Dynamical Systems Commons^™

Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Mechanika Płynów Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

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 …

Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov

Book chapter/book

This volume contains selected papers based on the talks,presentedat the Conference Integrability, Recursion Operators and Soliton Interactions, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. …

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Fundamental Domain Of Invariant Sets And Applications, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

Physics

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mikhail Khenner

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Systems Of Navier-Stokes Equations On Cantor Sets

Xiao-Jun Yang

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Dynamics Of The Fitzhugh-Nagumo Neuron Model, Zechariah Thurman

Physics

In this paper, the dynamical behavior of the Fitzhugh-Nagumo model is examined. The relationship between neuron input current and the firing frequency of the neuron is characterized. Various coupling schemes are also examined, and their effects on the dynamics of the system is discussed. The phenomenon of stochastic resonance is studied for a single uncoupled Fitzhugh-Nagumo neuron.

Boundary Value Problems For Discrete Fractional Equations, Pushp R. Awasthi

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we develop certain aspects of the theory of discrete fractional calculus. The author begins with an introduction to the discrete delta calculus together with the fractional delta calculus which is used throughout this dissertation. The Cauchy function, the Green's function and some of their important properties for a fractional boundary value problem for are developed. This dissertation is comprised of four chapters. In the first chapter we introduce the delta fractional calculus. In the second chapter we give some preliminary definitions, properties and theorems for the fractional delta calculus and derive the appropriate Green's function and give …

Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, Xiao-Jun Yang

Xiao-Jun Yang

This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.

The Effect Of The R1648h Sodium Channel Mutation On Neuronal Excitability: A Model Study, Christopher Locandro, Robert Clewley

Georgia State Undergraduate Research Conference

No abstract provided.

Rational Map Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder

Scholarship and Professional Work - LAS

Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013.

Tourbillion In The Phase Space Of The Bray-Liebhafsky Nonlinear Oscillatory Reaction And Related Multiple-Time-Scale Model, Zeljko D. Cupic

Zeljko D Cupic

The mixed-mode dynamical states found experimentally in the concentration phase space of the iodate catalyzed hydrogen peroxide decomposition (The Bray-Liebhafsky oscillatory reaction) are discussed theoretically in a related multiple-time-scale model, from the viewpoint of tourbillion. With aim to explain the mixed-mode oscillations obtained by numerical simulations of the various dynamical states of a model for the Bray-Liebhafsky reaction under CSTR conditions, the folded singularity points on the critical manifold of the full system and Andronov-Hopf bifurcation of the fast subsystem are calculated. The interaction between those singularities causes occurrence of tourbillion structure.

Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski

Wojciech Budzianowski

This article provides an analysis of processes for separation CO2 by using carbonic anhydrase enzyme with particular emphasis on reactive-membrane solutions. Three available processes are characterised. Main challenges and prospects are given. It is found that in view of numerous challenges practical applications of these processes will be difficult in near future. Further research is therefore needed for improving existing processes through finding methods for eliminating their main drawbacks such as short lifetime of carbonic anhydrase or low resistance of reactive membrane systems to impurities contained in flue gases from power plants.

Multibreathers In Klein-Gordon Chains With Interactions Beyond Nearest Neighbors, V. Koukouloyannis, Panos Kevrekidis, J. Cuevas, V. Rothos

Panos Kevrekidis

We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find crucial modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles emerge from or collide with the ones with standard phase difference profiles, …