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Senyange B. - One of the best experts on this subject based on the ideXlab platform.
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Characteristics of Chaos evolution in one-dimensional disordered nonlinear lattices
'American Physical Society (APS)', 2018Co-Authors: Senyange B., Manda B., Skopos C.Abstract:We numerically investigate the characteristics of Chaos evolution during wave-packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrodinger equation model. Completing previous investigations [Ch. Skokos et al., Phys. Rev. Lett. 111, 064101 ( 2013)], we verify that chaotic dynamics is slowing down for both the so-called weak and strong Chaos Dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent Lambda decays in time t as Lambda proportional to t(alpha Lambda) with alpha(Lambda) being different from the alpha(Lambda) = -1 value observed in cases of regular motion. In particular, alpha(Lambda) approximate to -0.25 (weak Chaos) and alpha(Lambda) approximate to -0.3 (strong Chaos) for both models, indicating the Dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with Lambda reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part
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Characteristics of Chaos evolution in one-dimensional disordered nonlinear lattices
'American Physical Society (APS)', 2018Co-Authors: Senyange B., Manda B. Many, Ch. SkokosAbstract:We numerically investigate the characteristics of Chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schr\"{o}dinger equation model. Completing previous investigations \cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak' and `strong Chaos' Dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $\Lambda$ decays in time $t$ as $\Lambda \propto t^{\alpha_{\Lambda}}$, with $\alpha_{\Lambda}$ being different from the $\alpha_{\Lambda}=-1$ value observed in cases of regular motion. In particular, $\alpha_{\Lambda}\approx -0.25$ (weak Chaos) and $\alpha_{\Lambda}\approx -0.3$ (strong Chaos) for both models, indicating the Dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $\Lambda$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.Comment: 11 pages, 10 figure
Ch. Skokos - One of the best experts on this subject based on the ideXlab platform.
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Characteristics of Chaos evolution in one-dimensional disordered nonlinear lattices
'American Physical Society (APS)', 2018Co-Authors: Senyange B., Manda B. Many, Ch. SkokosAbstract:We numerically investigate the characteristics of Chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schr\"{o}dinger equation model. Completing previous investigations \cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak' and `strong Chaos' Dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $\Lambda$ decays in time $t$ as $\Lambda \propto t^{\alpha_{\Lambda}}$, with $\alpha_{\Lambda}$ being different from the $\alpha_{\Lambda}=-1$ value observed in cases of regular motion. In particular, $\alpha_{\Lambda}\approx -0.25$ (weak Chaos) and $\alpha_{\Lambda}\approx -0.3$ (strong Chaos) for both models, indicating the Dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $\Lambda$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.Comment: 11 pages, 10 figure
Skopos C. - One of the best experts on this subject based on the ideXlab platform.
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Characteristics of Chaos evolution in one-dimensional disordered nonlinear lattices
'American Physical Society (APS)', 2018Co-Authors: Senyange B., Manda B., Skopos C.Abstract:We numerically investigate the characteristics of Chaos evolution during wave-packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrodinger equation model. Completing previous investigations [Ch. Skokos et al., Phys. Rev. Lett. 111, 064101 ( 2013)], we verify that chaotic dynamics is slowing down for both the so-called weak and strong Chaos Dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent Lambda decays in time t as Lambda proportional to t(alpha Lambda) with alpha(Lambda) being different from the alpha(Lambda) = -1 value observed in cases of regular motion. In particular, alpha(Lambda) approximate to -0.25 (weak Chaos) and alpha(Lambda) approximate to -0.3 (strong Chaos) for both models, indicating the Dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with Lambda reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part
Senyange Bob - One of the best experts on this subject based on the ideXlab platform.
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Chaotic behaviour of disordered nonlinear lattices
Department of Mathematics and Applied Mathematics, 2021Co-Authors: Senyange BobAbstract:In this work we systematically investigate the chaotic energy spreading in prototypical models of disordered nonlinear lattices, the so-called disordered Klein-Gordon (DKG) system, in one (1D) and two (2D) spatial dimensions. The normal modes' exponential localization in 1D and 2D heterogeneous linear media explains the phenomenon of Anderson Localization. Using a modified version of the 1D DKG model, we study the changes in the properties of the system's normal modes as we move from an ordered version to the disordered one. We show that for the ordered case, the probability density distribution of the normal modes' frequencies has a ‘U'-shaped profile that gradually turns into a plateau for a more disordered system, and determine the dependence of two estimators of the modes' spatial extent (the localization volume and the participation number) on the width of the interval from which the strengths of the on-site potentials are randomly selected. Furthermore, we investigate the numerical performance of several integrators (mainly based on the two part splitting approach) for the 1D and 2D DKG systems, by performing extensive numerical simulations of wave packet evolutions in the various Dynamical regimes exhibited by these models. In particular, we compare the computational efficiency of the integrators considered by checking their ability to correctly reproduce the time evolution of the systems' finite time maximum Lyapunov exponent estimator Λ and of various features of the propagating wave packets, and determine the best-performing ones. Finally we perform a numerical investigation of the characteristics of Chaos evolution for a spreading wave packet in the 1D and 2D nonlinear DKG lattices. We confirm the slowing down of the chaotic dynamics for the so-called weak, strong and selftrapping Chaos Dynamical regimes encountered in these systems, without showing any signs of a crossover to regular behaviour. We further substantiate the Dynamical dissimilarities between the weak and strong Chaos regimes by establishing different, but rather general, values for the time decay exponents of Λ. In addition, the spatio-temporal evolution of the deviation vector associated with Λ reveals the meandering of chaotic seeds inside the wave packets, supporting the assumptions for chaotic spreading theories of energy
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Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
'American Physical Society (APS)', 2020Co-Authors: Manda, Bertin Many, Senyange Bob, Skokos CharalamposAbstract:We reveal the generic characteristics of wave packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schr\"{o}dinger equation. We find that in both models (a) the wave packet's second moment asymptotically evolves as $t^{a_m}$ with $a_m \approx 1/5$ ($1/3$) for the weak (strong) Chaos Dynamical regime, in agreement with previous theoretical predictions [S.~Flach, Chem.~Phys.~{\bf 375}, 548 (2010)], (b) Chaos persists, but its strength decreases in time $t$ since the finite time maximum Lyapunov exponent $\Lambda$ decays as $\Lambda \propto t^{\alpha_{\Lambda}}$, with $\alpha_{\Lambda} \approx -0.37$ ($-0.46$) for the weak (strong) Chaos case, and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattice's excited part, which induces the wave packet's thermalization. We also propose a dimension-independent scaling between the wave packet's spreading and chaoticity, which allows the prediction of the obtained $\alpha_{\Lambda}$ values.Comment: 15 pages, 5 figures. Accepted for publication in PR
Teruhisa S Komatsu - One of the best experts on this subject based on the ideXlab platform.
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Energy conversion by autonomous regulation of Chaos: Dynamical mechanism of loose coupling
2020Co-Authors: Naoko Nakagawa, Kunihiko Kaneko, Teruhisa S KomatsuAbstract:Inspired by recent experiments of molecular motors, a Dynamical systems model for a flexible machine is proposed which converts injected energy to output directional motion. The output amount is distributed broadly, and thus the coupling between input energy and output motion is loose, as in the experiments. This energy conversion is shown to be robust against the change of surrounding environment. Stability analysis on the fixed point solutions of the model is presented, which suggests that transient chaotic motion, induced by temporal three-body motion, is relevant to the energy conversion. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1594511͔ How is energy converted from one form to another in order for a molecular machine to work? This question was addressed by Oosawa, who proposed that the coupling from chemical energy to mechanical work is not tightly fixed, but rather loose, in order that the molecular machine works under large thermal fluctuations although the amount of input energy is as small as an order of thermal fluctuations. Inspired by this problem, we propose a fluctuating flexible machine described by a Dynamical system with a few degrees of freedom, composed of a head with internal degrees of freedom, and a lattice. By numerical simulations of this simple model, we find that after excitation of some part of the system, energy is stored for some time, and is used step by step, allowing the head to move directionally along the lattice. The system can adjust the timing for its motion by itself, by taking advantage of internal dynamics. The obtained results provide a theoretical description for dynamics of the above ''loose coupling'' mechanism. The head motion along the lattice by crossing over an energy barrier is achieved by changing effective degrees of freedom autonomously, as studied in chaotic itinerancy. Although we use a specific model, the proposed mechanism is expected to be rather general and is applicable to other energy conversion problems on molecular scales, including nanomachines or biological processes at such scales