Index Catalog // Arch : Northwestern University Institutional Repository

Analytical Solutions and Optimization of the Time-Dependent Ginzburg-Landau Equation for Superconductors

Description:: The behavior of type-II superconductors is modeled using the time-dependent Ginzburg Landau equations (TDGLE). Pinning centers (inclusions) and geometries which maximize the critical current that can be passed through a superconductor are numerically obtained. Previous analytical results are summarized and new results are obtained for the critical current in one...
Keyword:: Phase Slips, Magnetic Vortices, Dynamical Systems, Optimization, and Superconductivity
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Gregory Jonathan Kimmel
Owner:: Scholarly Digital Publishing
Date Uploaded:: 02/12/2018
Date Modified:: 02/13/2018
Date Created:: 2016-01-01
Resource Type:: Dissertation

Mixing with Piecewise Isometries

Description:: Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich...
Keyword:: Mathematics and Piecewise
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Paul P Park
Owner:: Scholarly Digital Publishing
Date Uploaded:: 02/13/2018
Date Modified:: 02/13/2018
Date Created:: 2016-01-01
Resource Type:: Dissertation

Nonlocal Effects of Intraspecific Prey Competition on the Stability of Predator-Prey Equilibria

Description:: We studied the nonlocal effects of intraspecific prey competition on the stability of the critical points of the Rosenzweig-MacArthur model and the Holling-Tanner model, respectively, using linear stability analysis. In particular we focused on the study of the stability of the coexistence state influenced by the nonlocality for both models....
Keyword:: Applied Mathematics
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Jiang Zhuo
Owner:: Scholarly Digital Publishing
Date Uploaded:: 03/13/2018
Date Modified:: 03/13/2018
Date Created:: 2017-01-01
Resource Type:: Dissertation

Fractals by cutting-and-shuffling a hemispherical shell

Description:: A fractal is created by a Piecewise Isometry (PWI) which cuts a 2D object into pieces and rearranges those pieces to recreate the original object in a scrambled form. The PWI studied here splits a hemispherical shell into four pieces along cutting lines and rearranges them into a shuffled hemisphere....
Keyword:: crd18
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Thomas F. Lynn
Owner:: Scholarly Digital Publishing
Date Uploaded:: 06/04/2018
Date Modified:: 06/04/2018
Date Created:: 2018-04-10
Resource Type:: Video

Mixing by cutting-and-shuffling a hemispherical shell

Description:: Mixing due to cutting-and-shuffling is studied at a fundamental level using 2D mappings known as Piecewise Isometries (PWI) which can create beautiful mixing patterns. The PWI studied here splits a hemispherical shell (HS) into four curved triangular pieces that are rearranged to make a shuffled HS. Applying the PWI repeatedly...
Keyword:: crd18
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Thomas F. Lynn
Owner:: Scholarly Digital Publishing
Date Uploaded:: 06/04/2018
Date Modified:: 06/04/2018
Date Created:: 2018-04-10
Resource Type:: Image

Minimal Mathematical Models of Human and Animal Dynamical Systems

Description:: Minimal mathematical models are used to understand complex phenomena in the physical, biological, and social sciences. This modeling philosophy never claims, nor even attempts, to fully capture the mechanisms underlying the phenomena, and instead offers insights and predictions not otherwise possible. Here, we build and explore minimal dynamical systems models...
Keyword:: evolution, restaurant tipping, chronic pain, dynamical system, mobile health, and mathematical model
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Sara M. Clifton
Owner:: Scholarly Digital Publishing
Date Uploaded:: 10/09/2018
Date Modified:: 10/09/2018
Date Created:: 2017-01-01
Resource Type:: Dissertation

Investigations of Pattern Formation in Dryland Vegetation

Description:: Vegetation in dryland environments is often patchy in response to water limitation. This patchiness can take the form of periodic patterning at length scales much larger than that of an individual plant. Instances of patterns resembling leopard spots and tiger stripes are widespread in dry regions of Africa, Australia, and...
Keyword:: climate change
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Karna Gowda
Owner:: Scholarly Digital Publishing
Date Uploaded:: 10/21/2018
Date Modified:: 10/21/2018
Date Created:: 2017-01-01
Resource Type:: Dissertation

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

Description:: Bacterial biofilms are aggregates of cells that adhere to nearly any solid-fluid interface. While many have harmful effects, such as industrial damage and nosocomial infections, certain biofilm species are now generating renewable energy as the fundamental components of Microbial Fuel Cells (MFCs). In an MFC, bacteria consume organic waste and,...
Keyword:: biharmonic
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Jared Allen Hicks
Owner:: Scholarly Digital Publishing
Date Uploaded:: 01/09/2019
Date Modified:: 01/09/2019
Date Created:: 2017-01-01
Resource Type:: Dissertation

Bifurcation Analysis of a Piecewise-Smooth Arctic Energy Balance Model

Description:: This dissertation investigates a single-column model for Arctic energy balance in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero. This limit is a common modeling approximation used in conceptual climate models, and we explore the implications of taking this limit on bifurcations associated with the...
Keyword:: ice-albedo feedback, Filippov, climate tipping points, Arctic sea ice, and nonsmooth dynamical system
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Kaitlin Hill
Owner:: Scholarly Digital Publishing
Date Uploaded:: 02/09/2019
Date Modified:: 02/09/2019
Date Created:: 2017-01-01
Resource Type:: Dissertation

Methods for Large Scale Nonlinear and Stochastic Optimization

Description:: The goal of this thesis is to develop practical algorithms with sound theoretical properties for three different subfields of nonlinear optimization: (i) Optimization Algorithms for Supervised Machine Learning; (ii) Derivative-Free Optimization; and (iii) Distributed Optimization. As such, the thesis is divided into three main chapters. The focus of Chapter 2...
Keyword:: Engineering Sciences and Applied Mathematics
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Albert Solomon Berahas
Owner:: Scholarly Digital Publishing
Date Uploaded:: 02/22/2019
Date Modified:: 02/22/2019
Date Created:: 2018-01-01
Resource Type:: Dissertation

Methods for Images, Time Series, and Activation Functions with Deep Neural Networks

Description:: In this work, we explore the utility of the three main types of neural networks: feed forward, convolutional, and recurrent. While using these networks, we develop a new way to model multiagent trajectory data, explore the use of multiple activation functions for neurons at each layer of a neural network,...
Keyword:: Stock Prediction, Deep Learning, Basketball Trajectory, Activation Functions, and Machine Learning
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Mark Harmon
Owner:: Scholarly Digital Publishing
Date Uploaded:: 10/14/2019
Date Modified:: 10/14/2019
Date Created:: 2018-01-01
Resource Type:: Dissertation

Mathematical Models of Social Systems with Applications to Urban Scaling Laws and Political Party Polarization

Description:: Recent years have witnessed success in using mathematical models to understand complex social phenomena. In this dissertation, we develop and apply two mathematical models in the area of urban productivity and political elections. ', 'First, we investigate the puzzling superlinear scaling behavior of many outputs in urban areas, such as...
Keyword:: Applied mathematics
Subject:: Engineering Sciences and Applied Mathematics
Creator:: V. Chuqiao Yang
Owner:: Scholarly Digital Publishing
Date Uploaded:: 10/28/2019
Date Modified:: 10/28/2019
Date Created:: 2018-01-01
Resource Type:: Dissertation

Traveling Waves in Models of Population Dynamics with Nonlocal Interactions

Description:: This thesis focuses on ecological models of population dynamics and the traveling, migratory waves that can result when a stable state either displaces an unstable state, or displaces another stable state. We consider the effect of nonlocal interactions, where members of the species interact over a distance. This gives rise...
Keyword:: biological control, population dynamics, traveling waves, and nonlocality
Subject:: Engineering Sciences and Applied Mathematics
Creator:: Eric Arthur Autry
Owner:: Scholarly Digital Publishing
Date Uploaded:: 11/04/2019
Date Modified:: 11/06/2019
Date Created:: 2018-01-01
Resource Type:: Dissertation

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Analytical Solutions and Optimization of the Time-Dependent Ginzburg-Landau Equation for Superconductors

Mixing with Piecewise Isometries

Nonlocal Effects of Intraspecific Prey Competition on the Stability of Predator-Prey Equilibria

Fractals by cutting-and-shuffling a hemispherical shell

Mixing by cutting-and-shuffling a hemispherical shell

Minimal Mathematical Models of Human and Animal Dynamical Systems

Investigations of Pattern Formation in Dryland Vegetation

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

Bifurcation Analysis of a Piecewise-Smooth Arctic Energy Balance Model

Methods for Large Scale Nonlinear and Stochastic Optimization

Methods for Images, Time Series, and Activation Functions with Deep Neural Networks

Mathematical Models of Social Systems with Applications to Urban Scaling Laws and Political Party Polarization

Traveling Waves in Models of Population Dynamics with Nonlocal Interactions

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