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Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov 2019 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov

Articles

Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups GR ≃ Dh. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the GR-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with Dh symmetries are presented.


Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter 2019 Scripps College

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.


Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, Rosa Fallahpourghadikolaei 2019 Wilfrid Laurier University

Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, Rosa Fallahpourghadikolaei

Theses and Dissertations (Comprehensive)

Nanoscale systems fabricated with low-dimensional nanostructures such as carbon nanotubes, nanowires, quantum dots, and more recently graphene sheets, have fascinated researchers from different fields due to their extraordinary and unique physical properties. For example, the remarkable mechanical properties of nanoresonators empower them to have a very high resonant frequency up to the order of giga to terahertz. The ultra-high frequency of these systems attracted the attention of researchers in the area of bio-sensing with the idea to implement them for detection of tiny bio-objects. In this thesis, we originally propose and analyze a mathematical model for nonlinear vibrations of nanowire ...


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski 2018 Wojciech Budzianowski Consulting Services

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


A Companion To The Introduction To Modern Dynamics, David D. Nolte 2018 Purdue University

A Companion To The Introduction To Modern Dynamics, David D. Nolte

David D Nolte

A Jr/Sr Mechanics/Dynamics textbook from Oxford University Press, updating how we teach undergraduate physics majors with increased relevance for physics careers in changing times.

Additional materials, class notes and examples to go with the textbook Introduction to Modern Dynamics: Chaos, Networks, Space and Time (Oxford University Press, 2019).

The best parts of physics are the last topics that our students ever see.  These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many of our high-tech businesses.  Topics such as traffic on the World ...


Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright 2018 University of New Mexico

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to ...


17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof. 2018 Georgia State University

17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.

Georgia Undergraduate Research Conference (GURC)

Motivated by real-world networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of on-off connections. In the limit of fast switching, the relation between the ...


Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang 2018 The University of Western Ontario

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

Electronic Thesis and Dissertation Repository

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a ...


The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka 2018 Illinois State University

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari 2018 University of Colorado Boulder

Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon 2018 Illinois State University

Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak 2018 Illinois State University

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti 2018 Loyola Marymount University

Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Investigation Of Chaos In Biological Systems, Navaneeth Mohan 2018 The University of Western Ontario

Investigation Of Chaos In Biological Systems, Navaneeth Mohan

Electronic Thesis and Dissertation Repository

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different ...


Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack 2018 University of Massachusetts Amherst

Reduced Models Of Point Vortex Systems In Quasigeostrophic Fluid Dynamics, Jonathan Maack

Doctoral Dissertations

We develop a nonequilibrium statistical mechanical description of the evolution of point vortex systems governed by either the Euler, single-layer quasigeostrophic or two-layer quasigeostrophic equations. Our approach is based on a recently proposed optimal closure procedure for deriving reduced models of Hamiltonian systems. In this theory the statistical evolution is kept within a parametric family of distributions based on the resolved variables chosen to describe the macrostate of the system. The approximate evolution is matched as closely as possible to the true evolution by minimizing the mean-squared residual in the Liouville equation, a metric which quantifies the information loss rate ...


The Computational Study Of Fly Swarms & Complexity, Austin Bebee 2018 Linfield College

The Computational Study Of Fly Swarms & Complexity, Austin Bebee

Senior Theses

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...


Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr. 2018 The Graduate Center, City University of New York

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...


Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam 2018 Western Kentucky University

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...


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

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 ...


Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid 2018 Applied Mathematics,Western University

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 ...


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