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On going and planned activities by LAC group: Processing, Visualization and Analysis of Spatio-temporal Dynamics Reinaldo R. Rosa reinaldo@lac.inpe.br 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

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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

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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

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Solar Data: Yohkoh, soft X-rays

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Solar Active Loops:

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X Ray and Radio Data: Nobeyama Radioheliograph

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Space Weather Today:

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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.

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Spatio-Temporal Domain:

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* Characterization of Spatio-Temporal Pattern Formation and Evolution in: Chaotic Coupled Map Lattices Extended Difusion-Convection Osmosedimentation Reaction-Diffusion Systems: Amplitude Equations and Protein Folding 3D-Turbulence (Turbulator-Phase I) Granular Materials Extended Nonlinear Plasmas (Solar Physics) Activity Porosity * nonequilibrium regimes

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Nonequilibrium Regimes: Common Source: High Gradients in the Field Symmetry ( T, v or C) ==> system is driven away from thermodynamical equilibrium (initial system state becomes unstable)==> ==> symmetry breaking of the geometry ==> ==> spatial complex pattern formation (Grahams nonequilibrium potential) In this context: What types of main nonequilibrium regimes?

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Spatio-Temporal Nonequilibrium Regimes: Structure Fragmentation and Coalescence of Ch (spatio-temporal velocity) Hysteresis and Dissipative regimes Spatio-temporal chaos (activator-inhibitor model dynamics) Long range spatio-temporal correlations and structures synchronization => Local and Global spatio-temporal patterns stability rate (U x,y,0 coherence and U 0,0,t boundary influence) Pattern Relaxation: normal and abnormal

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Gradient Pattern Analysis (GPA) (P/ entender e interpretar as causas da relaxão e da estabilidade==> nova metodologia) G t = [E(x,y,t] t G t is represented by 4 n.s. gradients moments: g 1 (t) h 1 ({(r 1,1, 11 ) …, (r ij, ij ) …, (r kk kk )} t ) g 2 (t) h 2 ({(r 11 ), …, (r ij ), …, (r kk )} t ) g 3 (t) h 3 ({( 11 ), …, ( ij ), …, ( kk )} t ) g 4 (t) h 4 ({(z 11 ) …, (z ij ) …, (z kk )} t ) As {r} and { } are compact groups, spatially distributed, they can be geometrically constructed as Haar-like measures ==> rotational and amplitude translation invariant

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Gradient Pattern Analysis:

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How to compute g 1,g 2, g 3 e g 4 ? g 1 (C - V A )/V A, C > V A V A = amount of asymmetric vectors, (v1 + v2 0) C = amount of geometric correlation lines (Delaunay triangulation T D (C,V A ) ) (Asymmetric Amplitude Fragmentation - AAF, Rosa et al., Int. J. Mod. Phys. C, 10(1)(1999):147.) g 2 (r ij – r mn ) 2 /N ; g 3 ( ij – mn ) 2 /N g 4 : S z = - z i,j /z ln (z i,j /z) = Re(S z ) e iSz | g 4 |=Re(S z )=S(|z|) and (g 4 )=Im(S z ) Thus, |g 4 | and (g 4 ) are invariant measurements of norm and phase of the gradient entropy (Complex Entropic Form (CEF) by Ramos et al. Physica A283(2000):171.)

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Characterization of Asymmetric Fluctuations, Amplitude Dynamics and Nonlinear Pattern Stability (Relaxation Regimes): g 1 x t | g 4 | x t g 1 (t) x phase(g 4 )(t)

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g 1 = 0, g 2 = 0, g 3 = 0, |g 4 | = 0.20, (g 4 )=0 g 1 = (7 - 5) / 5 = 0.4, g 2 = 0, g 3 = 0.20, |g 4 | = 0.18, (g 4 )=0.20

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Some Important Dynamical Properties of the Gradient Moments: (1) Amplitude x Phase Dynamics | g 4 |/ t phase dynamics dominates and determine the relaxation ( g 1 / t > 0 => desordering vec. Norm) 2) Pattern Global Equilibrium (PGE) Conditions: C1: | g 4 |/ t = 0 + g 1 / t = 0 Weak PGE C2: C1 e g 4 / t = 0 Strong PGE ===> cluster around a characteristic point g 2, g 3 ) (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)

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Gradient Pattern Analysis of Relaxation Regimes Systems: Oscillated Granular Layer: (> 10 4 0.15-0.18 mm bronze spheres - from CND Un.Texas) Knobloch Amplitude Equation (Simplification of Proctors Model) t E = rE - ( 2 E + 1) 2 E +. (| 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.

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Spatio-Temporal Relaxation: is it an universal regime?

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Results(Considering Charac. Scales):

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Concluding Remarks System Relaxation GPE Boundary Influence Oscillons 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

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Modelling validation: B=f(t,x,y,z;d)

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