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Non-linear Dynamics

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Articles 241 - 270 of 447

Full-Text Articles in Applied Mathematics

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni Apr 2018

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in switched …


Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid Mar 2018

Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid

Western Research Forum

General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …


P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing Mar 2018

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.


Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Kyle D. Moore Mar 2018

Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Kyle D. Moore

Theses and Dissertations

Due to the many drawbacks associated with a traditional lighter than air vehicle (LTAV), there is a desire for a LTAV which generates lift from an internal vacuum. To date, two feasible designs (the icosahedron and the hexakis icosahedron) for this so called vacuum lighter than air vehicle (VLTAV) have been studied at the Air Force Institute of Technology (AFIT). This research looks to show the feasibility of a new design for a VLTAV, the celestial icosahedron. This research includes a boundary condition study which proves the symmetric nature of the celestial icosahedron's frame with laterally constrained and unconstrained vertices. …


Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier Feb 2018

Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

Electronic Theses and Dissertations

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …


Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher Jan 2018

Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher

Faculty Publications

Current hypotheses regarding the disappearance of Neanderthals (NEA) in Europe fall into two main categories: climate change, and competition. Here we review current research and existing mathematical models that deal with this question, and we propose an approach that incorporates and permits the investigation of the current hypotheses. We have developed a set of differential equations that model population dynamics of anatomically modern humans (AMH) and NEA, their ecological relations to prey species, and their mutual interactions. The model allows investigators to explore each of the two main categories or combinations of both, as well as various forms of competition …


Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona Jan 2018

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

Honors Undergraduate Theses

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …


Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang Jan 2018

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …


Particle Filters For State Estimation Of Confined Aquifers, Graeme Field Jan 2018

Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

UNF Graduate Theses and Dissertations

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including …


Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko Dec 2017

Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …


On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin Dec 2017

On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

Graduate Theses/Dissertations

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.


Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett Dec 2017

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.


Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly Nov 2017

Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly

Spora: A Journal of Biomathematics

As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical …


Height Transitions, Shape Evolution, And Coarsening Of Equilibrating Quantum Nanoislands, Mikhail Khenner Oct 2017

Height Transitions, Shape Evolution, And Coarsening Of Equilibrating Quantum Nanoislands, Mikhail Khenner

Mathematics Faculty Publications

No abstract provided.


Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo Oct 2017

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar, Elizabeth Rodriguez Oct 2017

Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar, Elizabeth Rodriguez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Stochastic And Deterministic Multigroup Epidemiology, Jordan Hasler, Chris Chang, Ananya Yammanuru, Lewis Oh, Esther Matthew, Mounisha Kovour Oct 2017

Stochastic And Deterministic Multigroup Epidemiology, Jordan Hasler, Chris Chang, Ananya Yammanuru, Lewis Oh, Esther Matthew, Mounisha Kovour

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann Oct 2017

A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Handicap Principle Implies Emergence Of Dimorphic Ornaments, Sara Clifton, Daniel M. Abrams, Rosemary I. Braun Oct 2017

Handicap Principle Implies Emergence Of Dimorphic Ornaments, Sara Clifton, Daniel M. Abrams, Rosemary I. Braun

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Food Web Control And Synchronization Using A Robust Feedback, Hector Puebla, Mariana Rodriguez-Jara, Cesar S. Lopez-Monsalvo, Eliseo Hernandez-Martinez, Alejandra Velasco-Perez Oct 2017

Food Web Control And Synchronization Using A Robust Feedback, Hector Puebla, Mariana Rodriguez-Jara, Cesar S. Lopez-Monsalvo, Eliseo Hernandez-Martinez, Alejandra Velasco-Perez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


The Effects Of Evolution On Food Web Diversity And Abundance, Rosalyn Rael Oct 2017

The Effects Of Evolution On Food Web Diversity And Abundance, Rosalyn Rael

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The California Coast, James Peirce, Olcay Akman, Abou Seck Oct 2017

Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The California Coast, James Peirce, Olcay Akman, Abou Seck

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner Aug 2017

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

Mathematics Faculty Publications

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 …


Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu May 2017

Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.


Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon May 2017

Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon

Biology and Medicine Through Mathematics Conference

No abstract provided.


Comparison Of The Regulatory Dynamics Of Related Small Gene Regulatory Networks That Control The Response To Cold Shock In Saccharomyces Cerevisiae, Natalie Williams May 2017

Comparison Of The Regulatory Dynamics Of Related Small Gene Regulatory Networks That Control The Response To Cold Shock In Saccharomyces Cerevisiae, Natalie Williams

Honors Thesis

The Dahlquist Lab investigates the global, transcriptional response of Sacchromyces cerevisiae, baker’s yeast, to the environmental stress of cold shock, using DNA microarrays for the wild type strain and strains deleted for a particular regulatory transcription factor. Gene regulatory networks (GRNs) consist of transcription factors (TF), genes, and the regulatory connections between them that control the resulting mRNA and protein expression levels. We use mathematical modeling to determine the dynamics of the GRN controlling the cold shock response to determine the relative influence of each transcription factor in the network. A family of GRNs has been derived from the …


Application Of Symplectic Integration On A Dynamical System, William Frazier May 2017

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …


Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh Mar 2017

Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh

Faculty Publications

The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …


P26. Global Exponential Stabilization On So(3), Soulaimane Berkane Mar 2017

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)


Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov Jan 2017

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion …