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Partial Differential Equations Commons

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All Articles in Partial Differential Equations

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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 ...


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.


Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops 2016 The University of Akron

Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops

Honors Research Projects

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore ...


Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland 2016 University of Akron

Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland

Honors Research Projects

In this thesis, a one dimensional model is developed to investigate the initial stages of corrosion in a fastener assembly consisting of a stainless steel fastener and aluminum 7075 as the plate. Differential equations are formulated and solved to determine the profiles for the potential, the oxygen concentration, and the aluminum ion concentration in the crevice, and also the potential in the bulk electrolyte. This fastener system exhibits galvanic corrosion, pitting corrosion, and crevice corrosion. It is found that the potential decreases monotonically down the length of the crevice, the oxygen concentration decreases exponentially down the length of the crevice ...


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.


Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability, Siddharth Nigam, Paige Balcom 2016 University of New Hampshire, Durham

Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability, Siddharth Nigam, Paige Balcom

Honors Theses and Capstones

Started in Fall 2015, Project OASIS (Optimizing Aquaponic Systems to Improve Sustainability) is an interdisciplinary capstone project with the goal of designing a sustainable and affordable small-scale aquaponic system for use in developing nations to tackle the problems of malnutrition and food insecurity. Aquaponics is a symbiotic relationship between fish and vegetables growing together in a recirculating system. The project’s goals were to minimize energy consumption and construction costs while using universally available materials. The computational fluid dynamics (CFD) software OpenFOAM was used to create transient and steady-state models of fish tanks to visualize velocity profiles, streamlines, and particle ...


Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells 2016 Georgia Southern University

Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells

Electronic Theses & Dissertations

This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton's Universal Gravitation constant also known as "Big G". This tool set is especially applicable to Bose--Einstein--condensed systems present in NASA's Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrödinger or Gross--Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of ...


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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