Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, 2012 University of Massachusetts - Amherst

#### Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, V. Achilleos, D. Yan, Panos Kevrekidis, D. Frantzeskakis

*Panos Kevrekidis*

We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding ...

Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, 2012 UMass, Amherst

#### Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, Qian-Yong Chen, Panos Kevrekidis, Boris A. Malomed

*Panos Kevrekidis*

We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose–Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in a BEC. The basic characteristics of ...

When A Mechanical Model Goes Nonlinear, 2012 Rhode Island College

#### When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

*Lisa D Humphreys*

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

Defect Modes In One-Dimensional Granular Crystals, 2012 UMass, Amherst

#### Defect Modes In One-Dimensional Granular Crystals, Y. Man, N. Boechler, G. Theocharis, Panos Kevrekidis, C. Daraio

*Panos Kevrekidis*

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally ...

Spatial Solitons Under Competing Linear And Nonlinear Diffractions, 2012 UMass, Amherst

#### Spatial Solitons Under Competing Linear And Nonlinear Diffractions, Y. Shen, Panos Kevrekidis, N. Whitaker

*Panos Kevrekidis*

We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons ...

Converting Fractional Differential Equations Into Partial Differential Equations, 2012 Soochow University

#### Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li

*Ji-Huan He*

A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.

Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., 2012 Wroclaw University of Technology

#### Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Materiały Odstresowujące, 2012 Wroclaw University of Technology

#### Materiały Odstresowujące, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, 2012 Bard College

#### Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, Stergios Mentesidis

*Senior Projects Spring 2012*

The paper focuses on Minsky's financial fragility hypothesis incorporated in a growth model and investigates whether an inherently unstable economy can be stabilized by a big and proactive government. Using dynamical systems theory and expanding a supply-driven growth model developed by Lin, Day and Tse (1992), the paper explores how different government spending programs and financing paths can affect the growth, as well as the stability of a capitalist economy. The results and implications of the new frameworks are analyzed, using analytical and numerical methods of bifurcation, to examine the dependence of optimal government intervention on the economic environment ...

Special Dual Like Numbers And Lattices, 2012 University of New Mexico

#### Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy

*Mathematics and Statistics Faculty and Staff Publications*

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b are positive reals greater ...

Dimension Of Stablesets And Scrambled Sets In Positive Finite Entropy Systems, 2011 UMass Amherst

#### Dimension Of Stablesets And Scrambled Sets In Positive Finite Entropy Systems, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Partially Hyperbolic Sets With Positive Measure And Acip For Partially Hyperbolic Systems, 2011 UMass Amherst

#### Partially Hyperbolic Sets With Positive Measure And Acip For Partially Hyperbolic Systems, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Escape Dynamics In The Discrete Repulsive Model, 2011 UMass, Amherst

#### Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey

*Panos Kevrekidis*

We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be “pulled back” from outside the well or to “drive over” the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain ...

Pointwise Dimension, Entropy And Lyapunov Exponents For C1 Maps, 2011 UMass Amherst

#### Pointwise Dimension, Entropy And Lyapunov Exponents For C1 Maps, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, 2011 University of Massachusetts - Amherst

#### Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, A. S. Rodrigues, Panos Kevrekidis, J. Cuevas, R. Carretero-Gonzalez, D. J. Frantzeskakis

*Panos Kevrekidis*

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in ...

Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, 2011 UMass, Amherst

#### Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, T. W. Neely, A. S. Bradley, E. C. Samson, S. J. Rooney, E. M. Wright, K. J. H. Law, R. Carretero-Gonz´Alez, Panos Kevrekidis, M. J. Davis, B. P. Anderson

*Panos Kevrekidis*

Under suitable forcing a fluid exhibits turbulence, with characteristics strongly a#11;ected by the fluid’s confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system a#11;ords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with k ...

Diffeomorphisms With Global Dominated Splittings Can Not Be Minimal, 2011 UMass Amherst

#### Diffeomorphisms With Global Dominated Splittings Can Not Be Minimal, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, 2011 UMass, Amherst

#### Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, N. I. Karachalios, B. Sánchez-Rey, Panos Kevrekidis, J. Cuevas

*Panos Kevrekidis*

We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below the prescribed lower bounds of the power which depend on the dimension, the parameters of the lattice as well as of the frequency of breathers. In the case of supercritical power nonlinearities we investigate the interplay of these estimates with the ...

Nonlinear Waves And Solitons On Contours And Closed Surfaces, 2011 Embry-Riddle Aeronautical University

#### Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu

*Andrei Ludu*

No abstract provided.

Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, 2011 Wroclaw University of Technology

#### Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski

*Wojciech Budzianowski*

Oxy-reforming is emerging as an interesting alternative to conventional methods of hydrogen generation. The current article characterises this process through analysis of individual reactions: SMR (steam methane reforming), WGS (water gas shift) and CPO (catalytic partial oxidation). Analyses relate to optimisation of thermal conditions thus enabling cost-effectivenes of the process.