Sandpile Models and Solar Flares: Eigenfunction Decomposition for Data Assimilation

2017 ◽  
Vol 13 (S335) ◽  
pp. 250-253
Author(s):  
Antoine Strugarek ◽  
Allan S. Brun ◽  
Paul Charbonneau ◽  
Nicole Vilmer
Keyword(s):  
Data Assimilation ◽  
Solar Flares ◽  
Similar Distribution ◽  
Significant Challenge ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Model Independent ◽  
Self Similar ◽  
Sandpile Models ◽  
Data Assimilation Technique

AbstractThe largest solar flares, of class X and above, are often associated with strong energetic particle acceleration. Based on the self-similar distribution of solar flares, self-organized criticality models such as sandpiles can be used to successfully reproduce their statistics. However, predicting strong (and rare) solar flares turns out to be a significant challenge. We build here on an original idea based on the combination of minimalistic flare models (sandpiles) and modern data assimilation techniques (4DVar) to predict large solar flares. We discuss how to represent a sandpile model over a reduced set of eigenfunctions to improve the efficiency of the data assimilation technique. This improvement is model-independent and continues to pave the way towards efficient near real-time solutions for predicting solar flares.

scholarly journals Predicting large solar flares with data assimilation

2015 ◽  
Vol 11 (A29B) ◽  
pp. 734-734
Author(s):  
Antoine Strugarek ◽  
Paul Charbonneau
Keyword(s):  
Data Assimilation ◽  
Solar Flares ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Sandpile Models

AbstractWe propose to use a deterministically-driven class of self-organized criticality sandpile models to carry out predictions of the largest, most dangerous, and hardest to predict solar flares.

Self-Similar Criticality

Fractals ◽  
2003 ◽  
Vol 11 (03) ◽  
pp. 221-231 ◽  
Author(s):  
Sarah F. Tebbens ◽  
Stephen M. Burroughs
Keyword(s):  
Power Law ◽  
Similar Distribution ◽  
Scaling Exponent ◽  
Cumulative Frequency ◽  
Size Distributions ◽  
Scaling Exponents ◽  
Natural Systems ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Self Similar

Cumulative frequency-size distributions associated with many natural phenomena follow a power law. Self-organized criticality (SOC) models have been used to model characteristics associated with these natural systems. As originally proposed, SOC models generate event frequency-size distributions that follow a power law with a single scaling exponent. Natural systems often exhibit power law frequency-size distributions with a range of scaling exponents. We modify the forest fire SOC model to produce a range of scaling exponents. In our model, uniform energy (material) input produces events initiated on a self-similar distribution of critical grid cells. An event occurs when material is added to a critical cell, causing that material and all material in occupied non-diagonal adjacent cells to leave the grid. The scaling exponent of the resulting cumulative frequency-size distribution depends on the fractal dimension of the critical cells. Since events occur on a self-similar distribution of critical cells, we call this model Self-Similar Criticality (SSC). The SSC model may provide a link between fractal geometry in nature and observed power law frequency-size distributions for many natural systems.

scholarly journals Renormalization scheme for self-organized criticality in sandpile models

1994 ◽  
Vol 72 (11) ◽  
pp. 1690-1693 ◽  
Author(s):  
L. Pietronero ◽  
A. Vespignani ◽  
S. Zapperi
Keyword(s):  
Renormalization Scheme ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Sandpile Models

scholarly journals Mulifractal phase transitions: the origin of self-organized criticality in earthquakes

1994 ◽  
Vol 1 (2/3) ◽  
pp. 191-197 ◽  
Author(s):  
C. Hooge ◽  
S. Lovejoy ◽  
D. Schertzer ◽  
S. Pecknold ◽  
J.-F. Malouin ◽  
...  
Keyword(s):  
Phase Transition ◽  
Spatial Distribution ◽  
Phase Transitions ◽  
Horizontal Plane ◽  
Spatial Location ◽  
Seismic Process ◽  
First Order ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Model Independent

Abstract. Fractal and occasionally multifractal behaviour has been invoked to characterize (independently of their magnitude) the spatial distribution of seismic epicenters, whereas more recently, the frequency distribution of magnitudes (irrespective of their spatial location) has been considered as a manifestation of Self-Organized Criticality (SOC). In this paper we relate these two aspects on rather general grounds, (i.e. in a model independent way), and further show that this involves a non-classical SOC. We consider the multifractal characteristics of the projection of the space-time seismic process onto the horizontal plane whose values are defined by the measured ground displacements, we show that it satisfies the requirements for a first order multifractal phase transition and by implication for a non-classical SOC. We emphasize the important consequences of the stochastic alternative to the classical (deterministic) SOC.

STATISTICAL PROPERTIES OF SOLAR FLARES AND COMPARISON TO OTHER IMPULSIVE ENERGY RELEASE EVENTS

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5609-5618 ◽  
Author(s):  
FABIO LEPRETI ◽  
VLADIMIR G. KOSSOBOKOV ◽  
VINCENZO CARBONE
Keyword(s):  
Solar Flare ◽  
Energy Release ◽  
Solar Flares ◽  
Statistical Properties ◽  
Universal Curve ◽  
Mhd Turbulence ◽  
Natural Systems ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Impulsive Processes

Impulsive energy release events are observed in many natural systems. Solar flares are certainly among the most remarkable examples of such processes. In the last years the study of solar flare statistical properties has received considerable attention in the context of solar flare models based on different approaches, such as Self Organized Criticality (SOC) or magnetohydrodynamic (MHD) turbulence. In this talk the main statistical properties of solar flares will be presented and compared to those of other well known impulsive processes, such as earthquakes and soft γ-ray flashes occurring on neutron stars. It is shown that the these phenomena are characterized by different statistics that cannot be rescaled onto a single, universal curve and that this holds even for the same phenomenon, when observed in different periods or at different locations. Our results indicate apparent complexity of impulsive energy release processes, which neither follow a common behavior nor could be attributed to a universal physical mechanism.

Self‐organized Criticality from Separator Reconnection in Solar Flares

2000 ◽  
Vol 542 (2) ◽  
pp. 1088-1099 ◽  
Author(s):  
D. W. Longcope ◽  
E. J. Noonan
Keyword(s):  
Solar Flares ◽  
Self Organized ◽  
Self Organized Criticality

Reail Space Renormalization Group for Self Organized Criticality in Sandpile Models

1994 ◽  
Vol 367 ◽  
Author(s):  
S. Zapperi ◽  
A. Vespignanit ◽  
L. Pietronero
Keyword(s):  
Renormalization Group ◽  
Stationary State ◽  
Group Approach ◽  
Self Organized ◽  
Change Of Scale ◽  
Renormalization Group Approach ◽  
Self Organized Criticality ◽  
Sandpile Models ◽  
Good Agreement

AbstractWe have introduced a new renormalization group approach that allows us to describe the critical stationary state of sandpile models (Phys. Rev. Lett. 72, 1690 (1994)). We define a characterization of the phase space in order to study the evolution of the dynamics under a change of scale. We obtain a non trivial actractive fixed point for the parameters of the model that clarifys the self organized critical nature of these models. We are able to compute the values of the critical exponents and the results are in good agreement with computer simulations. The method can be naturally extended to several other problems with non equilibrium stationary state.

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