arXiv subjects

Ch. Skokos

Publications and source records attributed to Ch. Skokos.

At least 19 recordsLinked to original sources

arXiv2021

Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials

We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral galaxies. These potentials are known for providing building blocks to support observed features such as the peanut, or X-shaped bulge, in the former case and the spiral arms in the latter. We investigate the possibility that these structures are reinforced, apart by regular orbits, also by orbits in the vicinity of complex unstable periodic orbits. We examine the evolution of the phase space structure in the immediate neighbourhood of the periodic orbits in cases where the stability of a family presents a successive transition from stability to complex instability and then to stability again, as energy increases. We find that we have a gradual reshaping of invariant structures close to the transition points and we trace this evolution in both models. We conclude that for time scales significant for the dynamics of galaxies, there are weakly chaotic orbits associated with complex unstable periodic orbits, which should be considered as structure-supporting, since they reinforce the morphological features we study.

astro-ph.GA↗

arXiv2020

Thermalization in the one-dimensional Salerno model lattice

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable) discrete nonlinear Schr{ö}dinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS towards AL) is varied, the region in the space of initial energy and norm-densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.

physics.class-ph↗

arXiv2020

Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves

We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an interesting problem as it can be used to model physically important systems like beam-like microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transport both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low frequency extended waves and a set of high frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place.

nlin.PS↗

arXiv2020

Properties of normal modes in a modified disordered Klein-Gordon lattice: From disorder to order

We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: $D$, which determines the range of the coefficients of the on-site potentials, and $W$, which defines the strength of the nearest-neighbor interactions. We fix $W=4$ and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. $D\rightarrow 0$. We show that the probability density distribution of the normal modes' frequencies takes a `U'-shaped profile as $D$ decreases. Furthermore, we use two quantities for estimating the modes' spatial extent, the so-called localization volume $V$ (which is related to the mode's second moment) and the mode's participation number $P$. We show that both quantities scale as $\propto D^{-2}$ when $D$ approaches zero and we numerically verify a proportionality relation between them as $V/P \approx 2.6$.

nlin.CD↗

arXiv2019

Chaotic dynamics of piezoelectric mems based on maximal Lyapunov exponent and Smaller Alignment Index computations

We characterize the dynamical states of a piezoelectric microelectromechanical system (MEMS) using several numerical quantifers including the maximal Lyapunov exponent, the Poincare Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS model and describe the behavior of some representative phase space orbits of the system. We show that the dynamics of the piezoelectric MEMS becomes considerably more complex as the natural frequency of the system's mechanical part decreases.This refers to the reduction of the stiffness of the piezoelectric transducer. Then, taking into account the effects of damping and time dependent forces on the piezoelectric MEMS, we derive the corresponding non-autonomous Hamiltonian and investigate its dynamical behavior. We find that the non-conservative system exhibits a rich dynamics, which is strongly influenced by the values of the parameters that govern the piezoelectric MEMS energy gain and loss. Our results provide further evidences of the ability of the SALI to efficiently characterize the chaoticity of dynamical systems.

physics.comp-ph↗

arXiv2018

Chaos and Anderson Localisation in Disordered Classical Chains: Hertzian vs FPUT models

We numerically investigate the dynamics of an one-dimensional disordered lattice using the Hertzian model, describing a granular chain, and the $α+β$ Fermi-Pasta-Ulam-Tsingou model (FPUT). The most profound difference between the two systems is the discontinuous nonlinearity of the granular chain appearing whenever neighboring particles are detached. We therefore sought to unravel the role of these discontinuities in the destruction of Anderson localization and their influence on the system's chaotic dynamics. Our results show that both models exhibit an energy range where localization coexists with chaos. However, the discontinuous nonlinearity is found to be capable of triggering energy spreading of initially localized modes, at lower energies than the FPUT model. A transition from Anderson localization to chaotic dynamics and energy equipartition is found for the granular chain and is associated with the"propagation" of the discontinuous nonlinearity in the chain. On the contrary, the FPUT chain exhibits an alternate behavior between localized and delocalized chaotic behavior which is strongly dependent on the initial energy of excitation.

nlin.CD↗

arXiv2018

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

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 Schrödinger 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 $Λ$ decays in time $t$ as $Λ\propto t^{α_Λ}$, with $α_Λ$ being different from the $α_Λ=-1$ value observed in cases of regular motion. In particular, $α_Λ\approx -0.25$ (weak chaos) and $α_Λ\approx -0.3$ (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 $Λ$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

nlin.CD↗

arXiv2017

Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices

We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical performance. For this purpose, we perform extensive numerical simulations by considering many different initial energy excitations and following the evolution of the created wave packets in the various dynamical regimes exhibited by these models. We compare the efficiency of the considered integrators by checking their ability to correctly reproduce several features of the wave packets propagation, like the characteristics of the created energy distribution and the time evolution of the systems' maximum Lyapunov exponent estimator. Among the tested integrators the fourth order $ABA864$ scheme \cite{BCFLMM13} showed the best performance as it needed the least CPU time for capturing the correct dynamical behavior of all considered cases when a moderate accuracy in conserving the systems' total energy value was required. Among the higher order schemes used to achieve a better accuracy in the energy conservation, the sixth order scheme $s11ABA82\_6$ exhibited the best performance.

physics.comp-ph↗

arXiv2017

Boxy Orbital Structures in Rotating Bar Models

We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or (almost) the bar itself. Our models originate in snapshots of an N-body simulation, which develops a strong bar. We consider three snapshots of the simulation and for the orbital study we treat each snapshot independently, as an autonomous Hamiltonian system. The calculated corotation-to-bar-length ratios indicate that in all three cases the bar rotates slowly, while the orientation of the orbits of the main family of periodic orbits changes along its characteristic. We characterize the orbits as regular, sticky, or chaotic after integrating them for a 10 Gyr period by using the GALI$_2$ index. Boxiness in the equatorial plane is associated either with quasi-periodic orbits in the outer parts of stability islands, or with sticky orbits around them, which can be found in a large range of energies. We indicate the location of such orbits in diagrams, which include the characteristic of the main family. They are always found about the transition region from order to chaos. By perturbing such orbits in the vertical direction we find a class of 3D non-periodic orbits, which have boxy projections both in their face-on and side-on views.

astro-ph.GA↗

arXiv2017

Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition

We investigate the dynamics of highly polydispersed finite granular chains. From the spatio-spectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities lead to chaotic dynamics and if so, does chaos destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, although the overall system behaves chaotically, it can exhibit long lasting energy localization for particular single particle excitations. On the other hand, for sufficiently strong nonlinearities, connected with contact breaking, the granular chain reaches energy equipartition and an equilibrium chaotic state, independent of the initial position excitation.

nlin.CD↗

arXiv2015

Energy transport in one-dimensional disordered granular solids

We investigate the energy transport in one-dimensional disordered granular solids by extensive numerical simulations. In particular, we consider the case of a polydisperse granular chain composed of spherical beads of the same material and with radii taken from a random distribution. We start by examining the linear case, in which it is known that the energy transport strongly depends on the type of initial conditions. Thus, we consider two sets of initial conditions: i) an initial displacement and ii) an initial momentum excitation of a single bead. After establishing the regime of sufficiently strong disorder, we focus our studies on the role of nonlinearity for both sets of initial conditions. By increasing the initial excitation amplitudes we are able to identify three distinct dynamical regimes with different energy transport properties: a near linear, a weakly nonlinear and a highly nonlinear regime. Although energy spreading is found to be increasing for higher nonlinearities, in the weakly nonlinear regime no clear asymptotic behavior of the spreading is found. In this regime, we additionally find that energy, initially trapped in a localized region, can be eventually detrapped and this has a direct influence on the fluctuations of the energy spreading. We also demonstrate that in the highly nonlinear regime, the differences in energy transport between the two sets of initial conditions vanish. Actually, in this regime the energy is almost ballistically transported through shock-like excitations.

nlin.CD↗

arXiv2015

The Smaller (SALI) and the Generalized (GALI) Alignment Indices: Efficient Methods of Chaos Detection

We provide a concise presentation of the Smaller (SALI) and the Generalized Alignment Index (GALI) methods of chaos detection. These are efficient chaos indicators based on the evolution of two or more, initially distinct, deviation vectors from the studied orbit. After explaining the motivation behind the introduction of these indices, we sum up the behaviors they exhibit for regular and chaotic motion, as well as for stable and unstable periodic orbits, focusing mainly on finite-dimensional conservative systems: autonomous Hamiltonian models and symplectic maps. We emphasize the advantages of these methods in studying the global dynamics of a system, as well as their ability to identify regular motion on low dimensional tori. Finally we discuss several applications of these indices to problems originating from different scientific fields like celestial mechanics, galactic dynamics, accelerator physics and condensed matter physics.

nlin.CD↗

arXiv2014

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schroedinger equation

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schroedinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS - a hotly debated subject in current scientific literature.

physics.comp-ph↗

arXiv2014

Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion in both cases in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as $10^9$, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic KAM torus and that diffusion continues to spread chaotically for arbitrarily long times.

nlin.CD↗

arXiv2014

Delocalization of wave packets in disordered nonlinear chains

We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrödinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single site, single mode and general finite size excitations, and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.

cond-mat.dis-nn↗

arXiv2013

Chaoticity without thermalisation in disordered lattices

We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schrödinger equation (DNLS). A symplectic integration method allows us to accurately obtain both the full phase space trajectories and their maximum Lyapunov exponents (mLEs), which characterize their chaoticity. We find that disorder destroys ergodicity by breaking up phase space into subsystems that are effectively disjoint on experimentally relevant timescales, even though energetically, classical localisation cannot occur. This leads us to conclude that the mLE is a very poor ergodicity indicator, since it is not sensitive to the trajectory being confined to a subregion of phase space. The eventual thermalization of a BEC in a disordered lattice cannot be predicted based only on the chaoticity of its phase space trajectory.

cond-mat.quant-gas↗

arXiv2012

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.

nlin.CD↗

arXiv2011

Improving beam stability in particle accelerator models by using Hamiltonian control

We derive a Hamiltonian control theory which can be applied to a 4D symplectic map that models a ring particle accelerator composed of elements with sextupole nonlinearity. The controlled system is designed to exhibit a more regular orbital behavior than the uncontrolled one. Using the Smaller Alignement Index (SALI) chaos indicator, we are able to show that the controlled system has a dynamical aperture up to 1.7 times larger than the original mode

physics.acc-ph↗