A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, 2015 AAR Aerospace Consulting, LLC

#### 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 ...

Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, 2015 Florida International University

#### Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh

*FIU Electronic Theses and Dissertations*

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca^{2+}) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and ...

Horizontal Well’S Path Planning: An Optimal Switching Control, 2015 Curtin University of Technology

#### Horizontal Well’S Path Planning: An Optimal Switching Control, Zhaohua Gong, Kok Lay Teo, Chongyang Liu, Enmin Feng

*Chongyang Liu*

In this paper, we consider a three-dimensional horizontal well’s path planning problem, where the well’s path evolves as a combination of several constant-curvature smooth turn segments. The problem is formulated as an optimal switching control problem subject to continuous state inequality constraints. By applying the time-scaling transformation and constraint transcription in conjunction with local smooth approximation technique, the optimal switching control problem is approximated by a sequence of optimal parameter selection problems with only box constraints, each of which is solvable by gradient-based optimization techniques. The optimal path planning problems of the wells Ci-16-Cp146 and Jin27 in Liaohe ...

Inżynieria Chemiczna Ćw., 2015 Wroclaw University of Technology

Tematyka Prac Doktorskich, 2015 Wroclaw University of Technology

#### Tematyka Prac Doktorskich, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, 2015 Virginia Commonwealth University

#### Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly

*Statistical Sciences and Operations Research Publications*

Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model ...

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, 2015 Virginia Commonwealth University

#### Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

*Theses and Dissertations*

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of *folding* - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation ...

Periodic State Revivals In Commensurate Waveguide Arrays, 2015 Vinca Institute of Nuclear Sciences

#### Periodic State Revivals In Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

Emerging optical and quantum computers require hardware capable of coherent transport of and operations on quantum states. Here, we investigate finite optical waveguide arrays with linear coupling as means of efficient and compact coherent state transfer. Coherent transfer with periodic state revivals is enabled by engineering coupling coefficients between neighbouring waveguides to yield commensurate eigenvalue spectrum. Particular cases of finite arrays have been actively studied to achieve the perfect state transfer by mirroring the input into the output state.

We explore a much wider scope of coherent propagation and revivals of both the state amplitude and phase. We analytically solve ...

An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, 2015 Virginia Commonwealth University

#### An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

*Theses and Dissertations*

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a ...

Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, 2015 Virginia Commonwealth University

#### 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 ...

An Examination Of Mathematical Models For Infectious Disease, 2015 The University of Akron

#### An Examination Of Mathematical Models For Infectious Disease, David M. Jenkins

*Williams Honors College, Honors Research Projects*

Starting with the original 1926 formulation of the SIR (Susceptible-Infected-Removed) model for infectious diseases, mathematical epidemiology continued to grow. Many extensions such as the SEIR, MSIR, and MSEIR models were developed using SIR as a basis to model diseases in a variety of circumstances. By taking the original SIR model, and reducing the system of three first-order equations to a single first-order equation, analysis shows that the model predicts two possible situations. This analysis is followed by discussion of an alternative use of the SIR model which allows for one to track the amount of sustainable genetic variation in a ...

Stability Of A Circular System With Multiple Asymmetric Laplacians, 2015 Czech Technical University, Prague

#### Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek

*Mathematics and Statistics Faculty Publications and Presentations*

We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also ...

On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, 2015 Technological University Dublin

#### On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov

*Articles*

The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.

A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, 2015 Technological University Dublin

#### A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov

*Articles*

We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), 2014 Wroclaw University of Technology

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

*Wojciech Budzianowski*

No abstract provided.

Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, 2014 The University of Western Ontario

#### Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian

*Electronic Thesis and Dissertation Repository*

This thesis contains two parts. In the first part, we investigate bifurcation of limit cycles around a singular point in planar cubic systems and quadratic switching systems. For planar cubic systems, we study cubic perturbations of a quadratic Hamiltonian system and obtain 10 small-amplitude limit cycles bifurcating from an elementary center, for which up to 5th-order Melnikov functions are used. Moreover, we prove the existence of 12 small-amplitude limit cycles around a singular point in a cubic system by computing focus values. For quadratic switching system, we develop a recursive algorithm for computing Lyapunov constants. With this efficient algorithm, we ...

Understanding Recurrent Disease: A Dynamical Systems Approach, 2014 The University of Western Ontario

#### Understanding Recurrent Disease: A Dynamical Systems Approach, Wenjing Zhang

*Electronic Thesis and Dissertation Repository*

Recurrent disease, characterized by repeated alternations between acute relapse and long re- mission, can be a feature of both common diseases, like ear infections, and serious chronic diseases, such as HIV infection or multiple sclerosis. Due to their poorly understood etiology and the resultant challenge for medical treatment and patient management, recurrent diseases attract much attention in clinical research and biomathematics. Previous studies of recurrence by biomathematicians mainly focus on in-host models and generate recurrent patterns by in- corporating forcing functions or stochastic elements. In this study, we investigate deterministic in-host models through the qualitative analysis of dynamical systems, to ...

Estimation Of Hidden Markov Models And Their Applications In Finance, 2014 The University of Western Ontario

#### Estimation Of Hidden Markov Models And Their Applications In Finance, Anton Tenyakov

*Electronic Thesis and Dissertation Repository*

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts ...

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, 2014 University College Cork

#### One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

*Articles*

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

On The Evolution Of Virulence, 2014 California State University - San Bernardino

#### On The Evolution Of Virulence, Thi Nguyen

*Electronic Theses, Projects, and Dissertations*

The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then *n* strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.