Intermittent stickiness synchronization

Abstract

This work uses the statistical properties of Finite-Time Lyapunov exponents (FTLEs) to investigate the Intermittent Stickiness Synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems. Full Stickiness Synchronization (SS) occurs when all FTLEs from a chaotic trajectory tend to zero for arbitrary long time-windows. This behavior is a consequence of the sticky motion close to regular structures which live in the high-dimensional phase space and affects all unstable directions proportionally by the same amount, generating a kind of collective motion. Partial SS occurs when at least one FTLE approaches to zero. Thus, distinct degrees of partial SS may occur, depending on the values of nonlinearity and coupling parameters, on the dimension of the phase space and on the number of positive FTLEs. Through filtering procedures used to precisely characterize the sticky motion, we are able to compute the algebraic decay exponents of the ISS and to obtain remarkable evidence about the existence of a universal behavior related to the decay of time correlations encoded in such exponents. In addition, we show that even though the probability to find full SS is small compared to partial SSs, the full SS may appear for very long times due to the slow algebraic decay of time correlations in mixed phase space. In this sense, observations of very late intermittence between chaotic motion and full SSs become rare events.

Numerical study of condensation in a Fermi-like model of counterflowing particles via Gini coefficient

“…Synchronous update: All particles are simultaneously updated. This choice was performed in [12]; 2. Asynchronous update: We select n part particles (the total number of the particles) distributed in L cells.…”

“…5. In order to conduct this study we use the Gini coefficient to investigate the phase transition between a mobile and a clogging phase (or condensate phase) as partially explored earlier [12]. We show that the Gini coefficient is capable of indicating important details of this transition.…”

“…Notwithstanding, such models exclude very important effects such as the self exclusion of particles. Thus, we have recently proposed a model [12] where the occupation of the next cells is given by a modified Fermi-Dirac distribution. This leads to the following choice for the damping function:…”

“…In section 2 we present the Fermi-Dirac directed random walk (FDDEW) model as a derivation of the TSPDES to a problem previously defined [12]. We obtain recurrence relations for this model and extend it to the continuous limit.…”

“…We also determine the Gini coefficient via Monte Carlo (MC) simulations with both synchronous and asynchronous updating schemes. We finish this work comparing these two strategies with regards to a mobility parameter previously defined [12].…”