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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
- Discipline
- Keyword
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- Solitons (4)
- Nonlinear Schrödinger equation (2)
- Pattern Formation (2)
- Vortex nucleation (2)
- Analysis of Designed Experiments (1)
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- Anti-continuum limit (1)
- Bifurcation. (1)
- Bogomolny energy bounds (1)
- Bose-Einstein Condensates (1)
- Bose-Einstein condensates (1)
- Bose-Einstein condensates. (1)
- Bose–Einstein condensation (1)
- Bright soliton (1)
- Collective coordinate method (1)
- Dark-Bright Solitons (1)
- Discrete models (1)
- Dissipative Gross-Pitaevskii equation. (1)
- Dynamics (1)
- Existence (1)
- Experimental Design (1)
- Fourier transform (1)
- Granular chain (1)
- Gross-Pitaevskii equation (1)
- Kink’s internal mode (1)
- Lattice skyrmions (1)
- Locally resonant (1)
- Mass in mass (1)
- Mass with mass (1)
- Multi-Component Systems (1)
- Multicomponent condensates (1)
Articles 1 - 30 of 33
Full-Text Articles in Physical Sciences and Mathematics
Formation Of Rarefaction Waves In Origami-Based Metamaterials, H. Yasuda, C. Chong, E. G. Charalampidis, P. G. Kevrekidis, J. Yang
Formation Of Rarefaction Waves In Origami-Based Metamaterials, H. Yasuda, C. Chong, E. G. Charalampidis, P. G. Kevrekidis, J. Yang
Mathematics and Statistics Department Faculty Publication Series
We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We …
Lattice Three-Dimensional Skyrmions Revisited, E G. Charalampidis, T A. Ioannidou, Panayotis G. Kevrekidis
Lattice Three-Dimensional Skyrmions Revisited, E G. Charalampidis, T A. Ioannidou, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
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 three dimensional 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 explored 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, …
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, Efstathios G. Charalampidis, Christopher Chong, Eunho Kim, Heetae Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, Chiara Daraio, Jianke Yang
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, Efstathios G. Charalampidis, Christopher Chong, Eunho Kim, Heetae Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, Chiara Daraio, Jianke Yang
Mathematics and Statistics Department Faculty Publication Series
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schr¨odinger (NLS) equation predicts the corresponding modes fairly well. We propose that nonlinear multi-modal …
Nonlinear Waves In A Strongly Nonlinear Resonant Granular Chain, Lifeng Liu, Guillaume James, Panayotis Kevrekidis, Anna Vainchtein
Nonlinear Waves In A Strongly Nonlinear Resonant Granular Chain, Lifeng Liu, Guillaume James, Panayotis Kevrekidis, Anna Vainchtein
Mathematics and Statistics Department Faculty Publication Series
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e., exponentially localized, time periodic states mounted on top of a non-vanishing background. We also identify conditions under which the system admits long-lived bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions …
Existence And Stability Of Pt-Symmetric Vortices In Nonlinear Two-Dimensional Square Lattices, Haitao Xu, P. G. Kevrekidis, Dmitry E. Pelinovsky
Existence And Stability Of Pt-Symmetric Vortices In Nonlinear Two-Dimensional Square Lattices, Haitao Xu, P. G. Kevrekidis, Dmitry E. Pelinovsky
Mathematics and Statistics Department Faculty Publication Series
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinger equation. The existence and stability of vortex configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. Our analytical predictions are found to be in good agreement with numerical computations.
Traveling Waves And Their Tails In Locally Resonant Granular Systems, H Xu, P G. Kevrekidis, A Stefanov
Traveling Waves And Their Tails In Locally Resonant Granular Systems, H Xu, P G. Kevrekidis, A Stefanov
Mathematics and Statistics Department Faculty Publication Series
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three 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 transformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) 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 …
Non-Holonomic Constraints And Their Impact On Discretizations Of Klein-Gordon Lattice Dynamical Models, Panayotis G. Kevrekidis, Vakhtang Putkaradze, Zoi Rapti
Non-Holonomic Constraints And Their Impact On Discretizations Of Klein-Gordon Lattice Dynamical Models, Panayotis G. Kevrekidis, Vakhtang Putkaradze, Zoi Rapti
Mathematics and Statistics Department Faculty Publication Series
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to retrieve the “proper” continuum limit of the model. Such discretizations are useful in exactly preserving a discrete analogue of the momentum. It is also shown that for generic initial data, the momentum and energy conservation laws cannot be achieved concurrently. Finally, direct numerical simulations illustrate that our models yield considerably higher mobility of strongly nonlinear solutions than the well-known “standard” discretizations, even in the …
Stabilization Of Ring Dark Solitons In Bose-Einstein Condensates, Wenlong Wang, P. G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, Tasso J. Kaper, Manjun Ma
Stabilization Of Ring Dark Solitons In Bose-Einstein Condensates, Wenlong Wang, P. G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, Tasso J. Kaper, Manjun Ma
Mathematics and Statistics Department Faculty Publication Series
Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensates are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. We also explore different proposed particle pictures considering the ring as a moving particle and find, where appropriate, …
Non-Conservative Variational Approximation For Nonlinear Schrödinger Equations., J. Rossi, R. Carretero-González, P. G. Kevrekidis
Non-Conservative Variational Approximation For Nonlinear Schrödinger Equations., J. Rossi, R. Carretero-González, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Recently, Galley [Phys. Rev. Lett. 110, 174301 (2013)] proposed an initial value problem formulation of Hamilton’s principle applied to non-conservative systems. Here, we explore this formulation for complex partial differential equations of the nonlinear Schrödinger (NLS) type, examining the dynamics of the coherent solitary wave structures of such models by means of a non-conservative variational approximation (NCVA). We compare the formalism of the NCVA to two other variational techniques used in dissipative systems; namely, the perturbed variational approximation and a generalization of the so-called Kantorovich method. All three variational techniques produce equivalent equations of motion for the perturbed NLS models …
Superdiffusive Transport And Energy Localization In Disordered Granular Crystals, Alejandro J. Martínez, Panayotis G. Kevrekidis, Mason A. Porter
Superdiffusive Transport And Energy Localization In Disordered Granular Crystals, Alejandro J. Martínez, Panayotis G. Kevrekidis, Mason A. Porter
Mathematics and Statistics Department Faculty Publication Series
We study the spreading of initially localized excitations in one-dimensional 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 (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. …
Kink Scattering From A Parity-Time-Symmetric Defect In The Φ 4 Model, Danial Saadatmand, Sergey V. Dmitriev, D. I. Borisov, Panayotis G. Kevrekidis, Minnekhan A. Fatykhov, Kurosh Javidan
Kink Scattering From A Parity-Time-Symmetric Defect In The Φ 4 Model, Danial Saadatmand, Sergey V. Dmitriev, D. I. Borisov, Panayotis G. Kevrekidis, Minnekhan A. Fatykhov, Kurosh Javidan
Mathematics and Statistics Department Faculty Publication Series
In this paper, we study the ϕ4 kink scattering from a spatially localized 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 sine-Gordon kink studied earlier, it is found that the ϕ4 kink approaching the defect from the gain side always passes through the …
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross–Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum 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 three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states …
Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed
Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We study a two component nonlinear Schrodinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes …
Effects Of Interactions On The Generalized Hong–Ou–Mandel Effect, B. Gertjerenken, P. G. Kevrekidis
Effects Of Interactions On The Generalized Hong–Ou–Mandel Effect, B. Gertjerenken, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We numerically investigate the influence of interactions on the generalized Hong–Ou–Mandel (HOM) effect for bosonic particles in a (quasi-)one-dimensional set-up with weak harmonic confinement and show results for the cases of N = 2, N = 3 and N = 4 bosons interacting with a beam splitter, whose role is played by a δ-barrier. In particular, we focus on the effect of attractive interactions and compare the results with the repulsive case, as well as with the analytically available results for the non-interacting case (that we use as a benchmark). We observe a fermionization effect both for growing repulsive and …
Nonlinear Instabilities Of Multi-Site Breathers In Klein–Gordon Lattices, Jesús Cuevas Maraver, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky
Nonlinear Instabilities Of Multi-Site Breathers In Klein–Gordon Lattices, Jesús Cuevas Maraver, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky
Mathematics and Statistics Department Faculty Publication Series
We explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stabl e. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and a …
Solitary Waves Of A Pt-Symmetric Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena, Fred Cooper, Avinash Khare, Andrew Comech, Carl M. Bender
Solitary Waves Of A Pt-Symmetric Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena, Fred Cooper, Avinash Khare, Andrew Comech, Carl M. Bender
Mathematics and Statistics Department Faculty Publication Series
Abstract—In the present work, we consider a prototypical example of a PT -symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the PT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the PT - transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of …
Existence, Stability And Dynamics Of Discrete Solitary Waves In A Binary Waveguide Array, Y. Shen, Panayotis G. Kevrekidis, G. Srinivasan, A. B. Aceves
Existence, Stability And Dynamics Of Discrete Solitary Waves In A Binary Waveguide Array, Y. Shen, Panayotis G. Kevrekidis, G. Srinivasan, A. B. Aceves
Mathematics and Statistics Department Faculty Publication Series
Recent work has explored binary waveguide arrays in the long-wavelength, near-continuum limit, here we examine the opposite limit, namely the vicinity of the so-called anti-continuum limit. We provide a systematic discussion of states involving one, two and three excited waveguides, and provide comparisons that illustrate how the stability of these states differ from the monoatomic limit of a single type of waveguide. We do so by developing a general theory which systematically tracks down the key eigenvalues of the linearized system. When we find the states to be unstable, we explore their dynamical evolution through direct numerical simulations. The latter …
Robust Optimization Of Biological Protocols, Patrick Flaherty, Ronald W. Davis
Robust Optimization Of Biological Protocols, Patrick Flaherty, Ronald W. Davis
Mathematics and Statistics Department Faculty Publication Series
When conducting high-throughput biological experiments, it is often necessary to develop a protocol that is both inexpensive and robust. Standard approaches are either not cost-effective or arrive at an optimized protocol that is sensitive to experimental variations. Here, we describe a novel approach that directly minimizes the cost of the protocol while ensuring the protocol is robust to experimental variation. Our approach uses a risk-averse conditional value-at-risk criterion in a robust parameter design framework. We demonstrate this approach on a polymerase chain reaction protocol and show that our improved protocol is less expensive than the standard protocol and more robust …
Stability Of Solitary Waves And Vortices In A 2d Nonlinear Dirac Model, Jesús Cuevas–Maraver, P. G. Kevrekidis, Avadh Saxena, Andrew Comech, Ruomeng Lan
Stability Of Solitary Waves And Vortices In A 2d Nonlinear Dirac Model, Jesús Cuevas–Maraver, P. G. Kevrekidis, Avadh Saxena, Andrew Comech, Ruomeng Lan
Mathematics and Statistics Department Faculty Publication Series
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions consisting of a soliton in one component and a vortex in the other to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These results pave the way for a systematic stability and dynamics analysis of higher dimensional waveforms …
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Mathematics and Statistics Department Faculty Publication Series
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schrodinger (NLS) equation predicts the corresponding ¨ modes fairly well. We propose that nonlinear …
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We consider a two-component, two-dimensional nonlinear Schr¨odinger system with unequal dispersion coefficients and self-defocusing nonlinearities. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component. We show that the potential well may support not only the fundamental bound state, which forms a vortex–bright (VB) soliton, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states …
Solitons In Multi-Component Nonlinear Schrödinger Models: A Survey Of Recent Developments, P. G. Kevrekidis, D. J. Frantzeskakis
Solitons In Multi-Component Nonlinear Schrödinger Models: A Survey Of Recent Developments, P. G. Kevrekidis, D. J. Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this review we try to capture some of the recent excitement induced by experimental developments, but also by a large volume of theoretical and computational studies addressing multi-component nonlinear Schrödinger models and the localized structures that they support. We focus on some prototypical structures, namely the dark-bright and dark-dark solitons. Although our focus will be on one-dimensional, two-component Hamiltonian models, we also discuss variants, including three (or more)-component models, higher-dimensional states, as well as dissipative settings. We also offer an outlook on interesting possibilities for future work on this theme.
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Mathematics and Statistics Department Faculty Publication Series
We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity …
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Mathematics and Statistics Department Faculty Publication Series
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves …
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of …
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Mathematics and Statistics Department Faculty Publication Series
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wavepacket, as well as via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression i.e., near the linear regime. …
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Mathematics and Statistics Department Faculty Publication Series
For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one dimensional amplitude equation that describes the slow …
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Mathematics and Statistics Department Faculty Publication Series
We numerically investigate an experimentally viable method, that we will refer to as the “chopsticks method”, for generating and manipulating on-demand several vortices in a highly oblate atomic Bose-Einstein condensate (BEC) in order to initialize complex vortex distributions for studies of vortex dynamics. The method utilizes moving laser beams (the “chopsticks”) to generate, capture and transport vortices inside and outside the BEC. We examine in detail this methodology and show a wide parameter range of applicability for the prototypical two-vortex case, and show case examples of producing and manipulating several vortices for which there is no net circulation, equal numbers …
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Mathematics and Statistics Department Faculty Publication Series
In the present work, we combine the notion of PT -symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which the corresponding solution of the regular …
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Mathematics and Statistics Department Faculty Publication Series
In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the “extended” solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Finally, …