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 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

ALIX binds a YPX(3)L motif of the GPCR PAR1 and mediates ubiquitin-independent ESCRT-III/MVB sorting.

The sorting of signaling receptors to lysosomes is an essential regulatory process in mammalian cells. During degradation, receptors are modified with ubiquitin and sorted by endosomal sorting complex required for transport (ESCRT)-0, -I, -II, and -III complexes into intraluminal vesicles (ILVs) of multivesicular bodies (MVBs). However, it remains unclear whether a single universal mechanism mediates MVB sorting of all receptors. We previously showed that protease-activated receptor 1 (PAR1), a G protein-coupled receptor (GPCR) for thrombin, is internalized after activation and sorted to lysosomes independent of ubiquitination and the ubiquitin-binding ESCRT components hepatocyte growth factor-regulated tyrosine kinase substrate and Tsg101. In this paper, we report that PAR1 sorted to ILVs of MVBs through an ESCRT-III-dependent pathway independent of ubiquitination. We further demonstrate that ALIX, a charged MVB protein 4-ESCRT-III interacting protein, bound to a YPX(3)L motif of PAR1 via its central V domain to mediate lysosomal degradation. This study reveals a novel MVB/lysosomal sorting pathway for signaling receptors that bypasses the requirement for ubiquitination and ubiquitin-binding ESCRTs and may be applicable to a subset of GPCRs containing YPX(n)L motifs

Dynamics of Elastic Excitable Media

The Burridge-Knopoff model of earthquake faults with viscous friction is equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with elastic coupling. The lubricated creep-slip friction law we use in the Burridge-Knopoff model describes the frictional sliding dynamics of a range of real materials. Low-dimensional structures including synchronized oscillations and propagating fronts are dominant, in agreement with the results of laboratory friction experiments. Here we explore the dynamics of fronts in elastic excitable media.Comment: Int. J. Bifurcation and Chaos, to appear (1999

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit http://www.imedea.uib.es/~victo

Seismic entangled patterns analyzed via multiresolution decomposition

This article explores a method for distinguishing entangled coherent structures embedded in geophysical images. The original image is decomposed in a series of j-scale-images using multiresolution decomposition. To improve the image processing analysis each j-image is divided in l-spacial regions generating set of (j, l)-regions. At each (j, l)-region we apply a continuous wavelet transform to evaluate <i>E</i><sub>ν</sub>, the spectrum of energy. <i>E</i><sub>ν</sub> has two maxima in the original data. Otherwise, at each scale <i>E</i><sub>ν</sub> hast typically one peak. The localization of the peaks changes according to the (j, l)-region. The intensity of the peaks is linked with the presence of coherent structures, or patterns, at the respective (j, l)-region. The method is successfully applied to distinguish, in scale and region, the ground roll noise from the relevant geologic information in the signal

Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms

We propose a nonlinear ocean forecasting technique based on a combination of genetic algorithms and empirical orthogonal function (EOF) analysis. The method is used to forecast the space-time variability of the sea surface temperature (SST) in the Alboran Sea. The genetic algorithm finds the equations that best describe the behaviour of the different temporal amplitude functions in the EOF decomposition and, therefore, enables global forecasting of the future time-variability.Comment: 15 pages, 3 figures; latex compiled with agums.st

Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients

We present a comprehensive study of phase transitions in single-field systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is instead similar to the one associated with noise-induced transitions a la Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems. To complement the theoretical analysis we present numerical simulations that confirm the findings of the mean-field theory