Physical Sciences and Mathematics Commons^™

Spreading Speeds And Traveling Waves In Some Population Models., Quancheng Meng

Electronic Theses and Dissertations

Virtually every ecosystem has been invaded by exotic organisms with potentially drastic consequences for the native fauna or flora. Studying the forms and rates of invading species has been an important topic in spatial ecology. We investigate two two-species competition models with Allee effects in the forms of reaction-diffusion equations and integro-difference equations. We discuss the spatial transitions from a mono-culture equilibrium to a coexistence equilibrium or a different mono-culture equilibrium in these models. We provide formulas for the spreading speeds based on the linear determinacy and show the results on the existence of traveling waves. We also study a …

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Publications & Presentations

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

Topographic Signatures Of Geodynamics, Samuel G. Roy

Electronic Theses and Dissertations

The surface of the Earth retains an imperfect memory of the diverse geodynamic, climatic, and surface transport processes that cooperatively drive the evolution of Earth. In this thesis I explore the potential of using topographic analysis and landscape evolution models to unlock past and/or present evidence for geodynamic activity. I explore the potential isolated effects of geodynamics on landscape evolution, particularly focusing on two byproducts of tectonic strain: rock displacement and damage. Field evidence supports a strong correlation between rock damage and erodibility, and a numerical sensitivity analysis supports the hypothesis that an order of magnitude weakening in rock, well …

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang Dr., Jiling Cao Prof.

Reza Moosavi Mohseni

The aim of the present study is to detect the chaotic behavior in the monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase the complexity of the system and leads to more chaotic behavior.

Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes

Mathematical Sciences Technical Reports (MSTR)

From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …

Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes

Rose-Hulman Undergraduate Research Publications

From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang, Jiling Cao

Reza Moosavi Mohseni

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Rooted In Hell: Predicting Invasion Rates Of Phragmites Australis, Jacob P. Duncan

Jacob P Duncan

No abstract provided.

Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon …

Dynamics Of Locally Coupled Oscillators With Next-Nearest-Neighbor Interaction, J. Herbrych, A. G. Chazirakis, N. Christakis, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A theoretical description of decentralized dynamics within linearly coupled, one-dimensional oscillators (agents) with up to next-nearest-neighbor interaction is given. Conditions for stability of such system are presented. Our results indicate that the stable systems have response that grow at least linearly in the system size. We give criteria when this is the case. The dynamics of these systems can be described with traveling waves with strong damping in the high frequencies. Depending on the system parameters, two types of solutions have been found: damped oscillations and reflectionless waves. The latter is a novel result and a feature of systems with …

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, 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, Kevin Daley

Georgia State Undergraduate Research Conference

gsurc 2015

Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper

Georgia State Undergraduate Research Conference

No abstract provided.

Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu

Chongyang Liu

In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of …

Video-To-Video Pose And Expression Invariant Face Recognition Using Volumetric Directional Pattern, Vijayan K. Asari, Almabrok Essa

Electrical and Computer Engineering Faculty Publications

Face recognition in video has attracted attention as a cryptic method of human identification in surveillance systems. In this paper, we propose an end-to-end video face recognition system, addressing a difficult problem of identifying human faces in video due to the presence of large variations in facial pose and expression, and poor video resolution. The proposed descriptor, named Volumetric Directional Pattern (VDP), is an oriented and multi-scale volumetric descriptor that is able to extract and fuse the information of multi frames, temporal (dynamic) information, and multiple poses and expressions of faces in input video to produce feature vectors, which are …

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment …

Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen

Philosophy Faculty Articles and Research

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …

Estimating Cost Adjustments Required To Accomplish Target Savings In Chronic Disease Management Interventions: A Simulation Study, Rafael Diaz, Joshua G. Behr, Bruce S. Britton

VMASC Publications

Chronic diseases are persistent ailments that are not preventable or curable with medication or vaccination. Many of the leading chronic conditions in industrialized societies may be related to lifestyle choices. The prevalence of these chronic conditions significantly affects the health, suffering, and longevity of patients. This paper demonstrates the utility of system dynamics as an approach to model and simulate the behavior of key cost factors in the implementation of population health management interventions. The study uses modeling and simulation as an evaluative method to identify potential savings stemming from an intervention within a well-defined population group. The model is …

Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

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Tematyka Prac Doktorskich, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram And Neutrosophic Degree Of Paradoxicity: Articles And Notes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book has four parts. In the first part, we collected five recent papers, published before in Progress in Physics, but reviewed. In the first paper, we approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists. That is the electron-positron plasma experiment of 2015 is the experimentum crucis verifying the mathematically predicted unmatter. In the second paper, we generalize the …

Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, Jonathan L. Hughes

Theses and Dissertations

Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model …

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.