Extreme events in nature and society PDF
Preview Extreme events in nature and society
the frontiers collection the frontiers collection SeriesEditors: D.Dragoman M.Dragoman A.C.Elitzur M.P.Silverman J.Tuszynski H.D.Zeh Thebooksinthiscollectionaredevotedtochallengingandopenproblemsattheforefront of modern physics and related disciplines, including philosophical debates. In contrast totypicalresearchmonographs,however,theystrivetopresenttheirtopicsinamanner accessiblealsotoscientificallyliteratenon-specialistswishingtogaininsightintothedeeper implicationsandfascinatingquestionsinvolved.Takenasawhole,theseriesreflectsthe needforafundamentalandinterdisciplinaryapproachtomodernscience.Itisintendedto encouragescientistsinallareastoponderoverimportantandperhapscontroversialissues beyondtheir own speciality. Extending from quantumphysics and relativity to entropy, time and consciousness – the Frontiers Collection will inspire readers to push back the frontiersoftheirownknowledge. InformationandItsRoleinNature ByJ.G.Roederer RelativityandtheNatureofSpacetime ByV.Petkov QuoVadisQuantumMechanics? EditedbyA.C.Elitzur,S.Dolev,N.Kolenda Life–AsaMatterofFat TheEmergingScienceofLipidomics ByO.G.Mouritsen Quantum–ClassicalAnalogies ByD.DragomanandM.Dragoman KnowledgeandtheWorld ChallengesBeyondtheScienceWars EditedbyM.Carrier,J.Roggenhofer,G.Küppers,P.Blanchard Quantum–ClassicalCorrespondence ByA.O.Bolivar Mind,MatterandQuantumMechanics ByH.Stapp QuantumMechanicsandGravity ByM.Sachs ExtremeEventsinNatureandSociety EditedbyS.Albeverio,V.Jentsch,H.Kantz S. Albeverio V. Jentsch H. Kantz (Eds.) EXTREME EVENTS IN NATURE AND SOCIETY With115Figures,7inColor 123 Prof.Dr.SergioAlbeverio Dr.VolkerJentsch Prof.Dr.HolgerKantz UniversitätBonn UniversitätBonn Max-Planck-Institut InterdisziplinäresZentrum InterdisziplinäresZentrum fürPhysikkomplexerSysteme fürKomplexeSysteme fürKomplexeSysteme NöthnitzerStraße38 undInstitut undInstitut 01187Dresden,Germany fürAngewandteMathematik fürAngewandteMathematik e-mail:[email protected] Wegelerstraße6 Wegelerstraße6 53115Bonn,Germany 53115Bonn,Germany e-mail:[email protected] e-mail:[email protected] SeriesEditors: Prof.DanielaDragoman UniversityofBucharest,PhysicsFaculty,SolidStateChair,POBoxMG-11, 76900Bucharest,Romania email:[email protected] Prof.MirceaDragoman NationalResearchandDevelopmentInstituteinMicrotechnology,POBox38-160, 023573Bucharest,Romania email:[email protected] Prof.AvshalomC.Elitzur Bar-IlanUniversity,UnitofInterdisciplinaryStudies, 52900Ramat-Gan,Israel email:[email protected] Prof.MarkP.Silverman DepartmentofPhysics,TrinityCollege, Hartford,CT06106,USA email:[email protected] Prof.JackTuszynski UniversityofAlberta,DepartmentofPhysics,Edmonton,AB, T6G2J1,Canada email:[email protected] Prof.H.DieterZeh UniversityofHeidelberg,InstituteofTheoreticalPhysics,Philosophenweg19, 69120Heidelberg,Germany email:[email protected] Cover figure: Detail from the image “Continuum Mechanics Models of DNA Molecules” by P. Furrer, J.H.Maddocks,R.S.Manning,R.C.PaffenrothandO.Gonzalesz LibraryofCongressControlNumber:2005937085 ISSN 1612-3018 ISBN-10 3-540-28610-1 SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-28610-3 SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned, specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproduction onmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofis permittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion, andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliabletoprosecutionunderthe GermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com ©CenterforFrontierSciences2006 PrintedinGermany Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. TypesettingbyStephenLyleusingaSpringerTEXmacropackage FinalprocessingbyLE-TEXJelonek,Schmidt&VöcklerGbR,Leipzig CoverdesignbyKünkelLopka,WerbeagenturGmbH,Heidelberg Printedonacid-freepaper SPIN:11308621 57/3141/YL-543210 Preface Somebodyonceremarkedonhowunjustitisthatchaoshasalwayshadsuch abadpress.Wheneverthereisatrafficjaminthemorning,whenthechildren don’t keep their things in order, when politics is turning crazy, it is always the fault of chaos. And yet, if there was no chaos, things would be pretty boring. Nothing unexpected would ever happen, and we could predict that the same dull things wouldhappen today as they did yesterday.That’s if we could predict anything at all – without chaos it would be quite likely that our thoughts would be trapped in some limited cycle and our brains would be quite useless! Thesamealsoappliesto extremes.Usually,whenonethinks ofextremes, negativeconnotationscometomind.Extremelyhotweatherisasunpleasant as extremely cold weather, and if its rains like crazy it is just as bad as when it is extremely dry. Extreme stock market fluctuations often result in large financial losses; earthquakes and floods can kill thousands of people, and global terrorism is strongly linked to political extremism. But now try to imagine a world without extremes. Putting grand events like the Big Bang or the extinction of the dinosaurs – without which we hu- manswouldnotexist–tooneside,consideraworldwithconstantlukewarm weather, where no-one ever fell in love, where there was never any deviation from the average. One can argue that even catastrophes have their positive sides,sincetheyforceustolookbeyondourcomfortable,welltroddenpaths. Although instinctively we would like to minimize their effects, that fact that we have to deal with them often leads to progress. Without extremes, there wouldbenoshake-upsleadingtonovelsituationsandopportunities.Andthe Olympic Games would not be much fun either! The present collection of articles, all written by well known experts in theirfields,demonstratesthesetwoaspectsofextremesperfectly.Ontheone hand, we have to cope with their unpleasant sides, by predicting them as much as possible and by minimizing their effects. Most of the articles are therefore written from the point of view of the engineer or applied scientist who has to deal with this. But despite of the diversity of extreme phenom- ena – ranging from economic and geologic disasters via the breaking of steel to extreme neural bursts in epileptic seizures – the authors manage to show thatthereisacommonunderlyingconceptualframethatlinksthem.Indeed, as well as being linked by these concepts, various mathematical tools can be VI Preface applied to most problems involving extremes. Therefore, this book demon- strates (without overstressing the point – just by providing the facts) that there is an emerging unifying and truly interdisciplinary science of extreme events. Finally, the authors would not be good scientists if the fascinating and exciting aspects of the science of extremes did not permeate through every page.Thisanotherpositiveaspectofextremes:thattheyhaveledtothisfas- cinatingbook,whichisa realpleasureto readandwhichis sureto stimulate much further research. Ju¨lich, June 2005 Peter Grassberger Acknowledgement We, the editors, would like thank the authors for providing the articles. We also thank Springer Verlag for his continuous help in editing this book. We are thankful to Hurshid Kadirov who produced its TEX version. Bonn, June 2005 Sergio Albeverio Volker Jentsch Holger Kantz Contents 1 Extreme Events: Magic, Mysteries, and Challenges Volker Jentsch, Holger Kantz, Sergio Albeverio ..................... 1 1.1 Why Study Xevents? ....................................... 1 1.2 What are Xevents? A First Approach ......................... 2 1.3 What are Xevents? A Second Approach ....................... 3 1.3.1 Statistical Characterisationof Xevents.................. 4 1.3.2 Dynamic Characterisation of Xevents................... 4 1.3.3 Shaping Evolution ................................... 5 1.3.4 Commonalities, Analogies, Universality ................. 5 1.3.5 Prediction, Anticipation and Management............... 6 1.3.6 Trends.............................................. 7 1.3.7 Building Models ..................................... 7 1.3.8 Observations ........................................ 8 1.3.9 Risk................................................ 8 1.4 How the Book is Organised.................................. 9 1.4.1 Background ......................................... 9 1.4.2 Rationale ........................................... 9 1.4.3 The Articles......................................... 10 1.5 Outlook: Research Programme ............................... 17 References ..................................................... 18 Part I General Considerations 2 Anticipating Extreme Events Mihai Nadin ................................................... 21 2.1 The Representation of Extreme Events........................ 21 2.2 From Signs to Anticipation .................................. 23 2.3 Descartes Rehabilitated ..................................... 25 2.4 Time, Clocks, Rhythms ..................................... 26 2.5 The Hybrid Solution........................................ 28 2.6 Can a Computer Simulate Anticipation? ...................... 35 2.7 A New Equilibrium......................................... 36 2.8 A Holistic View ............................................ 40 References ..................................................... 43 VIII Contents 3 Mathematical Methods and Concepts for the Analysis of Extreme Events Sergio Albeverio, Vladimir Piterbarg............................... 47 3.1 Introduction ............................................... 47 3.2 Statistical Extreme Value Theory............................. 48 3.2.1 Origins: Classical Univariate Case...................... 48 3.2.2 Dependent Data ..................................... 50 3.3 Extremes in Continuous Time: Stochastic Processes, Random Fields.......................... 52 3.3.1 Probabilities of Large Deviations: Exact Behaviour....... 53 3.3.2 Maxima and Excursions of Gaussian and Related Processes and Fields ...................... 56 3.3.3 Relationship Between Continuous and Discrete Time: Prediction of Extremes ............................... 58 3.3.4 Other Problems...................................... 60 3.4 Extremes and Statistical Mechanics........................... 61 3.5 Extremes and Dynamical Systems ............................ 62 3.6 Mapping Singularities and Catastrophe Theory: How Can They Be Related to Xevents? ....................... 63 References ..................................................... 65 4 Dynamical Interpretation of Extreme Events: Predictability and Predictions Holger Kantz, Eduardo G. Altmann, Sarah Hallerberg, Detlef Holstein, Anja Riegert ................................................... 69 4.1 Introduction ............................................... 69 4.2 Prediction versus Predictability .............................. 72 4.2.1 Predictability........................................ 74 4.2.2 Prediction Schemes for Deterministic and Stochastic Time Series............................ 80 4.2.3 Predictions Based on Markov Chain Models ............. 82 4.3 An Example: Turbulent Wind Gusts .......................... 84 4.4 Conclusions................................................ 90 References ..................................................... 93 5 Endogenous versus Exogenous Origins of Crises Didier Sornette ................................................. 95 5.1 Introduction ............................................... 95 5.2 Exogenous and Endogenous Shocks in Social Networks .......... 97 5.2.1 A Simple Epidemic Cascade Model of Social Interactions.. 98 5.2.2 Internet Download Shocks............................. 100 5.2.3 Book Sale Shocks .................................... 102 5.2.4 Social Shocks........................................ 107 Contents IX 5.3 Exogenous and Endogenous Shocks in Financial Markets ........ 109 5.3.1 Volatility Shocks..................................... 109 5.3.2 Financial Crashes .................................... 112 5.4 Concluding Remarks........................................ 114 References ..................................................... 116 Part II Scenarios 6 Epilepsy: Extreme Events in the Human Brain Klaus Lehnertz ................................................. 123 6.1 Introduction ............................................... 123 6.2 Basic Mechanisms .......................................... 124 6.3 EEG and Epilepsy.......................................... 126 6.4 Nonlinear EEG Analysis .................................... 128 6.4.1 State Space Reconstruction ........................... 129 6.4.2 Measures Based on the Correlation Sum ................ 130 6.4.3 Lyapunov Exponents ................................. 131 6.4.4 Synchronization and Interdependencies ................. 132 6.4.5 Testing for Nonlinearity............................... 134 6.5 Can Epileptic Seizures Be Anticipated? ....................... 135 6.6 Can Epileptic Seizures Be Controlled? ........................ 138 6.7 Conclusions................................................ 140 References ..................................................... 141 7 Extreme Events in the Geological Past Ju¨rgen Herget .................................................. 145 7.1 Introduction ............................................... 145 7.2 Extreme Events in the Geological Past ........................ 146 7.2.1 Events Driven by Plate Tectonics ...................... 146 7.2.2 Changes in the Earth’s Magnetic Field.................. 149 7.2.3 Periods and Cycles of Ice Ages......................... 151 7.2.4 Volcanism........................................... 153 7.2.5 Earthquakes......................................... 154 7.2.6 Meteoritic Impacts ................................... 155 7.2.7 Floods.............................................. 157 7.3 Predictions and Forecasts on the Geological Timescale .......... 159 7.4 Research Perspectives....................................... 161 References ..................................................... 164 8 Wind and Precipitation Extremes in the Earth’s Atmosphere Andreas Hense, Petra Friederichs ................................. 169 8.1 Introduction ............................................... 169 8.2 Atmospheric Scales ......................................... 170
The list of books you might like
