Publications (522)961.06 Total impact
 [Show abstract] [Hide abstract]
ABSTRACT: We consider a binary repulsive BoseEinstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two darkbright (DB) solitons. There are two different stationary solutions characterized by the phase difference in the bright component, inphase and outofphase states. We show that above a critical particle number in the bright component, a symmetry breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the outofphase state becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective doublewell picture, these can be understood as the characteristic features of a Bosonic Josephson Junction (BJJ), and we show within a twomode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying doublewell description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the threedimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed; and their stability under small perturbations is verified by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, especially so in the vicinity of the continuum limit. The corresponding bifurcation diagram is elucidated and a prescription for selecting the branch asymptoting to the wellknown continuum limit is given. Finally, the robustness of the solutions by virtue of direct numerical simulations is corroborated.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we consider timeperiodic structures of trimer granular crystals consisting of alternate chrome steel and tungsten carbide spherical particles yielding a spatial periodicity of three. The configuration at the left boundary is driven by a harmonic intime actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modes and the states dictated by the linear drive collide in a saddlenode bifurcation as the driving amplitude is increased, beyond which the dynamics of the system become chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental fullfield visualization of the timeperiodic structures.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study the motion of a vortex dipole in a BoseEinstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the GrossPitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasiperiodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system we are able to construct complex periodic orbits in the original, partial differential equation, meanfield model for BoseEinstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.10/2014; 
Article: Vector rogue waves and darkbright boomeronic solitons in autonomous and nonautonomous settings.
[Show abstract] [Hide abstract]
ABSTRACT: In this work we consider the dynamics of vector rogue waves and darkbright solitons in twocomponent nonlinear Schrödinger equations with various physically motivated timedependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and darkbright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.Physical review. E, Statistical, nonlinear, and soft matter physics. 10/2014; 90(41):042912.  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, we explore the case of a general PTsymmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr\"odinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and antisymmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.09/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We introduce a laddershaped chain with each rung carrying a $\mathcal{PT}$ symmetric gainloss dipole. The polarity of the dipoles is staggered along the chain, meaning that a rung bearing gainloss is followed by one bearing lossgain. This renders the system $\mathcal{PT}$symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schr\"{o}dinger (DNLS) equations with selffocusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton's method for identifying solutions and parametric continuation in the interrung coupling for following the associated branches, we construct families of $\mathcal{PT}$symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung, as well as ones from multiple rungs are identified. Dynamics of unstable solitons is presented too.09/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, we introduce a new $\mathcal{PT}$symmetric variant of the KleinGordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we obtain an explicit frequency condition, somewhat reminiscent of the classical VakhitovKolokolov criterion, which sharply separates the regimes of spectral stability and instability. Our numerical computations corroborate the relevant theoretical result.09/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance, and near the period3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single pendulum dynamics, and extend our analysis to consider multifrequency breathers connected to the period3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of onsite and offsite breathers.Physical review. E, Statistical, nonlinear, and soft matter physics. 09/2014; 90(41).  [Show abstract] [Hide abstract]
ABSTRACT: The dynamics of vortex ring pairs in the homogeneous nonlinear Schr\"odinger equation is studied. The generation of numericallyexact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of coaxial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of coaxial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the BiotSavart law.Physics of Fluids 09/2014; 26:097101. · 1.94 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a dynamically tunable mechanism of wave transmission in 1D helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylin drical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in crosstalking between inplane torsional and outofplane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion towards an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on/off through torsional waves.08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the GrossNeveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anticontinuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two and threesite excitations playing a role analogous to one and twosite, respectively, excitations of the discrete nonlinear Schr\"odinger analogue of the model. Stability exchanges between the two and threesite states are identified, as well as instabilities that appear to be persistent over the coupling strength $\epsilon$, for a subcritical value of the propagation constant $\Lambda$. Variations of the propagation constant, coupling parameter and nonlinearity exponent are all examined in terms of their existence and stability implications and long dynamical simulations are used to unravel the evolutionary phenomenology of the system (when unstable).08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPUtype lattice through both the Kortewegde Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both onesoliton and twosoliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.Physical Review E 08/2014; 90(21):022905. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider a PTPTsymmetric chain (laddershaped) system governed by the discrete nonlinear Schrödinger equation where the cubic nonlinearity is carried solely by two central “rungs” of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss nonreciprocity of the transmission associated with them. To relate these results to finitesize wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss.Physics Letters A 08/2014; · 1.63 Impact Factor 
Article: Generating Functions, Polynomials and Vortices with Alternating Signs in BoseEinstein Condensates
[Show abstract] [Hide abstract]
ABSTRACT: In this work, we construct suitable generating functions for vortices of alternating signs in the realm of BoseEinstein condensates. In addition to the vortexvortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, socalled, Tkachenko differential equation. From that equation, we reconstruct collinear fewvortex equilibria obtained in earlier work, as well as extend them to larger numbers of vortices. Moreover, particular moment conditions can be derived e.g. about the sum of the squared locations of the vortices for arbitrary vortex numbers. Furthermore, the relevant differential equation can be generalized appropriately in the twodimensional complex plane and allows the construction e.g. of polygonal vortex ring and multiring configurations, as well as ones with rings surrounding a vortex at the center that are again connected to earlier bibliography.07/2014;  [Show abstract] [Hide abstract]
ABSTRACT: The dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a twocomponent rubidium BoseEinstein condensate at the transition from miscible to immiscible with the additional control of linear interconversion. Excellent agreement is found between the detailed experimental time evolution and the corresponding numerical meanfield computations. Analyzing the dynamics of the system, we find clear indications of stationary states that we term nonlinear dressed states. A steady state bifurcation analysis reveals a smooth connection of these states with darkbright soliton solutions of the integrable twocomponent Manakov model.07/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study a twocomponent nonlinear Schr\"odinger system with repulsive nonlinear interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in the onecomponent. Treating it as a "frozen" one, we explore the possibility of the formation of bright solitonic bound states in the other component. We identify bifurcation points of such states in the linear limit for the bright component, and explore their continuation in the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes of potential stability not only of the singlepeak ground state (the darkbright solitary wave), but also of excited states with one or more zero crossings in the bright component. When the states are identified as unstable, direct numerical simulations are used to investigate the outcome of the instability manifestation.07/2014; 
Article: Vector rogue waves and darkbright boomeronic solitons in autonomous and nonautonomous settings
[Show abstract] [Hide abstract]
ABSTRACT: In this work, we consider the dynamics of vector rogue waves and darkbright solitons in twocomponent nonlinear Schr\"odinger equations with various physically motivated timedependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and darkbright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.07/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We consider a $\mathcal{PT}$symmetric chain (laddershaped) system governed by the discrete nonlinear Schr\"{o}dinger equation where the cubic nonlinearity is carried solely by two central "rungs" of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss nonreciprocity of the transmission associated with them. To relate these results to finitesize wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss.07/2014; 
Article: PTsymmetric sineGordon breathers
[Show abstract] [Hide abstract]
ABSTRACT: In this work, we explore a prototypical example of a genuine continuum breather (i.e., not a standing wave) and the conditions under which it can persist in a $\mathcal{P T}$symmetric medium. As our model of interest, we will explore the sineGordon equation in the presence of a $\mathcal{P T}$ symmetric perturbation. Our main finding is that the breather of the sineGordon model will only persist at the interface between gain and loss that $\mathcal{P T}$symmetry imposes but will not be preserved if centered at the lossy or at the gain side. The latter dynamics is found to be interesting in its own right giving rise to kinkantikink pairs on the gain side and complete decay of the breather on the lossy side. Lastly, the stability of the breathers centered at the interface is studied. As may be anticipated on the basis of their "delicate" existence properties such breathers are found to be destabilized through a Hopf bifurcation in the corresponding Floquet analysis.06/2014;
Publication Stats
6k  Citations  
961.06  Total Impact Points  
Top Journals
 Physical Review E (68)
 Physical Review A (56)
 Physics Letters A (38)
 Physica D Nonlinear Phenomena (31)
 Physical Review E (25)
Institutions

2001–2014

University of Massachusetts Amherst
 Department of Mathematics and Statistics
Amherst Center, Massachusetts, United States


2013

University of Hartford
 Department of Mathematics
West Hartford, CT, United States 
Technological Educational Institute of Lamia
Lamia, Central Greece, Greece 
University of Hamburg
Hamburg, Hamburg, Germany


2011–2013

Dickinson College
 Department of Physics and Astronomy
Carlisle, Pennsylvania, United States 
National and Kapodistrian University of Athens
Athínai, Attica, Greece


2005–2013

San Diego State University
 Department of Mathematics and Statistics
San Diego, CA, United States 
Columbia University
 Department of Applied Physics and Applied Mathematics
New York City, NY, United States 
Georgia Institute of Technology
 School of Physics
Atlanta, GA, United States 
University of New Mexico
 Department of Mathematics & Statistics
Albuquerque, NM, United States 
University of Vermont
 Department of Mathematics and Statistics
Burlington, VT, United States


2001–2013

Tel Aviv University
 Faculty of Engineering
Tell Afif, Tel Aviv, Israel


2012

University of the Aegean
 Department of Mathematics
Kastro, North Aegean, Greece


2006–2012

California Institute of Technology
 Department of Electrical Engineering
Pasadena, California, United States 
San Francisco State University
 Department of Physics and Astronomy
San Francisco, CA, United States 
University of Bristol
 Department of Engineering Mathematics
Bristol, ENG, United Kingdom


2001–2011

Universidad de Sevilla
 Departamento de Física Aplicada I
Sevilla, Andalusia, Spain


2010

Morehouse College
Atlanta, Georgia, United States 
Newcastle University
 School of Mathematics and Statistics
Newcastle upon Tyne, ENG, United Kingdom


2006–2010

Nankai University
 Applied Physics School (APS)
Tianjin, Tianjin Shi, China


2009

National Technical University of Athens
 Σχολή Εφαρμοσμένων Μαθηματικών & Φυσικών Επιστημών
Athens, Attiki, Greece 
University of Illinois, UrbanaChampaign
 Department of Mathematics
Urbana, IL, United States 
Aristotle University of Thessaloniki
 Department of Mathematical, Physical and Computational Sciences
Thessaloníki, Kentriki Makedonia, Greece


2008

Universität Heidelberg
 KirchhoffInstitute of Physics
Heidelberg, BadenWuerttemberg, Germany 
University of Oxford
 Oxford Centre for Industrial and Applied Mathematics
Oxford, ENG, United Kingdom 
University of Tuebingen
Tübingen, BadenWürttemberg, Germany 
Heidelberg University
Tiffin, Ohio, United States 
São Paulo State University
 Instituto de Física Teórica
Bauru, Estado de Sao Paulo, Brazil 
Western New England College
Springfield, Missouri, United States 
Calvin College
 Department of Mathematics and Statistics
Grand Rapids, MI, United States 
University of Kansas
 Department of Mathematics
Lawrence, KS, United States


2006–2008

Florida State University
 Department of Mathematics
Tallahassee, FL, United States


2007

Amherst College
 Department of Physics
Amherst Center, Massachusetts, United States 
University of Crete
Retimo, Crete, Greece 
Northwestern State University
Louisiana, United States


2004–2007

Escola Universitària Politècnica
Hispalis, Andalusia, Spain


2003–2007

The University of Tokyo
 Institute of Industrial Science
Tokyo, Tokyoto, Japan


2005–2006

McMaster University
 Department of Mathematics and Statistics
Hamilton, Ontario, Canada


2001–2006

Princeton University
 • Department of Chemical and Biological Engineering
 • Program in Applied and Computational Mathematics
Princeton, New Jersey, United States


2002

Osaka Institute of Technology
Ōsaka, Ōsaka, Japan


2001–2002

Los Alamos National Laboratory
 Center for Nonlinear Studies
Los Alamos, NM, United States


1999–2001

Rutgers, The State University of New Jersey
 Department Physics and Astronomy
New Brunswick, NJ, United States


2000

Brown University
 Department of Applied Mathematics
Providence, Rhode Island, United States
