Publications (534)1024.23 Total impact
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ABSTRACT: In the present paper we consider an optical system with a $\chi^{(2)}$type nonlinearity and unspecified $\mathcal{PT}$symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of $\mathcal{PT}$symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability analysis as a function of their amplitude parameters. Finally, we numerically explore the nonlinear dynamics of the associated waveforms to identify the outcome of the relevant dynamical instabilities of localized and extended states.01/2015;  [Show abstract] [Hide abstract]
ABSTRACT: In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as MassinMass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem. or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) of the problem in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, that will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric nonvanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of resonance conditions is identified for which solutions with genuinely monotonic decaying tails arise.12/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. 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 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. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets.Photonics. 12/2014; 1(4).  [Show abstract] [Hide abstract]
ABSTRACT: We consider a twodimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only singlesite excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the abovementioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios of instability development are exhibited through direct simulations.12/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, we theoretically propose and numerically illustrate a meanfield analogue of the HongOuMandel experiment with bright solitons. More specifically, we scatter two solitons off of each other (in our setup, the bright solitons play the role of a classical analogue to the quantum photons of the original experiment), while the role of the beam splitter is played by a repulsive Gaussian barrier. In our classical scenario, distinguishability of the particles yields, as expected, a $0.5$ split mass on either side. Nevertheless, for very slight deviations from the completely symmetric scenario a nearperfect transmission i.e., a $2,0>e$ or a $0,2 >$ state can be constructed instead, very similarly to the quantum mechanical output. We demonstrate this as a generic feature under slight variations of the relative soliton speed, or of the relative amplitude in a wide parametric regime. We also explore how variations of the properties of the "beam splitter" (i.e., the Gaussian barrier) affect this phenomenology.Physical Review A 12/2014; 90(6). · 2.99 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearityinduced coupling of the linearization's internal modes of negative energy with the wave continuum. In a broad class of nonlinear Schr{\"o}dinger (NLS) equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a doublewell potential, (b) a twisted localized mode in a onedimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a twodimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.12/2014; 
Article: Vortex Nucleation in a Dissipative Variant of the Nonlinear Schr\"odinger Equation under Rotation
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ABSTRACT: In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schr{\"o}dinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential $\mu$ of the system, increasing proportionally to $\mu^{2/3}$. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetrybreaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. These results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.12/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In the present work, we experimentally implement, numerically compute with and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locallyresonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a stronglylocalized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of highamplitude impacts without relying on damping in the system.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the $\phi^4$ kink scattering from a spatially localized $\mathcal{PT}$symmetric defect and the effect of the kink's internal mode (IM) is discussed. It is demonstrated that if a kink hits the defect from the gain side, a noticeable IM is excited, while for the kink coming from the opposite direction the mode excitation is much weaker. This asymmetry is a principal finding of the present work. Similar to the case of the sineGordon kink studied earlier, it is found that the $\phi^4$ kink approaching the defect from the gain side always passes through the defect, while in the opposite case it must have sufficiently large initial velocity, otherwise it is trapped by the loss region. It is found that for the kink with IM the critical velocity is smaller, meaning that the kink bearing IM can pass more easily through the loss region. This feature, namely the "increased transparency" of the defect as regards the motion of the kink in the presence of IM is the second key finding of the present work. A two degree of freedom collective variable model offered recently by one of the coauthors is shown to be capable of reproducing both principal findings of the present work. A simpler, analytically tractable single degree of freedom collective variable method is used to calculate analytically the kink phase shift and the kink critical velocity sufficient to pass through the defect. Comparison with the numerical results suggests that the collective variable method is able to predict these parameters with a high accuracy.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study spreading processes of initially localized excitations in onedimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Andersonlike) disorder and two types of correlated disorders (which are produced by random dimer arrangements). For all three types of disorder, the longtime asymptotic behavior of the second moment $\tilde{m}_2$ and the inverse participation ratio $P^{1}$ satisfy the following scaling relations: $\tilde{m}_2\sim t^{\gamma}$ and $P^{1}\sim t^{\eta}$. For the Andersonlike uncorrelated disorder, we find a transition from subdiffusive ($\gamma<1$) to superdiffusive ($\gamma>1$) dynamics that depends on the amount of precompression in the chain. By contrast, for the correlated disorders, we find that the dynamics is superdiffusive for all precompression levels that we consider. Additionally, for strong precompression, the inverse participation ratio decreases slowly (with $\eta<0.1$) for all three types of disorder, and the dynamics leads to a partial localization around the leading edge of the wave. This localization phenomenon does not occur in the sonicvacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar (roughly $\gamma\approx 1.7$ and $\eta\approx 1$) for all three types of disorder.11/2014;  [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.Physica Scripta 11/2014; 90(2). · 1.03 Impact Factor  [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: The scattering of kinks and lowfrequency breathers of the nonlinear sineGordon (SG) equation on a spatially localized paritytimesymmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kinkkink (kinkantikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kinkantikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied solitondefect interactions, the energy loss to radiation of smallamplitude extended waves is negligible.Physical Review E 11/2014; 90(51):052902. · 2.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Electrical flow control devices are fundamental components in electrical appliances and computers; similarly, optical switches are essential in a number of communication, computation and quantum informationprocessing applications. An acoustic counterpart would use an acoustic (mechanical) signal to control the mechanical energy flow through a solid material. Although earlier research has demonstrated acoustic diodes or circulators, no acoustic switches with wide operational frequency ranges and controllability have been realized. Here we propose and demonstrate an acoustic switch based on a driven chain of spherical particles with a nonlinear contact force. We experimentally and numerically verify that this switching mechanism stems from a combination of nonlinearity and bandgap effects. We also realize the OR and AND acoustic logic elements by exploiting the nonlinear dynamical effects of the granular chain. We anticipate these results to enable the creation of novel acoustic devices for the control of mechanical energy flow in highperformance ultrasonic devices.Nature Communications 10/2014; 5:5311. · 10.74 Impact Factor  [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.
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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.International Journal of Theoretical Physics 09/2014; · 1.19 Impact Factor  [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;
Publication Stats
7k  Citations  
1,024.23  Total Impact Points  
Top Journals
 Physical Review E (73)
 Physical Review A (59)
 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
