Exact Robot Navigation Using Power Diagrams, 2016 University of Pennsylvania

#### Exact Robot Navigation Using Power Diagrams, Omur Arslan, Daniel E. Koditschek

*Departmental Papers (ESE)*

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way. We use power diagrams, generalized Voronoi diagrams with additive weights, to identify the robot’s collision free convex neighborhood, and to generate the value of our proposed candidate solution vector field at any free configuration via evaluation of an associated convex ...

Computing All Isolated Invariant Sets At A Finite Resolution, 2016 College of William and Mary

#### Computing All Isolated Invariant Sets At A Finite Resolution, Martin Salgado-Flores

*Undergraduate Honors Theses*

Conley Index theory has inspired the development of rigorous computational methods to study dynamics. These methods construct outer approximations, combinatorial representations of the system, which allow us to represent the system as a combination of two graphs over a common vertex set. Invariant sets are sets of vertices and edges on the resulting digraph. Conley Index theory relies on isolated invariant sets, which are maximal invariant sets that meet an isolation condition, to describe the dynamics of the system. In this work, we present a computationally efficient and rigorous algorithm for computing all isolated invariant sets given an outer approximation ...

Mathematical Modeling Of Quadcopter Dynamics, 2016 Rose-Hulman Institute of Technology

#### Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)

*Rose-Hulman Undergraduate Research Publications*

Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion ...

On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, 2016 University of Richmond

#### On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, Jeremy Lecrone, Gieri Simonett

*Math and Computer Science Faculty Publications*

We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0

Study Of Infectious Diseases By Mathematical Models: Predictions And Controls, 2016 The University of Western Ontario

#### Study Of Infectious Diseases By Mathematical Models: Predictions And Controls, Sm Ashrafur Rahman

*Electronic Thesis and Dissertation Repository*

The aim of this thesis is to understand the spread, persistence and prevention mechanisms of infectious diseases by mathematical models. Microorganisms that rapidly evolve pose a constant threat to public health. Proper understanding of the transmission machinery of these existing and new pathogens may facilitate devising prevention tools. Prevention tools against transmissions, including vaccines and drugs, are evolving at a similar pace. Efficient implementation of these new tools is a fundamental issue of public health. We primarily focus on this issue and explore some theoretical frameworks.

Pre-exposure prophylaxis (PrEP) is considered one of the promising interventions against HIV infection as ...

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

Inżynieria Chemiczna Lab., 2016 Wroclaw University of Technology

Topological Data Analysis For Systems Of Coupled Oscillators, 2016 Harvey Mudd College

#### Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton

*HMC Senior Theses*

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a ...

A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, 2016 Virginia Commonwealth University

#### A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark

*Theses and Dissertations*

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

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.

Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, 2016 Iowa State University

#### Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, Davood Hajinezhad, Mingyi Hong, Tuo Zhao, Zhaoran Wang

*Industrial and Manufacturing Systems Engineering Conference Proceedings and Posters*

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum *N/* nonconvex *Li/N/ *smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into *N/ * subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves *e-1* stationary solution using...gradient evaluations, which can be up to *O(N)/ * times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex l1 penalized quadratic problems with polyhedral ...

Models Of Internal Waves In The Presence Of Currents, 2016 Technological University Dublin

#### Models Of Internal Waves In The Presence Of Currents, Alan Compelli, Rossen Ivanov

*Conference papers*

A fluid system consisting of two domains is examined. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. An internal wave propagating in one direction, driven by gravity, acts as a free common interface between the fluids. Various current profiles are considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are formulated. The presented models provide potential applications to modelling of internal geophysical ...

The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, 2016 Technological University Dublin

#### The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov

*Articles*

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised ...

Border-Collision Bifurcations Of Cardiac Calcium Cycling, 2015 University of Tennessee - Knoxville

#### Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle

*Masters Theses*

In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States.

Simulating And Animating The Spatial Dynamics Of Interacting Species Living On A Torus, 2015 CUNY New York City College of Technology

#### Simulating And Animating The Spatial Dynamics Of Interacting Species Living On A Torus, Boyan Kostadinov

*Publications and Research*

The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled ...

Transition Orbits Of Walking Droplets, 2015 California Polytechnic State University - San Luis Obispo

#### Transition Orbits Of Walking Droplets, Joshua Parker

*Physics*

It was recently discovered that millimeter-sized droplets bouncing on the surface of an oscillating bath of the same fluid can couple with the surface waves it produces and begin walking across the fluid bath. These walkers have been shown to behave similarly to quantum particles; a few examples include single-particle diffraction, tunneling, and quantized orbits. Such behavior occurs because the drop and surface waves depend on each other to exist, making this the first and only known macroscopic pilot-wave system. In this paper, the quantized orbits between two identical drops are explored. By sending a perturbation to a pair of ...

Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, 2015 Bowdoin College

#### Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg

*Honors Projects*

No abstract provided.

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, 2015 Ursinus College

#### Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

*Mathematics Honors Papers*

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided ...

Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, 2015 Georgia State University

#### Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, Kevin Daley

*Georgia State Undergraduate Research Conference*

gsurc 2015

Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, 2015 Georgia State University

#### Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper

*Georgia State Undergraduate Research Conference*

No abstract provided.