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Partial Differential Equations Commons

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

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

Mikhail Khenner

Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence a film dewetting. The analysis is based on the extended Mullins equation, where the effects are cast as functions of the film thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80, 5381 (1998)) includes the oscillation of the surface energy with thickness caused by electrons confinement. By systematically comparing the effects, their contributions into the ...


An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger 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 R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.


Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, Haley Renee Dozier 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, Nicholas Spizzirri 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, Jia Zhao 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, Hildur Knutsdottir 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, Sofya Zaytseva, Leah Shaw, Rom Lipcius, Junping Shi 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., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry 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, Tracy Stepien, Erica Rutter, Meng Fan, Yang Kuang 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., Dietmar B. Oelz 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, Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe 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, Mark A. McKibben 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, Brian Daniel Allen 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), Wojciech Budzianowski 2016 Wroclaw University of Technology

Procesy Cieplne I Aparaty (Lab), Wojciech Budzianowski

Wojciech Budzianowski

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2. Population, Ruth Dover 2016 Illinois Mathematics and Science Academy

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.


4. Dragging Along, Ruth Dover 2016 Illinois Mathematics and Science Academy

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.


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

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.


Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin 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, Shu Gu 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 ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.


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