Variational Approximations In Discrete Nonlinear Schrödinger Equations With Next-Nearest-Neighbor Couplings, 2011 UMass, Amherst

#### Variational Approximations In Discrete Nonlinear Schrödinger Equations With Next-Nearest-Neighbor Couplings, Panos Kevrekidis, C. Chong, R. Carretero-González, B. Malomed

*Panos Kevrekidis*

Solitons of a discrete nonlinear Schr\"{o}dinger equation which includes the next-nearest-neighbor interactions are studied by means of a variational approximation and numerical computations. A large family of multi-humped solutions, including those with a nontrivial phase structure which are a feature particular to the next-nearest-neighbor interaction model, are accurately predicted by the variational approximation. Bifurcations linking solutions with the trivial and nontrivial phase structures are also captured remarkably well, including a prediction of critical parameter values.

Pt-Symmetric Oligomers: Analytical Solutions, Linear Stability, And Nonlinear Dynamics, 2011 UMass, Amherst

#### Pt-Symmetric Oligomers: Analytical Solutions, Linear Stability, And Nonlinear Dynamics, K. Li, Panos Kevrekidis

*Panos Kevrekidis*

In the present work we focus on the case of (few-site) configurations respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such “oligomers” with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear PT-symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations ...

Nonlinear Excitations, Stability Inversions, And Dissipative Dynamics In Quasi-One-Dimensional Polariton Condensates, 2011 UMass, Amherst

#### Nonlinear Excitations, Stability Inversions, And Dissipative Dynamics In Quasi-One-Dimensional Polariton Condensates, J. Cuevas, A. S. Rodrigues, R. Carretero-Gonz´Alez, Panos Kevrekidis, D. J. Frantzeskakis

*Panos Kevrekidis*

We study the existence, stability, and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, for a quasi-one-dimensional polariton condensate in the presence of nonresonant pumping and nonlinear damping. We find a series of remarkable features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates. For some sizable parameter ranges, the nodeless (“ground”) state becomes unstabletoward the formation of stable nonlinear single- or multi-dark-soliton excitations. It is also observed that for suitable parametric choices, the instability of single dark solitons can nucleate multi-dark-soliton states. Also, for other parametric ...

Dark-Bright Gap Solitons In Coupled-Mode One-Dimensional Saturable Waveguide Arrays, 2011 UMASS, Amherst

#### Dark-Bright Gap Solitons In Coupled-Mode One-Dimensional Saturable Waveguide Arrays, Rong Dong, Christian E. Ruter, Detlef Kip, Jesus Cuevas, Panos Kevrekidis, Daohong Song, Jingjun Xu

*Panos Kevrekidis*

In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment that illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or nonsymbiotic ones where the bright ...

Nonlinear Waves In Lattices: Past, Present, Future, 2011 UMass, Amherst

#### Nonlinear Waves In Lattices: Past, Present, Future, Panos Kevrekidis

*Panos Kevrekidis*

In the present work, we attempt a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include non-linear optics, atomic physics, mechanical systems, electrical lattices, non-linear metamaterials, plasma dynamics and granular crystals. We give some of the recent developments in each one of these areas and speculate on some of the potentially interesting directions for future study.

Finding The Beat In Music: Using Adaptive Oscillators, 2011 Harvey Mudd College

#### Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

*HMC Senior Theses*

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and ...

Noise, Delays, And Resonance In A Neural Network, 2011 Harvey Mudd College

#### Noise, Delays, And Resonance In A Neural Network, Austin Quan

*HMC Senior Theses*

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential ...

A Stochastic Model For Wind Turbine Power Quality Using A Levy Index Analysis Of Wind Velocity Data, 2011 Technological University Dublin

#### A Stochastic Model For Wind Turbine Power Quality Using A Levy Index Analysis Of Wind Velocity Data, Jonathan Blackledge, Eugene Coyle, Derek Kearney

*Conference papers*

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. After a brief review of the statistics of typical wind speed data, a non- Gaussian model for the wind velocity is introduced that is based on a Levy distribution. It is shown how this distribution can be used to derive a stochastic fractional diusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index numerical analysis is then performed on wind velocity data for both ...

Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, 2011 Western Kentucky University

#### Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, Nezihe Turhan

*Masters Theses & Specialist Projects*

The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential ...

Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, 2011 UMASS, Amherst

#### Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, H. Susanto, Panos Kevrekidis, F. Kh. Abdullaev, Boris A. Malomed

*Panos Kevrekidis*

We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing type. We identify stability regions for fundamental onsite discrete symmetric solitons (single-site modes with equal norms in both components), as well as for two-site in-phase and twisted modes, the in-phase ones being completely ...

Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, 2011 UMass, Amherst

#### Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, G. P. Veldes, J. Cuevas, Panos Kevrekidis, D. J. Frantzeskakis

*Panos Kevrekidis*

We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical ...

Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, 2011 UMASS, Amherst

#### Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, N. Boechler, J. Yang, G. Theocharis, Panos Kevrekidis, C. Daraio

*Panos Kevrekidis*

We investigate the tunable vibration filtering properties of statically compressed one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (sphere-cylinder-sphere) in which the length of the cylinder is varied systematically. We investigate the response of these granular crystals, given small amplitude dynamic displacements relative to those due to the static compression, and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of three distinct ...

Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, 2011 UMass, Amherst

#### Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, A. Alvarez, J. Cuevas, F. Romero, Panos Kevrekidis

*Panos Kevrekidis*

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions ...

Radial Standing And Self-Similar Waves For The Hyperbolic Cubic Nls In 2d, 2011 UMASS, Amherst

#### Radial Standing And Self-Similar Waves For The Hyperbolic Cubic Nls In 2d, Panos Kevrekidis, Andrea R. Nahmod, Chongchun Zeng

*Panos Kevrekidis*

In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities.

Control Of The Symmetry Breaking In Double-Well Potentials By The Resonant Nonlinearity Management, 2011 UMass, Amherst

#### Control Of The Symmetry Breaking In Double-Well Potentials By The Resonant Nonlinearity Management, H. Nistazakis, B. Malomed, Panos Kevrekidis, D. Frantzeskakis

*Panos Kevrekidis*

We introduce a one-dimensional model of Bose–Einstein condensates (BECs), combining the double-well potential, which is a usual setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity that is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In ...

Impact Of Anisotropy On Vortex Clusters And Their Dynamics, 2011 UMass, Amherst

#### Impact Of Anisotropy On Vortex Clusters And Their Dynamics, J. Stockhofe, S. Middelkamp, Panos Kevrekidis, P. Schmelcher

*Panos Kevrekidis*

We investigate the effects of anisotropy on the stability and dynamics of vortex cluster states which arise in Bose-Einstein condensates. Sufficiently strong anisotropies are shown to stabilize states with arbitrary numbers of vortices that are highly unstable in the isotropic limit. Conversely, anisotropy can be used to destabilize states which are stable in the isotropic limit. Near the linear limit, we identify the bifurcations of vortex states including their emergence from linear eigenstates, while in the strongly nonlinear limit, a particle-like description of the dynamics of the vortices in the anisotropic trap is developed. Both are in very good agreement ...

Nucleation Of Breathers Via Stochastic Resonance In Nonlinear Lattices, 2011 University of Massachusetts - Amherst

#### Nucleation Of Breathers Via Stochastic Resonance In Nonlinear Lattices, D Cubero, J Cuevas, Pg Kevrekidis

*Panos Kevrekidis*

By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the spontaneous formation and destruction of discrete breathers with a selected frequency due to thermal fluctuations. The phenomenon exhibits the striking features of stochastic resonance: a nonmonotonic behavior as noise is increased and breather generation under subthreshold conditions. The corresponding peak is associated with a matching between the external driving frequency and the breather frequency at the average energy given by ambient temperature.

Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., 2011 Wroclaw University of Technology

#### Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

The Analysis Of Heat Transfer In A Gas-Gas Heat Exchanger Operated Under A Heat-Recirculating Mode, 2011 Wroclaw University of Technology

#### The Analysis Of Heat Transfer In A Gas-Gas Heat Exchanger Operated Under A Heat-Recirculating Mode, Mariusz Salaniec, Wojciech M. Budzianowski

*Wojciech Budzianowski*

The present paper presents the analysis of heat transfer in a gas-gas heat exchanger operated in a heat-recirculating mode.

An Overview Of Technologies For Upgrading Of Biogas To Biomethane, 2011 Wroclaw University of Technology

#### An Overview Of Technologies For Upgrading Of Biogas To Biomethane, Wojciech M. Budzianowski

*Wojciech Budzianowski*

The present contribution presents an overview of technologies available for upgrading of biogas to biomethane. Technologies under study include pressure swing adsorption (PSA), high-pressure water wash (HPWW), reactive absorption (RA), physical absorption (PA), membrane separation (MS) and cryogenic separation (CS).