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*

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.

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 Averaging Method For Advection-Diffusion Equations, 2016 Graduate Center, City University of New York

#### An Averaging Method For Advection-Diffusion Equations, Nicholas Spizzirri

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

Many models for physical systems have dynamics that happen over various different time scales. For example, contrast the everyday waves in the ocean with the larger, slowly moving global currents. The method of multiple scales is an approach for approximating the solutions of differential equations by separating out the dynamics at slower and faster time scales. In this work, we apply the method of multiple scales to generic advection-diffusion equations (both linear and non-linear, and in arbitrary spatial dimensions) and develop a method for 'averaging out' the faster scale phenomena, giving us an 'effective' solution for the slower scale dynamics ...

Mathematical Models Of Biofilm For Antimicrobial Persistence, 2016 University of North Carolina at Chapel Hill

#### Mathematical Models Of Biofilm For Antimicrobial Persistence, Jia Zhao

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System, 2016 University of British Columbia

#### Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System, Hildur Knutsdottir

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Spatial Patterning In The York River Tidal Marshes Through The Interaction Of Cordgrass, Mussels And Sediment, 2016 College of William and Mary

#### Spatial Patterning In The York River Tidal Marshes Through The Interaction Of Cordgrass, Mussels And Sediment, Sofya Zaytseva, Leah Shaw, Rom Lipcius, Junping Shi

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., 2016 Georgia Institute of Technology

#### Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry

*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.

Force Generation And Contraction Of Random Actomyosin Bundles., 2016 Courant Institute (NYU)

#### Force Generation And Contraction Of Random Actomyosin Bundles., Dietmar B. Oelz

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Solution Techniques And Error Analysis Of General Classes Of Partial Differential Equations, 2016 Boise State University

#### Solution Techniques And Error Analysis Of General Classes Of Partial Differential Equations, Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe

*Boise State University Theses and Dissertations*

While constructive insight for a multitude of phenomena appearing in the physical and biological sciences, medicine, engineering and economics can be gained through the analysis of mathematical models posed in terms of systems of ordinary and partial differential equations, it has been observed that a better description of the behavior of the investigated phenomena can be achieved through the use of functional differential equations (FDEs) or partial functional differential equations (PFDEs). PFDEs or functional equations with ordinary derivatives are subclasses of FDEs. FDEs form a general class of differential equations applied in a variety of disciplines and are characterized by ...

General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, 2016 West Chester University of Pennsylvania

#### General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, Mark A. Mckibben

*Mathematics*

Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal ...

Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, 2016 University of Tennessee - Knoxville

#### Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, Brian Daniel Allen

*Doctoral Dissertations*

We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in Hyperbolic space and show long time existence of the flow as well as asymptotic convergence to horospheres. Along the way many important local estimates as well as global estimates are obtained. In addition, we develop a useful family of cutoff functions for IMCF as well as a non-compact ODE maximum principle at infinity which are integral tools used throughout the document.

Procesy Cieplne I Aparaty (Lab), 2016 Wroclaw University of Technology

2. Population, 2016 Illinois Mathematics and Science Academy

#### 2. Population, Ruth Dover

*Differential Equations*

Introduction to logistic population growth.

4. Dragging Along, 2016 Illinois Mathematics and Science Academy

3: Drugs And De's, 2016 Illinois Mathematics and Science Academy

#### 3: Drugs And De's, Ruth Dover

*Differential Equations*

Making a connection between discrete recursion and differential equations.

1. Coffee, 2016 Illinois Mathematics and Science Academy

Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, 2016 University of Vienna

#### Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin

*Articles*

We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

Homogenization Of Stokes Systems With Periodic Coefficients, 2016 University of Kentucky

#### Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu

*Theses and Dissertations--Mathematics*

In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and *L*^{∞} estimates for the pressure as well as Liouville property for solutions in ℝ^{d}. We are able to obtain the boundary W^{{1,p}} estimates in a bounded *C*^{1} domain for any 1 < *p* < ∞. We also study the convergence rates in *L*^{2} and *H*^{1} of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.