BDA WORKSHOP
04-05/9/2003, INPE
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
LABORATÓRIO ASSOCIADO DE COMPUTAÇÃO
E MATEMÁTICA APLICADA
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 posdocs
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:
•
•
•
•
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
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
(Graham’s nonequilibrium potential)
In this context: What types of main nonequilibrium regimes?
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 (Ux,y,0 coherence and U0,0,t boundary
influence)
• Pattern Relaxation: normal and abnormal
Gradient Pattern Analysis (GPA)
(P/ entender e interpretar as causas da relaxão e da estabilidade==>
nova metodologia)
• Gt = [E(x,y,t]t
• Gt is represented by 4 n.s. gradients moments:
g1(t) h1 ({(r1,1, 11) … , (rij, ij) … , (rkk kk)}t)
g2(t) h2 ({(r11), … , (rij), … , (rkk)}t)
g3(t) h3 ({(11), … , (ij), … , (kk)}t)
g4(t) h4 ({(z11) … , (zij) … , (zkk)}t)
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
Nonlinear Pattern Stability (Relaxation Regimes):
g1 x t
| g4| x t
g1 (t) x phase(g4 )(t)
g1 = 0 , g2 = 0 , g3 = 0 , |g4| = 0.20 , (g4)=0
g1 = (7 - 5) / 5 = 0.4, g2 = 0 , g3 = 0.20 , |g4| = 0.18, (g4)=0.20
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
Oscillons
normal
Knobloch abnormal
GPE
Boundary Influence
simple
low
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
g1 x time-step
1
0,98
0,96
0,94
Seqüência1
0,92
0,9
0,88
1
2
3
4
5
6
7
8
Modelling validation:
B=f(t,x,y,z;d)