Self-Organized CriticalitySelf-Organized Criticalityand Turbulence and Turbulence

1 1stst ISSI Team Meeting ISSI Team MeetingIntroductionIntroduction

Team Coordinator: Markus J. AschwandenTeam Coordinator: Markus J. Aschwanden

2012 October 15-19 2012 October 15-19 International Space Science Institute (ISSI)International Space Science Institute (ISSI) Hallerstrasse 6, Bern, SwitzerlandHallerstrasse 6, Bern, Switzerland

http://www.issibern.ch/teams/s-o-turbulence/index.htmlhttp://www.issibern.ch/teams/s-o-turbulence/index.html

Introduction:Introduction:

- SOC ISSI Team MembersSOC ISSI Team Members- Program of MeetingProgram of Meeting- Interdisciplinary AspectsInterdisciplinary Aspects- Scope and Goal of MeetingScope and Goal of Meeting

Interdisciplinary aspectInterdisciplinary aspect

Solar PhysicsSolar Physics

AstrophysicsAstrophysics

GeophysicsGeophysics

BiophysicsBiophysicsMagnetosphericMagnetospheric PhysicsPhysics

SocialSocialSciencesSciences

Self-OrganizedSelf-OrganizedCriticality SystemsCriticality Systems

Interdisciplinary aspects:Interdisciplinary aspects:

-SOC occurs in many different physical systems !SOC occurs in many different physical systems !

-What properties of SOC are common in all physical systems?What properties of SOC are common in all physical systems?

-Are there statistical aspects that are universal in all systems?Are there statistical aspects that are universal in all systems?

-Are there universal parameters (fractal dimensions, powerlaw slopes) ?Are there universal parameters (fractal dimensions, powerlaw slopes) ?

-Where does the physics play a role (scaling laws of physical parameters)?Where does the physics play a role (scaling laws of physical parameters)?

-Can we come up with a SOC theory that includes both universalCan we come up with a SOC theory that includes both universal statistical aspects and the physical scaling laws of a particular system?statistical aspects and the physical scaling laws of a particular system?

What is Self-Organized Criticality ?What is Self-Organized Criticality ?

Original idea of SOC;Original idea of SOC;Bak, Tang, & Wiesenfeld (1987)Bak, Tang, & Wiesenfeld (1987)

Norvegian rice pileNorvegian rice pileExperimentExperiment

Powerlaw distributionPowerlaw distribution of rice avalanche sizesof rice avalanche sizes with slope a=2.04with slope a=2.04 (Frette et al. 1996)(Frette et al. 1996)

SOC in Human ActivitiesSOC in Human Activities

Zanette 2008Zanette 2008-Urban growth, city sizesUrban growth, city sizes-Word frequency in languageWord frequency in language-Cotton pricesCotton prices-Stock marketStock market-Traffic jamsTraffic jams-War casualtiesWar casualties-Social networks, internet trafficSocial networks, internet traffic

SOC in BiophysicsSOC in Biophysics

Sepkovski 1993Sepkovski 1993-Evolution and extinctionsEvolution and extinctions-Neuron firing in brainNeuron firing in brain-Neural reverberations of spiking nerve cellsNeural reverberations of spiking nerve cells-Learning and memoryLearning and memory-Breathing in lung, heart rateBreathing in lung, heart rate-Epileptic seizuresEpileptic seizures-Spreads of diseases, measles epidemicsSpreads of diseases, measles epidemics-Flying formation of birdsFlying formation of birds

SOC in GeophysicsSOC in Geophysics

Turcotte 1999Turcotte 1999-EarthquakesEarthquakes-LandslidesLandslides-Turbidite depositionsTurbidite depositions-Volcanic eruptionsVolcanic eruptions-Snow avalanchesSnow avalanches-Rainfall, river fluctuationsRainfall, river fluctuations-Cloud formation, climate fluctuationsCloud formation, climate fluctuations-Forest firesForest fires

SOC in Magnetospheric PhysicsSOC in Magnetospheric Physics

Lui et al. 2000Lui et al. 2000

-Magnetotail current disruptionsMagnetotail current disruptions-Substorm current disruptionsSubstorm current disruptions-Bursty bulk flow eventsBursty bulk flow events-Magnetotail magnetic field fluctuationsMagnetotail magnetic field fluctuations-Auroral UV and optical imagesAuroral UV and optical images-Auroral electron jet index (AE)Auroral electron jet index (AE)

SOC in Planetary PhysicsSOC in Planetary Physics

-Saturn’s ringsSaturn’s rings-Asteroid beltAsteroid belt-Lunar cratersLunar craters

Cross (1996) – Mare TranquillitatisCross (1996) – Mare Tranquillitatis (Ranger 8)(Ranger 8)

SOC in Solar PhysicsSOC in Solar Physics

-Solar flare, microflares, nanoflaresSolar flare, microflares, nanoflares-Flare gamma rays, hard X-rays, soft X-raysFlare gamma rays, hard X-rays, soft X-rays-Flare ultraviolet, EUV, H-alphaFlare ultraviolet, EUV, H-alpha-Solar energetic particle events (SEP)Solar energetic particle events (SEP)-Coronal mass ejectionsCoronal mass ejections-Solar wind fluctuationsSolar wind fluctuations

Dennis (1985), Crosby et al. (1993)Dennis (1985), Crosby et al. (1993)

SOC in Stellar PhysicsSOC in Stellar Physics

-Stellar flares (dME stars)Stellar flares (dME stars)-Cataclysmic Variable (CV) starsCataclysmic Variable (CV) stars-Accretion disksAccretion disks-Black holesBlack holes-Pulsar glitchesPulsar glitches-Soft gamma repeaters (SGR)Soft gamma repeaters (SGR)

Audard et al. (2000)Audard et al. (2000)

SOC in Galactic Physics and CosmologySOC in Galactic Physics and Cosmology

-Active galactic nuclei (AGNs)Active galactic nuclei (AGNs)-BlazarsBlazars-Interstellar medium formationInterstellar medium formation-Galactic spiral structure, elliptical galaxy formationGalactic spiral structure, elliptical galaxy formation-Interstellar magnetic field, starburstsInterstellar magnetic field, starbursts-Cosmology, big-bang, (multiple ?) inflationsCosmology, big-bang, (multiple ?) inflations

2D Cellular Automaton – Avalanche Event #16282D Cellular Automaton – Avalanche Event #1628

Dimension: 2DDimension: 2DLattice grid: 64 x 64Lattice grid: 64 x 64Initiation: tInitiation: tSOCSOC=4 x 10=4 x 1077 time steps time steps

(to develop SOC state)(to develop SOC state)

Largest avalanche #1628 after tLargest avalanche #1628 after tSOCSOC

Starting point: (x=41, y=4)Starting point: (x=41, y=4)Duration: T=712 time stepsDuration: T=712 time stepsPeak energy dissipation rate P=2300Peak energy dissipation rate P=2300Total energy: E=5 x 10Total energy: E=5 x 1055

Note: Note: -Diffusive boundary increase x(t)Diffusive boundary increase x(t)-Fractal energy dissipation areas a(t)Fractal energy dissipation areas a(t)

Aschwanden (2012)Aschwanden (2012)

Goals identified in our ISSI proposal :Goals identified in our ISSI proposal :

(1)(1)Data analysis of statistical datasets of SOC phenomena,Data analysis of statistical datasets of SOC phenomena, using new and comprehensive data sets: using new and comprehensive data sets:

Can we expect new observational results at 2Can we expect new observational results at 2ndnd ISSI Team meeting in 2013? ISSI Team meeting in 2013?

Goals and problems identified in our ISSI proposal :Goals and problems identified in our ISSI proposal :

(1)(1)Data analysis of statistical datasets of SOC phenomena,Data analysis of statistical datasets of SOC phenomena, using new and comprehensive data setsusing new and comprehensive data sets

(2) Improve diagnostics of powerlaw-like distributions:(2) Improve diagnostics of powerlaw-like distributions: How to identify scaling and universality in experimentalHow to identify scaling and universality in experimental and computational data? (Finite-size effects, variable drivers?)and computational data? (Finite-size effects, variable drivers?)

(3) How to identify and characterize between SOC and(3) How to identify and characterize between SOC and non-SOC mechanisms? (turbulence? network theory?)non-SOC mechanisms? (turbulence? network theory?)

(4) What part of SOC phenomena is captured by lattice models(4) What part of SOC phenomena is captured by lattice models and is there a route to basic theories and first-principle equations?and is there a route to basic theories and first-principle equations?

Metrics of Observables, Statistical DistributionsMetrics of Observables, Statistical Distributions and Physical Processes that need to be defined and Physical Processes that need to be defined in order to discriminate SOC from non-SOC processesin order to discriminate SOC from non-SOC processes

Metrics of Physical ProcessesMetrics of Physical Processesvs. Observational Propertiesvs. Observational Properties

Can we refine the metrics ?Can we refine the metrics ?

The fascination of sandpiles ………………The fascination of sandpiles ………………