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- Solitons (5)
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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
Capturing Data Uncertainty In Highvolume Stream Processing, Yanlei Diao, Boduo Li, Anna Liu, Liping Peng, Charles Sutton, Thanh Tran, Michael Zink
Capturing Data Uncertainty In Highvolume Stream Processing, Yanlei Diao, Boduo Li, Anna Liu, Liping Peng, Charles Sutton, Thanh Tran, Michael Zink
Mathematics and Statistics Department Faculty Publication Series
We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random variables such as many types of sensor data. To provide an end-to-end solution, our system employs probabilistic modeling and inference to generate uncertainty description for raw data, and then a suite of statistical techniques to capture changes of uncertainty as data propagates through query operators. To cope with high-volume streams, we explore advanced approximation techniques for both space and time efficiency. We are …
Soliton Dynamics In Linearly Coupled Discrete Nonlinear Schrodinger Equations, A Trombettoni, He Nistazakis, Z Rapti, Dj Frantzeskakis, Pg Kevrekidis
Soliton Dynamics In Linearly Coupled Discrete Nonlinear Schrodinger Equations, A Trombettoni, He Nistazakis, Z Rapti, Dj Frantzeskakis, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled …
Non-Nearest-Neighbor Interactions In Nonlinear Dynamical Lattices, Pg Kevrekidis
Non-Nearest-Neighbor Interactions In Nonlinear Dynamical Lattices, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrödinger equation. Our approach offers a systematic way of analyzing the existence and stability of solutions of the system near the so-called anti-continuum limit of zero coupling. This affords us a number of analytical insights such as the fact that, for instance, next-nearest-neighbor interactions allow for solutions with nontrivial phase structure in infinite one-dimensional lattices; in the case of purely nearest-neighbor interactions, such phase structure is disallowed. On the other hand, such non-nearest-neighbor interactions can critically affect the stability of unstable …
Azimuthal Modulational Instability Of Vortices In The Nonlinear Schrodinger Equation, Rm Caplan, Qe Hoq, R Carretero-Gonzalez, Pg Kevrekidis
Azimuthal Modulational Instability Of Vortices In The Nonlinear Schrodinger Equation, Rm Caplan, Qe Hoq, R Carretero-Gonzalez, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady-state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, …
Linear Koszul Duality And Affine Hecke Algebras, I Mirkovic, S Richie
Linear Koszul Duality And Affine Hecke Algebras, I Mirkovic, S Richie
Mathematics and Statistics Department Faculty Publication Series
n this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.
Manipulation Of Vortices By Localized Impurities In Bose-Einstein Condensates, Mc Davis, R Carretero-Gonzalez, Z Shi, Kjh Law, Pg Kevrekidis, Bp Anderson
Manipulation Of Vortices By Localized Impurities In Bose-Einstein Condensates, Mc Davis, R Carretero-Gonzalez, Z Shi, Kjh Law, Pg Kevrekidis, Bp Anderson
Mathematics and Statistics Department Faculty Publication Series
We consider the manipulation of Bose-Einstein condensate vortices by optical potentials generated by focused laser beams. It is shown that for appropriate choices of the laser strength and width it is possible to successfully transport vortices to various positions inside the trap confining the condensate atoms. Furthermore, the full bifurcation structure of possible stationary single-charge vortex solutions in a harmonic potential with this type of impurity is elucidated. The case when a moving vortex is captured by a stationary laser beam is also studied, as well as the possibility of dragging the vortex by means of periodic optical lattices.
Wave Patterns Generated By A Supersonic Moving Body In A Binary Bose-Einstein Condensate, Yg Gladush, Am Kamchatnov, Z Shi, Pg Kevrekidis, Dj Frantzeskakis, Ba Malomed
Wave Patterns Generated By A Supersonic Moving Body In A Binary Bose-Einstein Condensate, Yg Gladush, Am Kamchatnov, Z Shi, Pg Kevrekidis, Dj Frantzeskakis, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called “ship waves” are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, …
Multistable Solitons In Higher-Dimensional Cubic-Quintic Nonlinear Schrodinger Lattices, C Chong, R Carretero-Gonzalez, Ba Malomed, Pg Kevrekidis
Multistable Solitons In Higher-Dimensional Cubic-Quintic Nonlinear Schrodinger Lattices, C Chong, R Carretero-Gonzalez, Ba Malomed, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete …
Perfect Forms Over Totally Real Number Fields, Pe Gunnells, D Yasaki
Perfect Forms Over Totally Real Number Fields, Pe Gunnells, D Yasaki
Mathematics and Statistics Department Faculty Publication Series
A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such that f(v) = m. This concept was introduced by Vorono¨ý and later generalized by Koecher to arbitrary number fields. One knows that up to a natural “change of variables” equivalence, there are only finitely many perfect forms, and given an initial perfect form one knows how to explicitly compute all perfect forms up to equivalence. In this paper we investigate perfect forms over totally real number fields. Our main result …
Excited States In The Thomas–Fermi Limit: A Variational Approach, M Cole, D E. Pelinovsky, Pg Kevrekidis
Excited States In The Thomas–Fermi Limit: A Variational Approach, M Cole, D E. Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Excited states of Bose–Einstein condensates are considered in the semi-classical (Thomas- Fermi) limit of the Gross–Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark solitons (density dips on the localized condensate) with respect to the harmonic potential and to each other is approximated using the averaged Lagrangian method. This permits a complete characterization of the equilibrium positions of the dark solitons as a function of the chemical potential parameter. It also yields an analytical handle on the oscillation frequencies of dark solitons around such equilibria. The asymptotic predictions are generalized for an arbitrary number …
The Spectral Curve Of A Quaternionic Holomorphic Line Bundle Over A 2-Torus, C Bohle, F Pedit, U Pinkall
The Spectral Curve Of A Quaternionic Holomorphic Line Bundle Over A 2-Torus, C Bohle, F Pedit, U Pinkall
Mathematics and Statistics Department Faculty Publication Series
A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain Dirac type operator on a quaternionic line bundle associated to the immersion. The paper provides a detailed description of the geometry and asymptotic behavior of the spectral curve. If this curve has finite genus the Dirichlet energy of a map from a 2-torus to the 2-sphere or the Willmore energy of an immersion from a 2-torus into the 4-sphere is given by the residue of a specific meromorphic differential on the curve. …
Littelmann Patterns And Weyl Group Multiple Dirichlet Series Of Type D, G Chinta, Pe Gunnells
Littelmann Patterns And Weyl Group Multiple Dirichlet Series Of Type D, G Chinta, Pe Gunnells
Mathematics and Statistics Department Faculty Publication Series
We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A series given by Brubaker, Bump, Friedberg, and Hoffstein [3] in terms of Gelfand–Tsetlin patterns. Our conjecture is given in terms of patterns for irreducible representations of even orthogonal Lie algebras developed by Littelmann [13].
Group Actions On 4-Manifolds: Some Recent Results And Open Questions, Wm Chen
Group Actions On 4-Manifolds: Some Recent Results And Open Questions, Wm Chen
Mathematics and Statistics Department Faculty Publication Series
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and homological rigidity and boundedness of group actions. We also take this opportunity to include several results and questions which did not appear elsewhere.
Localized Breathing Modes In Granular Crystals With Defects, G Theocharis, M Kavousanakis, Pg Kevrekidis, C Daraio, Ma Porter, Ig Kevrekidis
Localized Breathing Modes In Granular Crystals With Defects, G Theocharis, M Kavousanakis, Pg Kevrekidis, C Daraio, Ma Porter, Ig Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem’s linear limit, we identify the system’s eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in …
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Interlaced Solitons And Vortices In Coupled Dnls Lattices, J Cuevas, Qe Hoq, H Susanto, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort …
Discrete Breathers In A Forced-Damped Array Of Coupled Pendula: Modeling, Computation, And Experiment, J Cuevas, Lq English, Pg Kevrekidis, M Anderson
Discrete Breathers In A Forced-Damped Array Of Coupled Pendula: Modeling, Computation, And Experiment, J Cuevas, Lq English, Pg Kevrekidis, M Anderson
Mathematics and Statistics Department Faculty Publication Series
In this work, we present a mechanical example of an experimental realization of a stability reversal between on-site and intersite centered localized modes. A corresponding realization of a vanishing of the Peierls-Nabarro barrier allows for an experimentally observed enhanced mobility of the localized modes near the reversal point. These features are supported by detailed numerical computations of the stability and mobility of the discrete breathers in this system of forced and damped coupled pendula. Furthermore, additional exotic features of the relevant model, such as dark breathers are briefly discussed.
Solitons In Quasi-One-Dimensional Bose-Einstein Condensates With Competing Dipolar And Local Interactions, J Cuevas, Ba Malomed, Pg Kevrekidis, Dj Frantzeskakis
Solitons In Quasi-One-Dimensional Bose-Einstein Condensates With Competing Dipolar And Local Interactions, J Cuevas, Ba Malomed, Pg Kevrekidis, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for \textit{subfundamental solitons} (SFSs) is found in the second …
Matter-Wave Solitons In The Presence Of Collisional Inhomogeneities: Perturbation Theory And The Impact Of Derivative Terms, S Middelkamp, Pg Kevrekidis, Dj Frantzeskakkis, P Schmelcher
Matter-Wave Solitons In The Presence Of Collisional Inhomogeneities: Perturbation Theory And The Impact Of Derivative Terms, S Middelkamp, Pg Kevrekidis, Dj Frantzeskakkis, P Schmelcher
Mathematics and Statistics Department Faculty Publication Series
We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity is found to lead to a gravitational potential, as well as to a renormalization of the parabolic potential coefficient. This feature allows one to influence the motion of fundamental as well as higher-order solitons.
Existence, Stability, And Dynamics Of Bright Vortices In The Cubic-Quintic Nonlinear Schr¨Odinger Equation, R M. Caplan, R Carretero-Gonzalez, Pg Kevrekidis
Existence, Stability, And Dynamics Of Bright Vortices In The Cubic-Quintic Nonlinear Schr¨Odinger Equation, R M. Caplan, R Carretero-Gonzalez, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the existence and azimuthal modulational stability of vortices in the two-dimensional (2D) cubic-quintic nonlinear Schr¨odinger (CQNLS) equation. We use a variational approximation (VA) based on an asymptotically derived ansatz, seeding the result as an initial condition into a numerical optimization routine. Previously known existence bounds for the vortices are recovered by means of this approach. We study the azimuthal modulational stability of the vortices by freezing the radial direction of the Lagrangian functional of the CQNLS, in order to derive a quasi-1D azimuthal equation of motion. A stability analysis is then done in the Fourier space of the …
On The Stability Of Multibreathers In Klein-Gordon Chains, V Koukouloyannis, Pg Kevrekidis
On The Stability Of Multibreathers In Klein-Gordon Chains, V Koukouloyannis, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In this paper, a theorem, which determines the linear stability of multibreathers excited over adjacent coupled oscillators in Klein–Gordon chains, is proven. Specifically, it is shown that for soft nonlinearities, and positive nearest–neighbour inter-site coupling, only structures with adjacent sites excited out of phase may be stable, while only in-phase ones may be stable for negative coupling. The situation is reversed for hard nonlinearities. This method can be applied to n-site breathers, where n is any finite number and provides a detailed count of the number of real and imaginary characteristic exponents of the breather, based on its configuration. In …
Discrete Holomorphic Geometry I. Darboux Transformations And Spectral Curves, C Bohle, F Pedit, U Pinkall
Discrete Holomorphic Geometry I. Darboux Transformations And Spectral Curves, C Bohle, F Pedit, U Pinkall
Mathematics and Statistics Department Faculty Publication Series
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an approach to discrete conformality that is based on the concept of holomorphic line bundles over “discrete surfaces”, by which we mean the vertex sets of triangulated surfaces with bi-colored set of faces. The resulting theory of discrete conformality is simultaneously Möbius invariant and based on linear equations. In the special case of maps into the 2-sphere we obtain a reinterpretation of the theory of complex holomorphic functions on …
Power Residues Of Fourier Coefficients Of Elliptic Curves With Complex Multiplication, T Weston, E Zaurova
Power Residues Of Fourier Coefficients Of Elliptic Curves With Complex Multiplication, T Weston, E Zaurova
Mathematics and Statistics Department Faculty Publication Series
Fix m greater than one and let E be an elliptic curve over Q with complex multiplication. We formulate conjectures on the density of primes p (congruent to one modulo m) for which the pth Fourier coefficient of E is an mth power modulo p; often these densities differ from the naive expectation of 1/m. We also prove our conjectures for m dividing the number of roots of unity lying in the CM field of E; the most involved case is m = 4 and complex multiplication by Q(i).
The Higher-Dimensional Ablowitz-Ladik Model: From (Non-)Integrability And Solitary Waves To Surprising Collapse Properties And More Exotic Solutions, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schr¨odinger (NLS) model. We use singularity confinement techniques to suggest that the relevant discretization should not be integrable. More importantly, we identify the prototypical solitary waves of the model and examine their stability, illustrating the remarkable feature that near the continuum limit, this discretization leads to the absence of collapse and complete spectral wave stability, in stark contrast to the standard discretization of the NLS. We also briefly touch upon the three-dimensional case and generalizations of our considerations therein, and also present some more …
Geometric Stabilization Of Extended S=2 Vortices In Two-Dimensional Photonic Lattices: Theoretical Analysis, Numerical Computation, And Experimental Results, Kjh Law, D Song, Pg Kevrekidis, J Xu, Zg Chen
Geometric Stabilization Of Extended S=2 Vortices In Two-Dimensional Photonic Lattices: Theoretical Analysis, Numerical Computation, And Experimental Results, Kjh Law, D Song, Pg Kevrekidis, J Xu, Zg Chen
Mathematics and Statistics Department Faculty Publication Series
In this work, we focus on the subject of nonlinear discrete self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation, and experimental demonstration. We revisit earlier findings about S=2 vortices with a discrete model and find that S=2 vortices extended over eight lattice sites can indeed be stable (or only weakly unstable) under certain conditions, not only for the cubic nonlinearity previously used, but also for a saturable nonlinearity more relevant to our experiment with a biased photorefractive nonlinear crystal. We then use the discrete analysis as a guide toward numerically identifying stable (and unstable) …
Two-Dimensional Paradigm For Symmetry Breaking: The Nonlinear Schroumldinger Equation With A Four-Well Potential, C Wang, G Theocharis, Pg Kevrekidis, N Whitaker, Kjh Law, Dj Frantzeskakis, Ba Malomed
Two-Dimensional Paradigm For Symmetry Breaking: The Nonlinear Schroumldinger Equation With A Four-Well Potential, C Wang, G Theocharis, Pg Kevrekidis, N Whitaker, Kjh Law, Dj Frantzeskakis, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective “static” features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore “dynamic” features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.
Collisionally Inhomogeneous Bose-Einstein Condensates In Double-Well Potentials, C Wang, Pg Kevrekidis, N Whitaker, Dj Frantzeskakis, S Middelkamp, P Schmelcher
Collisionally Inhomogeneous Bose-Einstein Condensates In Double-Well Potentials, C Wang, Pg Kevrekidis, N Whitaker, Dj Frantzeskakis, S Middelkamp, P Schmelcher
Mathematics and Statistics Department Faculty Publication Series
In this work, we consider quasi-one-dimensional Bose–Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double-well potentials. In particular, we study a setup in which such a “collisionally inhomogeneous” BEC has the same (attractive–attractive or repulsive–repulsive) or different (attractive–repulsive) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle–node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle–node tends to infinity and eventually only …
Phase Separation And Dynamics Of Two-Component Bose-Einstein Condensates, R Navarro, R Carretero-Gonzalez, Pg Kevrekidis
Phase Separation And Dynamics Of Two-Component Bose-Einstein Condensates, R Navarro, R Carretero-Gonzalez, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility …
Spinor Bose-Einstein Condensate Flow Past An Obstacle, As Rodrigues, Pg Kevrekidis, R Carretero-Gonzalez, Dj Frantzeskakis, P Schmelcher, Tj Alexander, Ys Kivshar
Spinor Bose-Einstein Condensate Flow Past An Obstacle, As Rodrigues, Pg Kevrekidis, R Carretero-Gonzalez, Dj Frantzeskakis, P Schmelcher, Tj Alexander, Ys Kivshar
Mathematics and Statistics Department Faculty Publication Series
We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions, and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings, respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.
Higher-Order Effects And Ultrashort Solitons In Left-Handed Metamaterials, Nl Tsitsas, N Rompotis, I Kourakis, Pg Kevrekidis, Dj Frantzeskakis
Higher-Order Effects And Ultrashort Solitons In Left-Handed Metamaterials, Nl Tsitsas, N Rompotis, I Kourakis, Pg Kevrekidis, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
Starting from Maxwell’s equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrödinger equation, describing ultrashort solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.
Highly Nonlinear Solitary Waves In Heterogeneous Periodic Granular Media, Ma Porter, C Daraio, I Szelengowicz, Eb Herbold, Pg Kevrekidis
Highly Nonlinear Solitary Waves In Heterogeneous Periodic Granular Media, Ma Porter, C Daraio, I Szelengowicz, Eb Herbold, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, brass, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and …