Integrability, Recursion Operators And Soliton Interactions, 2014 Bulgarian Academy of Sciences

#### 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 ...

Fundamental Domain Of Invariant Sets And Applications, 2013 UMass Amherst

#### Fundamental Domain Of Invariant Sets And Applications, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Viscosity Dependence Of Faraday Wave Formation Thresholds, 2013 California Polytechnic State University - San Luis Obispo

#### 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, 2013 Western Kentucky University

#### 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, 2013 Western Kentucky University

#### 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, 2013 D. Baleanu

#### 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, 2013 California Polytechnic State University - San Luis Obispo

#### 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, 2013 University of Nebraska-Lincoln

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

*Dissertations, Theses, and Student Research Papers in Mathematics*

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 ...

Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, 2013 W. H. Su

#### 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, 2013 Georgia State University

#### 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.

Control, Stability, And Qualitative Theory Of Dynamical Systems, 2013 Eastern Mediterranean University

#### Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

*Mathematics*

No abstract provided.

Tourbillion In The Phase Space Of The Bray-Liebhafsky Nonlinear Oscillatory Reaction And Related Multiple-Time-Scale Model, 2013 Institute of Chemistry, Technology and Metallurgy

#### 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., 2013 Wroclaw University of Technology

#### Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, 2013 Wroclaw University of Technology

#### 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.

Rational Map Of Cp^2 With No Invariant Foliation, 2013 Butler University

#### 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.

Solutions Of Dynamic Equations On Time Scales With Jumps, 2013 Bowling Green State University - Main Campus

#### Solutions Of Dynamic Equations On Time Scales With Jumps, Kayode Daniel Olumoyin

*Theses, Dissertations and Capstones*

To obtain the solution of first order dynamic equations on time scales with jumps, a good question to ask is, how many initial conditions will be needed? We shall show that you only need the initial condition that gives you either the initial position or the initial velocity. The solution at each left scattered point in the time scale can be obtained analytically. With this approach we shall write the general form of the solution of a first order dynamic equations on time scales with jumps. To do this we shall use the Hilger derivative, anti-derivatives, the Hilger Complex plane ...

Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, 2013 Aberystwyth University

#### Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young

*Mathematics Publications*

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These ...

Electrical Current In Sinai Billiards Under General Small Forces, 2012 UMass Amherst

#### Electrical Current In Sinai Billiards Under General Small Forces, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Multibreathers In Klein-Gordon Chains With Interactions Beyond Nearest Neighbors, 2012 UMass, Amherst

#### 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 ...

Determination Of Kinetic Parameters From The Thermogravimetric Data Set Of Biomass Samples, 2012 Wroclaw University of Technology

#### Determination Of Kinetic Parameters From The Thermogravimetric Data Set Of Biomass Samples, Karol Postawa, Wojciech M. Budzianowski

*Wojciech Budzianowski*

This article describes methods of the determination of kinetic parameters from the thermogravimetric data set of biomass samples. It presents the methodology of the research, description of the needed equipment, and the method of analysis of thermogravimetric data. It describes both methodology of obtaining quantitative data such as kinetic parameters as well as of obtaining qualitative data like the composition of biomass. The study is focused mainly on plant biomass because it is easy in harvesting and preparation. Methodology is shown on the sample containing corn stover which is subsequently pyrolysed. The investigated sample show the kinetic of first order ...