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 ...

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.

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 Faculty Publications*

No abstract provided.

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 ...

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 ...

Asymmetric Wave Propagation Through Nonlinear Pt-Symmetric Oligomers, 2012 UMASS, Amherst

#### Asymmetric Wave Propagation Through Nonlinear Pt-Symmetric Oligomers, J. D’Ambroise, Panos Kevrekidis, S. Lepri

*Panos Kevrekidis*

In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schr¨odinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be unstable except in the vicinity of the linear limit ...

Nonlinear Pt-Symmetric Plaquettes, 2012 University of Massachusetts - Amherst

#### Nonlinear Pt-Symmetric Plaquettes, Kai Li, Panos Kevrekidis, Boris A. Malomed, Uwe Günther

*Panos Kevrekidis*

We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient, . Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct ...

Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, 2012 UMASS, Amherst

#### Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis

*Panos Kevrekidis*

We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for ...

The Octonions And The Exceptional Lie Algebra G2, 2012 Utah State University

#### The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson

*Research Vignettes*

The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2.

PDF and Maple worksheets can be downloaded from the links below.

Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, 2012 UMASS, Amherst

#### Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis

*Panos Kevrekidis*

In this paper, we derive and study two versions of the short pulse equation (SPE) in (2 + 1) dimensions. Using Maxwell’s equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab wave guides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting (2 + 1)-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort one-dimensional breathers appear to ...

Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, 2012 UMASS, Amherst

#### Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez

*Panos Kevrekidis*

We consider nonlinear analogs of parity-time- (PT-) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and odd excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter ɛ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as ɛ is further increased, the ground state and first excited state, as well as branches of higher multisoliton (multivortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT phase transition ...

Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, 2012 UMass, Amherst

#### Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis

*Panos Kevrekidis*

In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they may also feature both prototypical types of instabilities, namely exponential and oscillatory ones ...

Beating Dark–Dark Solitons In Bose–Einstein Condensates, 2012 University of Massachusetts - Amherst

#### Beating Dark–Dark Solitons In Bose–Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, M. Hoefer, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, J. Cuevas

*Panos Kevrekidis*

Motivated by recent experimental results, we study beating dark–dark (DD) solitons as a prototypical coherent structure that emerges in two-component Bose–Einstein condensates. We showcase their connection to dark–bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating ...