Physical Sciences and Mathematics Commons^™

Discrete Solitons And Vortices In Anisotropic Hexagonal And Honeycomb Lattices, Q E. Hoq, Panayotis G. Kevrekidis, A R. Bishop

Mathematics and Statistics Department Faculty Publication Series

In the present work, we consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. We quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation …

Scattering Of Waves By Impurities In Precompressed Granular Chains, Panos Kevrekidis, Alejandro Martinez, Hiromi Yasuda, Eunho Kim, Mason Porter, Jinkyu Yang

Mathematics and Statistics Department Faculty Publication Series

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the re ection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber k → ± π), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance—enabling full transmission at a particular …

Energy Criterion For The Spectral Stability Of Discrete Breathers, Panos Kevrekidis, Jesus Cuevas-Maraver, Dmitry Pelinovsky

Mathematics and Statistics Department Faculty Publication Series

No abstract provided.

Dark-Bright Soliton Interactions Beyond The Integrable Limit, G. Katsimiga, J. Stockhofe, Panos Kevrekidis, P. Schmelcher

Mathematics and Statistics Department Faculty Publication Series

In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork …

A Pt-Symmetric Dual-Core System With The Sine-Gordon Nonlinearity And Derivative Coupling, Jesus Cuevas-Maraver, Boris Malomed, Panos Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel-Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-antikink (KA) complexes are explored …

Performing Hong-Ou-Mandel-Type Numerical Experiments With Repulsive Condensates: The Case Of Dark And Dark-Bright Solitons, Panos Kevrekidis, Zhi-Yuan Sun, Peter Kruger

Mathematics and Statistics Department Faculty Publication Series

The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously reach-ing a 50:50 beam splitter to emerge on the same port through two-photon interference.Motivated by this phenomenon, we consider numerical experiments of the same flavor forclassical, wave objects in the setting of repulsive condensates. We examine dark solitonsinteracting with a repulsive barrier, a case in which we find no significant asymmetries inthe emerging waves after the collision, presumably due to their topological nature. We alsoconsider case examples of two-component systems, where the dark solitons trap a brightstructure in the second-component (dark-bright solitary waves). For these, pronouncedasymmetries upon collision are possible for the non-topological …

Vector Dark-Antidark Solitary Waves In Multi-Component Bose-Einstein Condensates, Panos Kevrekidis, I. Danaila, M. Khamehchi, V. Gokhroo, P. Engels

Mathematics and Statistics Department Faculty Publication Series

Multi-component Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work, the notion of magnetic solitons has been introduced. Here we generalize this concept to vector dark-antidark solitary waves in multi-component Bose-Einstein condensates. We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and inter-component repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform …

Gemini: A Computationally-Efficient Search Engine For Large Gene Expression Datasets, Timothy Defreitas, Hachem Saddiki, Patrick Flaherty

Mathematics and Statistics Department Faculty Publication Series

Background

Low-cost DNA sequencing allows organizations to accumulate massive amounts of genomic data and use that data to answer a diverse range of research questions. Presently, users must search for relevant genomic data using a keyword, accession number of meta-data tag. However, in this search paradigm the form of the query – a text-based string – is mismatched with the form of the target – a genomic profile.

Results

To improve access to massive genomic data resources, we have developed a fast search engine, GEMINI, that uses a genomic profile as a query to search for similar genomic profiles. GEMINI …

Collapse For The Higher-Order Nonlinear Schrödinger Equation, V. Achilleos, S. Diamantidis, D. J. Frantzeskakis, T. P. Horikis, N. I. Karachalios, P. G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrödinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are …

Multifrequency And Edge Breathers In The Discrete Sine-Gordon System Via Subharmonic Driving: Theory, Computation And Experiment, F. Palmero, J. Han, L. Q. English, T. J. Alexander, P. G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu et al. (2014) [21]. In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response …