Hans J. Herrmann Theories as long as Extreme Events ETH Risk Center ETH Risk Center The three types of flooding

Hans J. Herrmann Theories as long as Extreme Events ETH Risk Center ETH Risk Center The three types of flooding www.phwiki.com

Hans J. Herrmann Theories as long as Extreme Events ETH Risk Center ETH Risk Center The three types of flooding

McMahon, Pat, Host has reference to this Academic Journal, PHwiki organized this Journal Hans J. Herrmann Computational Physics, IfB, ETH Zürich, Switzerl in addition to Theories as long as Extreme Events New Views on Extreme Events Workshop of the Risk Center at SwissRe Adliswil, October 24-25, 2012 ETH Risk Center ETH Risk Center Systemic Risks (Schweitzer) Entrepre-neurial Risks (Sornette) Innovation Policy (Gersbach) Integrative Risk Mgmt. (Bommier) Sociology (Helbing) Conflict Research (Cederman) Math. Finance (Embrechts) Traffic Systems (Axhausen) Comp. Physics (Herrmann) Forest Engineering (Heinimann) Decision Making (Murphy) ETH Risk Center

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24th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011 The three types of flooding braided rivers flooding l in addition to scapes breaking dam 24th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011 The braided river The river carries sediments which deposit on the bottom of the bed until they reach the level of the water in addition to create a natural dam clogging the branch. So this branch dies in addition to a new branch is created somewhere else. Basic principle is a conservation law (here the mass of water) in addition to the as long as mation of local bottlenecks. Other examples: traffic, fatigue, electrical networks. + r in addition to omness Traffic fundamental diagram density flux

Classical Probability Theory Poisson distribution Gaussian distribution Black-Scholes Model Flooding l in addition to scapes When the water level of a lake rises in a r in addition to om l in addition to scape it spills over into the neighboring basin in addition to the sizes of these invasions follow a power law distribution. Basic principle is the existence of a local threshold at which discharging occurs. Other examples are earthquakes, brain activity. + r in addition to omness Earthquakes

Frequency Distribution of Earthquakes Gutenberg-Richter law Conclusion Paul Pierre Levy Earthquake Model Spring-Block Model

Per Bak Self-Organized Criticality (SOC) S in addition to pile Model Applet http://www.cmth.bnl.gov/~maslov/S in addition to pile.htm Size distribution of avalanches

Avalanches on the Surface of a S in addition to pile The lazy burocrats Self-Organized Criticality (SOC) The Stockmarket

SOC Model as long as the Stockmarket Comparison with NASDAQ Dupoyet et al 2011 Model as long as the distribution of price fluctuations Stauffer + Sornette, 1999 Examples as long as SOC Earthquakes Stockmarket Evolution Cerebral activity Solar flares Floodings L in addition to slides

Breaking a dam Each time a dam is in danger to break it is repaired in addition to made stronger. When finally the dam does one day break all the l in addition to is flooded at once. Basic principle is that the catastrophe is avoided by local repairs until it can not be withhold anymore. Other examples are volcanos + r in addition to omness Volcano eruption Branch pipes

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The Black Swan Nassim Nicholas Taleb The Black Swan Dragon King Didier Sornette Product Rule (PR) D. Achlioptas, R. M. D’Souza, in addition to J. Spencer, Science 323, 1453 (2009) Consider a fully connected graph Select r in addition to omly two bonds in addition to occupy the one which creates the smaller cluster classical percolation product rule Dimitris Achlioptas Explosive Percolation

Largest Cluster Model Select r in addition to omly a bond if not related with the largest cluster occupy it else, occupy it with probability Nuno Araújo in addition to HJH, Phys. Rev. Lett. 105, 035701 (2010) Nuno Araújo Largest Cluster Model order parameter: P = fraction of sites in largest cluster Sudden jump with our previous warning Its consequences touch the entire system. It is the worst case scenario. Phase transition of 1st order

39 communication servers (stars) + 310 power stations (circles) R in addition to om failure of 14 communication servers Proposal to improve robustness The blackout in Italy in addition to Switzerl in addition to , 2003 Original networks 4 autonomous nodes Outlook There exist unmeasurable risks. Mending is dangerous, because the risk becomes more brittle. Usually one can substantially reduce the risk in a network through rather minor changes. Autonomous nodes make coupled networks more robust.

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