Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.Comment: 20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nep

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.Comment: 10 pages including 12 postscript figures, revtex. Additional work in http://www.imedea.uib.es/Nonlinear . The paper with higher-resolution figures can be obtained from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Synchronization of Spatiotemporal Chaos: The regime of coupled Spatiotemporal Intermittency

Synchronization of spatiotemporally chaotic extended systems is considered in the context of coupled one-dimensional Complex Ginzburg-Landau equations (CGLE). A regime of coupled spatiotemporal intermittency (STI) is identified and described in terms of the space-time synchronized chaotic motion of localized structures. A quantitative measure of synchronization as a function of coupling parameter is given through distribution functions and information measures. The coupled STI regime is shown to dissapear into regular dynamics for situations of strong coupling, hence a description in terms of a single CGLE is not appropiate.Comment: 4 pages, LaTeX 2e. Includes 3 figures made up of 8, 4 (LARGE),and 2 postscript files. Includes balanced.st

Analysis of the acoustic cut-off frequency and HIPs in six Kepler stars with stochastically excited pulsations

Gravito-acoustic modes in the Sun and other stars propagate in resonant cavities with a frequency below a given limit known as the cut-off frequency. At higher frequencies, waves are no longer trapped in the stellar interior and become traveller waves. In this article we study six pulsating solar-like stars at different evolutionary stages observed by the NASA Kepler mission. These high signal-to-noise targets show a peak structure that extends at very high frequencies and are good candidates for studying the transition region between the modes and the interference peaks or pseudo-modes. Following the same methodology successfully applied on Sun-as-a-star measurements, we uncover the existence of pseudo-modes in these stars with one or two dominant interference patterns depending on the evolutionary stage of the star. We also infer their cut-off frequency as the midpoint between the last eigenmode and the first peak of the interference patterns. By using ray theory we show that, while the period of one of the interference pattern is very close to half the large separation the other, one depends on the time phase of mixed waves, thus carrying additional information on the stellar structure and evolution.Comment: Accepted for publication in A&A. 14 pages, 28 figure

Infrared Study of Fullerene Planetary Nebulae

We present a study of 16 PNe where fullerenes have been detected in their Spitzer spectra. This large sample of objects offers an unique opportunity to test conditions of fullerene formation and survival under different metallicity environments as we are analyzing five sources in our own Galaxy, four in the LMC, and seven in the SMC. Among the 16 PNe under study, we present the first detection of C60 (possibly also C70) fullerenes in the PN M 1-60 as well as of the unusual 6.6, 9.8, and 20 um features (possible planar C24) in the PN K 3-54. Although selection effects in the original samples of PNe observed with Spitzer may play a potentially significant role in the statistics, we find that the detection rate of fullerenes in C-rich PNe increases with decreasing metallicity (5% in the Galaxy, 20% in the LMC, and 44% in the SMC). CLOUDY photoionization modeling matches the observed IR fluxes with central stars that display a rather narrow range in effective temperature (30,000-45,000 K), suggesting a common evolutionary status of the objects and similar fullerene formation conditions. The observed C60 intensity ratios in the Galactic sources confirm our previous finding in the MCs that the fullerene emission is not excited by the UV radiation from the central star. CLOUDY models also show that line- and wind-blanketed model atmospheres can explain many of the observed [NeIII]/[NeII] ratios by photoionization suggesting that possibly the UV radiation from the central star, and not shocks, are triggering the decomposition of the circumstellar dust grains. With the data at hand, we suggest that the most likely explanation for the formation of fullerenes and graphene precursors in PNe is that these molecular species are built from the photo-chemical processing of a carbonaceous compound with a mixture of aromatic and aliphatic structures similar to that of HAC dust.Comment: Accepted for publication in ApJ (43 pages, 11 figures, and 4 tables). Small changes to fit the proof-corrected article to be published in Ap