Applied Mathematics Commons^™

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

Biology Faculty Research

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, Nihad E. Daidzic Ph.D., Sc.D.

International Journal of Aviation, Aeronautics, and Aerospace

The main objective of this original research article is to understand the short-term dynamic behavior of the transport-category airplane during landing flare elevator control application. Increasing the pitch angle to arrest the sink rate, the elevator will have to produce negative lift to rotate the airplane’s nose upward. This has an immediate adverse effect of initially accelerating airplane downward. A mathematical model of landing flare based on the flat-Earth longitudinal dynamics of rigid airplane was developed which is realistic only on very short time-scales as pitch stiffness and damping were neglected. Pilot control scenarios using impulse and step elevator pull-up …

On Quasilinear Parabolic Evolution Equations In Weighted Lp-Spaces Ii, Jeremy Lecrone, Mathias Wilke, Jan Prüss

Department of Math & Statistics Faculty Publications

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in 2010, is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.

A Coupled Pde Model For The Morphological Instability Of A Multi-Component Thin Film During Surface Electromigration, Mahdi Bandegi

Masters Theses & Specialist Projects

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics …

Mathematical Equations And System Identification Models For A Portable Pneumatic Bladder System Designed To Reduce Human Exposure To Whole Body Shock And Vibration, Ezzat Aziz Ayyad

UNLV Theses, Dissertations, Professional Papers, and Capstones

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose …

Stability Of An Inhomogeneous Damped Vibrating String, Siddhartha Misra, Ganesh C. Gorain

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the vibrations of an inhomogeneous damped string under a distributed disturbing force which is clamped at both ends. The well-possedness of the system is studied. We prove that the amplitude of such vibrations is bounded under some restriction of the disturbing force. Finally, we establish the uniform exponential stabilization of the system when the disturbing force is insignificant. The results are established directly by means of an exponential energy decay estimate.

Experimental Evidence For Heterogeneous Expectations In A Simple New Keynesian Framework, Atticus David Holm Graven

Business and Economics Honors Papers

This paper is a two-dimensional analysis of agent behavior in a standard New Keynesian (NK) Macroeconomic model. On the dimension of pure mathematics, we analyze the parameters of the NK model and of possible prediction rules. On the other dimension we continue a practice of empirical study of heterogeneous expectations with an experiment. The experiment will ask participants to make predictions of future output and inflation. Their responses will create a data-set upon which analysis will be performed to illuminate and corroborate current theories of economic decision making. The literature has shown that most agents' forecasting rules can be modeled …

Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand …

Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson

Theses, Dissertations and Capstones

In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one unified theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall’s …

Examples Of G-Strand Equations, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincare´ reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of G-strand constructions, including …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Comments On The Paper “An Alternative Combination Rule For Evidential Reasoning” By Sebbak Et Al., Published In Fusion 2014 Conference, Salamanca, Spain, July 2014, Florentin Smarandache, Jean Dezert, Arnaud Martin

Branch Mathematics and Statistics Faculty and Staff Publications

In this note we want to show that the PCR6 fusion rule works and redistributes the conflicting mass properly, contrarily to the authors’ assertion that “the focal element {v3} absorbs almost all of the conflicting mass (the majority).” We also question the validity of the new CREC rule of combination presented by the authors.

Two-Source Energy Balance Model To Calculate E, T, And Et: Comparison Of Priestley-Taylor And Penman-Monteith Formulations And Two Time Scaling Methods, Paul D. Colaizzi, Nurit Agam, Judy A. Tolk, Steven R. Evett, Terry A. Howell, Prasanna H. Gowda, Susan A. O'Shaughnessy, William P. Kustas, Martha C. Anderson

United States Department of Agriculture-Agricultural Research Service / University of Nebraska-Lincoln: Faculty Publications

The two-source energy balance (TSEB) model calculates the energy balance of the soil-canopy-atmosphere continuum, where transpiration is initially determined by the Priestley-Taylor equation. The TSEB was revised recently using the Penman-Monteith equation to replace the Priestley-Taylor formulation, thus better accounting for the impact of large and varying vapor pressure deficits (VPD) typical of advective, semiarid climates. This study is a comparison of the Priestley- Taylor and Penman-Monteith versions of the TSEB (termed TSEB-PT and TSEB-PM, respectively). Evaporation (E), transpiration (T), and evapotranspiration (ET) calculated by the TSEB-PT and TSEB-PM versions were compared to measurements obtained with microlysimeters, sap flow gauges, …

Using Delay-Differential Equations For Modeling Calcium Cycling In Cardiac Myocytes, Ryan Thompson

Theses

The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an …

Stability And Entanglement In An Optomechanical System, Matthew Schumacher

Theses

Optomechanical systems are currently of great interest as they lie at the boundary between quantum and classical mechanics, promising fundamental insights as well as new technologies. The practical operation of an optomechanical system requires that it satisfy the criteria of mechanical stability. Further, for quantum applications, it is important to characterize the degree of nonclassical correlation present between the mechanical and optical subsystems. In this study, we analyze the stability and entanglement in an optomechanical system where couplings linear as well as quadratic in the mechanical displacement are present simultaneously. Such systems can be realized experimentally. Our analysis of the …

A Population Model For Walleye In Nebraska Irrigation Reservoirs, Robert A. Kill

School of Natural Resources: Dissertations, Theses, and Student Research

Understanding how and why fish population size changes between years is a central theme in fisheries ecology. Fishery agencies have limited time and financial resources, thus there is a need for a quantitative way to direct the limited time and financial resources so agencies can manage fisheries more efficiently. I developed a tool for fishery managers that synthesizes common population indices and evaluated the relative importance of those indices given varying uncertainty in age-0 walleye Sander vitreus survival. Under most circumstances, I determined that resources are best utilized in reducing age-0 survival uncertainty when understanding walleye population growth. I applied …

Graphic Illustration Of The Transmission Resonances For The Dkp Particles, B. Boutabia-Chéraitia, Abdenacer Makhlouf

Applications and Applied Mathematics: An International Journal (AAM)

We consider the Duffin-Kemmer-Petiau (DKP) equation in the presence of a spatially one-dimensional Woods-Saxon (WS) potential and we show by graphics how the zero-reflection condition on the Klein interval depends on the shape of the potential.

Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the …

Analysis Of Time-Dependent Integrodifference Population Models, Taylor J. Mcadam

HMC Senior Theses

The population dynamics of species with separate growth and dispersal stages can be described by a discrete-time, continuous-space integrodifference equation relating the population density at one time step to an integral expression involving the density at the previous time step. Prior research on this model has assumed that the equation governing the population dynamics remains fixed over time, however real environments are constantly in flux. We show that for time-varying models, there is a value Λ that can be computed to determine a sufficient condition for population survival. We also develop a framework for analyzing persistence of a population for …