Ademilson Zanandrea

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 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.

Characterization of local self-similarity and criticality in the solar active regions

From solar radio burst data we computed wavelet transforms and frequency distribution for investigation of self-similar temporal variability and power-laws, as the fundamental conditions for characterization of dynamical criticality (self or forced) in the solar active regions. The main result indicates that, as for the global activity, the local coronal magnetic field, in millisecond time scales, can be in a critical state where the dynamics of solar active regions works as avalanches of many small intermittent particle acceleration events.

Analysis of geomagnetic pulsations using multiwavelets spectral and polarization method

In this paper, we present an algorithm based on the multi-wavelet transform and on the multitaper spectral and polarization methods to estimate polarization parameters of a non-stationary geomagnetic pulsations signals. Through the first right-singular vector and the singular values, obtained from singular value decomposition (SVD) of the multiwavelet eigenspectra matrix M(f,t) of the three-component geomagnetic pulsations we determined the polarization parameters of the hydromagnetic waves in the time–frequency plane. It was used in the multiwavelet polarization analysis to estimate the polarization parameters of geomagnetic pulsations signals obtained from a large geomagnetic storm on March 24, 1991. The results showed that this method is a powerful tool to find events with high degree of polarization and allow to determine the polarization parameters continually in both time and frequency, giving an appropriate resolution to study pulsations that have narrow spectral band and short-lived components.

Asymmetry and self-similarity in the wavelet spectrum

One of the most remarkable properties of wavelet transform is its ability to separate data into different scale contents. For data that show self-similar characteristics in every scale, like fractal landscape, the wavelet spectrum also shows self-similarity. Nevertheless, the situation is not so clear for time dependent data, like seismic geology, solar flares, among others systems that are known to contain self-organized criticality. It is not obvious that these properties will be present in the wavelet spectrum in the form of self-similarity. In this work, we apply two gradient field computational operators R2 yields R, the Complex Entropic Form and the Asymmetric Amplitude Fragmentation, as a mean to differentiate self-similarity from different sources.

Characterization of solar multi‐scaling magnetic loop interactions

Solar magnetic loop structures can exist in a broad range of spatio‐temporal scales and their mutual interactions are described by nonlinear processes of magnetic reconnection triggered as a secondary regime by a primary MHD instability. From the application of wavelet analysis on decimetric time series as a counterpart of spatio‐temporal flare loop observations we derive, using Tajima’s model for quasi‐periodic MHD coalescence, possible ranges of minimum Sagdeev potential. From this parameter we obtain the Alfven period of nonlinear oscillation for a typical mutual solar loop interaction observed by SOHO and TRACE.

Characterization of the spatio-temporal patterns in the osmosedimentation process

In the present work we investigate the problem of pattern formation by fluid flow and mass transport in a viscous binary fluid mixture under osmosedimentation. We perform a numerical investigation of these patterns using spatial computational operators (R2→R), computed from the spatial mass distribution field over time. Our main goal is to determine different dynamical regimes through analysis of the complex patterns arising from the osmosedimentation process. The results show that the pattern formation dynamics in the osmosedimentation process can be well characterized by means of these computational operators.