Reinaldo R. Rosa

Characterization Of Asymmetric Fragmentation Patterns In Spatially Extended Systems

Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator, , for the characterization of asymmetric amplitude fragmentation in extended systems. For a given matrix of amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straight lines. The parameter (I-L)/L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.

Non-extensive statistics and three-dimensional fully developed turbulence

In this paper, we present further evidence, based on new data from the Large Scale Biosphere Atmosphere Experiment in Amazonia (LBA), that the generalized thermostatistics provides a simple and accurate framework for modeling the statistical behavior of fully developed turbulence.

Characterization of localized turbulence in plasma extended systems

We have analysed, for the first time, the high-resolution X-ray images of the solar corona, obtained by the Yohkoh Mission, as non-linear extended systems. To quantify the spatio-temporal complexity in this extended system, we use an asymmetric spatial fragmentation parameter computed from a matrix representing an image. Choosing different spatial scales on the same image, wave numbers are computed from the intensity contours and this yields fragmentation spectra. The dynamics and spectra of the fine structures of the contours can suggest the origin of the observed fragmentation to be a localized weak turbulence process occurring in an evolving coronal active region.

Analysis of chaotic saddles in high-dimensional dynamical systems: The Kuramoto–Sivashinsky equation

This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence.

Multiscale analysis from turbulent time series with wavelet transform

We present a multiscale signal analysis based on the multifractal spectrum obtained by the Wavelet Transform Modulus Maxima technique. We analyze time series from turbulent data: the first step is to obtain the PDF of the flutuations for velocities records and then to fit them by means of the Tsallis generalized thermodynamics (Tsallis, J. Stat. Phys. 52 (1998) 479) the second step is to obtain the multifractal spectra of the time series by the wavelet transform (Muzy et al., Phys. Rew. Lett. 67 (1991) 3515). The aim of this approach was to investigate a possible phenomenological connection between the entropic parameter (q) and the multifractal spectrum for turbulence.

Generalized complex entropic form for gradient pattern analysis of spatio-temporal dynamics

In this paper we describe a new computational operator, called generalized complex entropic form (GEF), for pattern characterization of spatially extended systems. Besides of being a measure of regularity, this operator permits to quantify the degree of phase disorder associated with a given gradient field. An application of GEF to the analysis of the gradient pattern dynamics of a logistic Coupled Map Lattice is presented. Simulations using a Gaussian and random initial condition, provide interesting insights on the system gradual transition from order/symmetry to disorder/randomness.

Multifractal model for eddy diffusivity and counter-gradient term in atmospheric turbulence

A new approach for eddy diffusivity and counter-gradient term in atmospheric turbulent fluxes is developed. This scheme is based on the Taylor statistical theory of turbulence and on a multifractal approach to the turbulent spectrum of energy. The non-extensive thermodynamics description is used to obtain a multifractal model.

Gradient pattern analysis of structural dynamics: application to molecular system relaxation

This paper describes an innovative technique, the gradient pattern analysis (GPA), for analysing spatially extended dynamics. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. The GPA technique is applied for the first time in 3D-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

Gradient pattern analysis of short nonstationary time series: an application to Lagrangian data from satellite tracked drifters

Based on the gradient pattern analysis (GPA) technique we introduce a new methodology for analyzing short nonstationary time series. Using the asymmetric amplitude fragmentation (AAF) operator from GPA we analyze Lagrangian data observed as velocity time series for ocean flow. The results show that quasi-periodic, chaotic and turbulent regimes can be well characterized by means of this new geometrical approach.

Gradient pattern analysis of Swift–Hohenberg dynamics: phase disorder characterization

In this paper, we analyze the onset of phase-dominant dynamics in a uniformly forced system. The study is based on the numerical integration of the Swift–Hohenberg equation and adresses the characterization of phase disorder detected from gradient computational operators as complex entropic form (CEF). The transition from amplitude to phase dynamics is well characterized by means of the variance of the CEF phase component.