On going and planned activities by LAC group: Processing, Visualization and Analysis of Spatio-temporal Dynamics Reinaldo R. Rosa [email protected]•Adriana P. Mattedi, Roberto A. Costa Junior, Erico L. Rempel. •Cristiane P. Camilo, Márcia Rodrigues, Rogério C. Brito, Mariana Baroni •F.M. Ramos , A Wilter Souza da Silva, A. Assireu, I. B. T. de Lima, N. Vijaykumar, A. Zanandrea, R. Sych , J. Pontes , H. Swinney , • A. J. Preto, S. Stephany, J.Demisio da Silva, Maria Conceição Andrade , NÚCLEO PARA SIMULAÇÃO E ANÁLISE DE SISTEMAS COMPLEXOS - NUSASC BDA WORKSHOP 04-05/9/2003, INPE
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On going and planned activities by LAC group: Processing, Visualization and Analysis of Spatio-temporal Dynamics Reinaldo R. Rosa [email protected].
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On going and planned activities by LAC
group: Processing, Visualization and Analysis of Spatio-temporal Dynamics
•Adriana P. Mattedi, Roberto A. Costa Junior, Erico L. Rempel.
•Cristiane P. Camilo, Márcia Rodrigues, Rogério C. Brito, Mariana Baroni
•F.M. Ramos, A Wilter Souza da Silva, A. Assireu, I. B. T. de Lima, N. Vijaykumar, A. Zanandrea, R. Sych, J. Pontes, H. Swinney,
• A. J. Preto, S. Stephany, J.Demisio da Silva, Maria Conceição Andrade,
NÚCLEO PARA SIMULAÇÃO E ANÁLISE DE SISTEMAS COMPLEXOS - NUSASC
LABORATÓRIO ASSOCIADO DE COMPUTAÇÃO
E MATEMÁTICA APLICADA
BDA WORKSHOP
04-05/9/2003, INPE
Related BDA Research at LAC:• Time Series Analysis of Solar Bursts and modelling
for emission mechanisms• Loop Tomography• Image Processing, Interface Data Base Softwares and
High Performance Computing• Neuronetworks for Solar Active Region Pattern
Recognition• Space Weather using Gradient Pattern Analysis and
Wavelets• 1997-2003: 08 papers, 05 masters and 02 pos-docs
Space Weather Data and Scientific Computing
processing, visualization, data base, data mining and analysis
Real time data: Time series (time and space) and Spectrograms from the solar-terrestrial plasma
environment + warning devices + making decision tools
Solar Data: Yohkoh, soft X-rays
Solar Active Loops:
X Ray and Radio Data:Nobeyama Radioheliograph
Space Weather Today:
“A Dinâmica de Padrões Espaço-Temporais é uma teoria fenomenológica que sistematiza as leis empíricas, sobre regimes não-lineares no domínio espaço-temporal, que ocorrem durante a formação e evolução de estruturas dinâmicas macroscópicas”
Falaremos aqui sobre uma nova teoria geométrica analítica conhecida como Análise de Padrões Gradientes ( Gradient Pattern Analysis - GPA) cuja principal propriedade é a sua extrema sensibilidade para detectar flutuações não-lineares no domínio espaço-temporal.
Spatio-Temporal Domain:
*Characterization of Spatio-Temporal Pattern Formation and Evolution in:
As {r} and {} are compact groups, spatially distributed, they can be geometrically constructed as Haar-like measures ==> rotational and amplitude translation invariant
Gradient Pattern Analysis:
How to compute g1,g2, g3 e g4 ?
g1 (C - VA)/VA , C > VA
VA = amount of asymmetric vectors, (v1 + v2 0)C = amount of geometric correlation lines (Delaunay triangulation
TD(C,VA) )(Asymmetric Amplitude Fragmentation - AAF, Rosa et al.,
Int. J. Mod. Phys. C, 10(1)(1999):147.)
g2 (rij – rmn)2 /N ; g3 ( ij – mn)2 /N
g4 : Sz = - zi,j/z ln (zi,j/z) = Re(Sz) eiSz
| g4|=Re(Sz)=S(|z|) and (g4)=Im(Sz) Thus, |g4| and (g4) are invariant measurements of norm and
phase of the gradient entropy(Complex Entropic Form (CEF) by Ramos et al. Physica
A283(2000):171.)
Characterization of Asymmetric Fluctuations, Amplitude Dynamics and
Some Important Dynamical Properties of the Gradient Moments:
(1) Amplitude x Phase Dynamics
|g4|/ t < 0 ==> phase dynamics dominates and determine the relaxation (g1/ t > 0 => desordering vec. Norm)
2) Pattern Global Equilibrium (PGE) Conditions:
C1: |g4|/ t = 0 + g1/ t = 0 “Weak PGE”
C2: C1 e g4/ t = 0 “Strong PGE”
===> cluster around a characteristic point g2 ,g3)(More than 01 cluster ==> complex equilibrium regimes
mainly due to more than 01 dynamical constraint (ex. Boundary)Physica A 283:156(2000), Physica D 168:397(2002), PRL (2003)
Gradient Pattern Analysis of Relaxation Regimes
Systems:
• Oscillated Granular Layer: (> 104 0.15-0.18 mm bronze spheres - from CND Un.Texas)
• Knobloch Amplitude Equation (Simplification of Proctor’s Model)
tE = rE - (2E + 1)2E + . (|E|2 E),where E(x,y,t) is a measure of the vertically averaged
temperature perturbation due to fluid motion. When the parameter r > 0, the conductive solution E=0 is unstable.
Spatio-Temporal Relaxation: is it an universal regime?
Results(Considering Charac. Scales):
Concluding Remarks System Relaxation GPE Boundary InfluenceOscillons normal simple low Knobloch abnormal complex (3sR) high
• Abnormal relaxation comes from a strong Amplitude x Phase Dynamics where the amplitudes are very asymmetric in z (amplitude equations are not models for discrete oscillons)
• Gradient moments from active regions time series:Monitoring + forecasting + modelling validation