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Item Open Access SPATIAL CONTROL OF LOCALIZED OSCILLATIONS IN ARRAYS OF COUPLED LASER DIMERS(PHYSICAL REVIEW E, 2020) Shena, Joniald; Kominis, Yannis; Bountis, Anastasios; Kovanis, VassiliosArrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial controllability of oscillation amplitudes in an array of coupled photonic dimers, each consisting of two semiconductor lasers driven by differential pumping rates. We consider parameter values for which each dimer’s stable phase-locked state has become unstable through a Hopf bifurcation and we show that, by assigning appropriate pumping rate values to each dimer, high-amplitude oscillations coexist with negligibly low amplitude oscillations. The spatial profile of the amplitude of oscillations across the array can be dynamically controlled by appropriate pumping rate values in each dimer. This feature is shown to be quite robust, even for random detuning between the lasers, and suggests a mechanism for dynamically reconfigurable production of a large diversity of spatial profiles of laser amplitude oscillationsItem Open Access The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport(Scientific Reports, 2016-09-19) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.Item Open Access The effect of long–range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on–site potential(arXiv, 2018-04) Christodoulidi, H.; Bountis, Tassos; Drossos, L.We examine the role of long–range interactions on the dynamical and statistical properties of two 1D lattices with on–site potentials that are known to support discrete breathers: the Klein–Gordon (KG) lattice which includes linear dispersion and the Gorbach–Flach (GF) lattice, which shares the same on–site potential but its dispersion is purely nonlinear. In both models under the implementation of long–range interactions (LRI) we find that single–site excitations lead to special low–dimensional solutions, which are well described by the undamped Duffing oscillator. For random initial conditions we observe that the maximal Lyapunov exponent scales as N−0.12 in the KG model and as N−0.27 in the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from those of the FPU model.Item Open Access Stability through asymmetry: Modulationally stable nonlinear supermodes of asymmetric non-Hermitian optical couplers(Physical Review A, 2017-06-21) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT ) symmetry point the coupler is unstable. Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of these broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations. The lack of symmetry requirements is expected to facilitate experimental implementations and relevant photonics applications.Item Open Access Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer(arXiv, 2018-08) Kominis, Yannis; Kovanis, Vassilios; Bountis, TassosThe fundamental active photonic dimer consisting of two coupled quantum well lasers is inves- tigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The opti- cal spectral signatures of system bifurcations and exceptional points are manifested in terms of self-termination effects and observable drastic variations of the spectral line shape that can be controlled in terms of optical detuning and inhomogeneous pumping.Item Open Access Lotka–Volterra systems satisfying a strong Painlevé property(Physics Letters A, 2016-09) Bountis, Tassos; Vanhaecke, PolWe use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj, i =j, and require that all variables diverge as t−1. We also require that the leading terms depend on n −2free parameters. We thus discover a cocycle relation among the coefficients aijof the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixiis added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.Item Open Access Homoclinic Points of 2-D and 4-D Maps via the Parametrization Method(arXiv, 2017-09) Anastassiou, Stavros; Bountis, Tassos; B¨acker, ArndAn interesting problem in solid state physics is to compute discrete breather solutions in N coupled 1–dimensional Hamiltonian particle chains and investigate the richness of their interactions. One way to do this is to compute the homoclinic intersections of invariant manifolds of a saddle point located at the origin of a class of 2N–dimensional invertible maps. In this paper we apply the parametrization method to express these manifolds analytically as series expansions and compute their intersections numerically to high precision. We first carry out this procedure for a 2–dimensional (2–D) family of generalized H´enon maps (N = 1), prove the existence of a hyperbolic set in the non-dissipative case and show that it is directly connected to the existence of a homoclinic orbit at the origin. Introducing dissipation we demonstrate that a homoclinic tangency occurs beyond which the homoclinic intersection disappears. Proceeding to N = 2, we use the same approach to accurately determine the homoclinic intersections of the invariant manifolds of a saddle point at the origin of a 4–D map consisting of two coupled 2–D cubic H´enon maps. For small values of the coupling we determine the homoclinic intersection, which ceases to exist once a certain amount of dissipation is present. We discuss an application of our results to the study of discrete breathers in two linearly coupled 1–dimensional particle chains with nearest–neighbor interactions and a Klein–Gordon on site potential.Item Open Access Exceptional Points in Two Dissimilar Coupled Diode Lasers(arXiv, 2018-06) Kominis, Yannis; Choquette, Kent D.; Bountis, Anastassios; Kovanis, VassiliosWe show the abundance of Exceptional Points in the generic asymmetric configuration of two coupled diode lasers, under nonzero optical detuning and differential pumping. We pinpoint the location of these points with respect to the stability domains and the Hopf bifurcation points, in the solution space as well as in the space of experimentally controlled parameters.Item Open Access Controllable Asymmetric Phase-Locked States of the Fundamental Active Photonic Dimer(arXiv, 2018-03-07) Kominis, Yannis; Kovanis, Vassilios; Bountis, TassosCoupled semiconductor lasers are systems possessing complex dynamics that are interesting for numerous applications in photonics. In this work, we investigate the existence and the stability of asymmetric phase-locked states of the fundamental active photonic dimer consisting of two coupled lasers. We show that stable phase-locked states of arbitrary asymmetry exist for extended regions of the parameter space of the system and that their field amplitude ratio and phase difference can be dynamically controlled by appropriate current injection. The model includes the important role of carrier density dynamics and shows that the phase-locked state asymmetry is related to operation conditions providing, respectively, gain and loss in the two lasersItem Open Access Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using q-Statistics(arXiv, 2018-03-19) Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, SergejIn the study of subdiffusive wave-packet spreading in disordered Klein- Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q−Gaussian probability distribu- tion functions of sums of position observables with q > 1 always approach pure Gaussians (q = 1) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this sys- tem in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t = 10Item Metadata only Lotka–Volterra systems satisfying a strong Painlevé property(Physics Letters A, 2016-12-09) Bountis, Tassos; Vanhaecke, Pol; Tassos, BountisAbstract We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj,i≠j, and require that all variables diverge as t−1. We also require that the leading terms depend on n−2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.Item Metadata only Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics(Chaos, Solitons & Fractals, 2017-11-01) Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, Sergej; Chris G., AntonopoulosAbstract In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q−Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaussians (q=1) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t=109.Item Metadata only Fractal attractors and singular invariant measures in two-sector growth models with random factor shares(Communications in Nonlinear Science and Numerical Simulation, 2018-05-01) La Torre, Davide; Marsiglio, Simone; Mendivil, Franklin; Privileggi, Fabio; Davide, La TorreAbstract We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler–Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley’s fern attractor.Item Metadata only Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces(Journal of Mathematical Analysis and Applications, 2017-03-01) Betancor, Jorge J.; Castro, Alejandro J.; Fariña, Juan C.; Rodríguez-Mesa, L.; Jorge J., BetancorAbstract In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1Item Metadata only On the theory of function-valued mappings and its application to the processing of hyperspectral images(Signal Processing, 2017-05-01) Otero, Daniel; La Torre, Davide; Michailovich, Oleg; Vrscay, Edward R.; Daniel, OteroAbstract The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.Item Metadata only A note on the convexity of the Moore–Penrose inverse(Linear Algebra and its Applications, 2018-02-01) Nordström, Kenneth; Kenneth, NordströmAbstract This note is a sequel to an earlier study (Nordström [7]) on convexity properties of the inverse and Moore–Penrose inverse, in which the following question was raised. Given nonnegative definite matrices A and B with Moore–Penrose inverses A+ and B+, respectively, can one show that(λA+λ‾B)+⩽λA++λ‾B+ holding for a single λ∈]0,1[ is enough to guarantee its validity for all λ∈]0,1[? (The ordering above is the partial ordering, induced by the convex cone of nonnegative definite matrices, and λ‾:=1−λ.) In this note an affirmative answer is provided to this question.Item Metadata only The heart of the Banach spaces(Journal of Pure and Applied Algebra, 2017-11-01) Wegner, Sven-Ake; Sven-Ake, WegnerAbstract Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beĭlinson, Bernstein and Deligne consider in this setting a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by Waelbroeck already in 1962. In the current article, we give a direct and rigorous construction of the latter category by considering first the monomorphism category. Then we localize with respect to a multiplicative system. Our approach gives rise to a heart-like category not only for the Banach spaces. In particular, the main results apply to categories in which the set of all kernel–cokernel pairs does not form an exact structure. Such categories arise frequently in functional analysis.Item Metadata only On K-means algorithm with the use of Mahalanobis distances(Statistics & Probability Letters, 2014-01-01) Melnykov, Igor; Melnykov, Volodymyr; Igor, MelnykovAbstract The K-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices.Item Open Access Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers(ArXiv, 2017-06-23) Kominis, Yannis; Bountis, Tassos; Flach, SergejWe analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT) symmetry point the coupler is unstable. Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of these broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations. The lack of symmetry requirements is expected to facilitate experimental implementations and relevant photonics applications.Item Open Access Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer(ArXiv, 2017-10-04) Kominis, Yannis; Kovanis, Vassilios; Bountis, TassosThe fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-tigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The optical spectral signatures of system bifurcations and exceptional points are manifested in terms of self-termination effects and observable drastic variations of the spectral line shape that can be controlled in terms of optical detuning and inhomogeneous pumping.