

#### Feasible Computation In Symbolic And Numeric Integration, Robert H.C. Moir

*Electronic Thesis and Dissertation Repository*

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term *feasible computation* to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently.

Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity ...

Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, 2017 University of Tennessee, Knoxville

#### Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, John Timothy Cummings

*Doctoral Dissertations*

We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which ...

Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, 2017 College of William and Mary

#### Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, Xiang Liu

*Undergraduate Honors Theses*

In this paper, efforts will be made to study an extended Neoclassic economic growth model derived from Solow-Swan Model and Ramsey-Cass-Koopsman Model. Some growth models (e.g. Solow-Swan Model) attempt to explain long-run economic growth by looking at capital accumulation, labor or population growth, and in- creases in productivity, while our derived model tends to look at growth from individual household and how their choice of saving, consumption and money holdings would affect the overall economic capital accumulation over a long period of time.

First an optimal control model is set up, and a system of differential equations and algebraic ...

Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, 2017 Stanford University

#### Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla

*Spora: A Journal of Biomathematics*

The circadian clock, responsible for coordinating organism function with daily and seasonal changes in the day-night cycle, is controlled by a complex protein network that constitutes a robust biochemical oscillator. Deterministic ordinary differential equation models have been used extensively to model the behavior of these central clocks. However, due to the small number of proteins involved in the circadian oscillations, mathematical models that track stochastic variations in the numbers of clock proteins may reveal more complex and biologically relevant behaviors. In this paper, we compare the response of a robust yet detailed deterministic model for the mammalian circadian clock with ...

Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, 2017 Eastern University

#### Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly

*Spora: A Journal of Biomathematics*

As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical ...

Heads And Tails, 2017 The California Maritime Academy

#### Heads And Tails, Julie Simons

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

No abstract provided.

A Cellular Automaton Modeling Approach To Chestnut Blight Canker Development, 2017 Illinois State University

#### A Cellular Automaton Modeling Approach To Chestnut Blight Canker Development, Samuel Iselin

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

No abstract provided.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, 2017 Cylance, Inc.

#### Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

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

No abstract provided.

A Method For Sensitivity Analysis And Parameter Estimation Applied To A Large Reaction-Diffusion Model Of Cell Polarization, 2017 The Ohio State University

#### A Method For Sensitivity Analysis And Parameter Estimation Applied To A Large Reaction-Diffusion Model Of Cell Polarization, Marissa Renardy, Tau-Mu Yi, Dongbin Xiu, Ching-Shan Chou

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

No abstract provided.

High-Order Relaxed Multirate Infinitesimal Step Methods For Multiphysics Applications, 2017 Southern Methodist University

#### High-Order Relaxed Multirate Infinitesimal Step Methods For Multiphysics Applications, Jean Sexton

*Mathematics Theses and Dissertations*

In this work, we consider numerical methods for integrating multirate ordinary differential equations. We are interested in the development of new multirate methods with good stability properties and improved efficiency over existing methods. We discuss the development of multirate methods, particularly focusing on those that are based on Runge-Kutta theory. We introduce the theory of Generalized Additive Runge-Kutta methods proposed by Sandu and Günther. We also introduce the theory of Recursive Flux Splitting Multirate Methods with Sub-cycling described by Schlegel, as well as the Multirate Infinitesimal Step methods this work is based on. We propose a generic structure called Flexible ...

Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, 2017 The University of Southern Mississippi

#### Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson

*Dissertations*

In the numerical solution of partial differential equations (PDEs), there is a need for solving large scale problems. The Radial Basis Function Differential Quadrature (RBFDQ) method and local RBF-DQ method are applied for the solutions of boundary value problems in annular domains governed by the Poisson equation, inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. By choosing the collocation points properly, linear systems can be obtained so that the coefficient matrices have block circulant structures. The resulting systems can be efficiently solved using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). For the local RBFDQ method, the ...

Analysis And Implementation Of Numerical Methods For Solving Ordinary Differential Equations, 2017 Western Kentucky University

#### Analysis And Implementation Of Numerical Methods For Solving Ordinary Differential Equations, Muhammad Sohel Rana

*Masters Theses & Specialist Projects*

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It ...