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.

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 ...

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 ...

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 ...

Modelling Three-Phase Flow In Metallurgical Processes, 2012 Aalto University - School of Chemical Technology

#### Modelling Three-Phase Flow In Metallurgical Processes, Christoph Goniva, Gijsbert Wierink, Kari Heiskanen, Stefan Pirker, Christoph Kloss

*Gijsbert Wierink*

The interaction between gasses, liquids, and solids plays a critical role in many processes, such as coating, granulation and the blast furnace process. In this paper we present a comprehensive numerical model for three phase flow including droplets, particles and gas. By means of a coupled Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) approach the physical core phenomena are pictured at a detailed level. Sub-models for droplet deformation, breakup and coalescence as well as droplet-particle and wet particle-particle interaction are applied. The feasibility of this model approach is demonstrated by its application to a rotating drum coater. The described ...

Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, 2012 UMass, Amherst

#### Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, V. Achilleos, Panos Kevrekidis, V. M. Rothos, D. J. Frantzeskakis

*Panos Kevrekidis*

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with results ...

Transfer And Scattering Of Wave Packets By A Nonlinear Trap, 2012 UMass, Amherst

#### Transfer And Scattering Of Wave Packets By A Nonlinear Trap, Kai Li, Panos Kevrekidis, Boris Malomed, D. Frantzeskakis

*Panos Kevrekidis*

In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by “nonlinear tweezers,” as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding “radiation.” A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy ...

Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, 2012 UMASS, Amherst

#### Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, M. Pola, J. Stockhofe, P. Schmelcher, Panos Kevrekidis

*Panos Kevrekidis*

The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the brightwave function between the two vortex “wells.” We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition ...

G-Strands, 2012 Imperial College London

#### G-Strands, Darryl Holm, Rossen Ivanov, James Percival

*Articles*

A *G*-strand is a map *g(t,s)*: **R**x**R** --> *G* for a Lie group *G* that follows from Hamilton's principle for a certain class of *G*-invariant Lagrangians. The SO(3)-strand is the *G*-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3)_{K}-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For ...