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MÉMOIRE D'HABILITATION À DIRIGER DES RECHERCHES Université Claude Bernard - Lyon 1 Spécialité : Physique présenté par: OSVANNY RAMOS Soutenue publiquement le 27 juillet 2015 Devant le jury composé de : M. Ernesto Altshuler (Examinateur) M. Eric Clément (Examinateur) M. Jean-Christophe Géminard (Examinateur) M. Ferenc Kun (Rapporteur) M. Knut Jørgen Måløy (Examinateur) Mme. Anne Tanguy (Rapporteur) M. Renaud Toussaint (Rapporteur) AVALANCHES & other major RISKS

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Page 1: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

MÉMOIRE D'HABILITATION À DIRIGER DES RECHERCHES

Université Claude Bernard - Lyon 1 Spécialité : Physique

présenté par:

OSVANNY RAMOS

Soutenue publiquement le 27 juillet 2015

Devant le jury composé de :

M. Ernesto Altshuler (Examinateur) M. Eric Clément (Examinateur) M. Jean-Christophe Géminard (Examinateur) M. Ferenc Kun (Rapporteur) M. Knut Jørgen Måløy (Examinateur) Mme. Anne Tanguy (Rapporteur) M. Renaud Toussaint (Rapporteur)

AVALANCHES & other major RISKS

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Contents

Introduction 7

Résumé en français 9Projets actuels . . . . . . . . . . . . . . . . . . . . . . . . 12

Acknowledgments 15

Chapter 1: A little bit of history 19Current projects . . . . . . . . . . . . . . . . . . . . . . . 26

Chapter 2: Scale-Invariant Avalanches 312.1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2: Classification of scale invariant avalanches . . . . . . . 32

2.2.1: Fractals and scale invariant avalanches: the expo-nent value . . . . . . . . . . . . . . . . . . . . . . 32

2.2.2: The origin of logarithmic scales . . . . . . . . . . 33

2.2.3: Classifying scale invariant avalanches . . . . . . . 35

2.2.4: Integrated probability . . . . . . . . . . . . . . . . 36

2.2.5: Mean value of avalanche size . . . . . . . . . . . . 36

2.2.6: Energy balance in slowly driven systems . . . . . 37

2.2.7: The distribution of earthquakes . . . . . . . . . . 38

2.3: Avalanches in critical phenomena . . . . . . . . . . . . 40

2.3.1: Avalanches & fluctuations in the Ising model . . 41

2.3.2: Experiments: from the micro to the macro-world 45

2.4: Criticality in scale invariant avalanches . . . . . . . . . 47

2.4.1: Models without spatial structure . . . . . . . . . 47

2.4.2: Avalanches in two and three dimensions . . . . . 47

2.4.3: Losing criticality . . . . . . . . . . . . . . . . . . . 48

2.5: Towards prediction and Control . . . . . . . . . . . . . 52

2.5.1: Predicting scale invariant avalanches . . . . . . . 52

2.5.2: Origin & Control . . . . . . . . . . . . . . . . . . . 57

2.6: Future projetcs . . . . . . . . . . . . . . . . . . . . . . . . 58

Chapter 3: Other major Risks 593.1: Fracturing slowly . . . . . . . . . . . . . . . . . . . . . . 59

3.1.1: Where are the safety margins in subcritical fracture? 60

3.1.2: When very long processes require very fast mea-surements . . . . . . . . . . . . . . . . . . . . . . 60

3.1.3: Future projects: fracturing at the micro-scales . . 61

3.2: Pedestrians in Panic . . . . . . . . . . . . . . . . . . . . . 62

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3.2.1: Future projects: jamming under panic . . . . . . 64

Bibliography 65

Appendix: Curriculum Vitae 75List of publications . . . . . . . . . . . . . . . . . . . . . 78

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To Ernesto, Menka and Melanie.

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Introduction

Defending the Habilitation1 is a nice moment in a scientific career. 1 "L’Habilitation à Diriger desRecherches sanctionne la reconnais-sance du haut niveau scientifique ducandidat, du caractère original desa démarche dans un domaine de lascience, de son aptitude à maîtriserune stratégie de recherche dans undomaine scientifique ou technologiquesuffisamment large et de sa capacité àencadrer de jeunes chercheurs" (arrêtédu 23 novembre 1988).

From the comfort of a permanent position, and a few years of expe-rience, we can thank the people that were essential in our scientificformation, while currently focusing on the same process that theydid: developing science while forming young researchers (as in a newcycle of a spiral).

Contributing to the formation of young researchers is a challenging,but essential task: How to motivate them? How to cultivate their cu-riosity, creativity, ambition, endurance, independence and leadershiprequired for being a good scientist and supervisor? How involvingthem (and remain fair) when making tough decisions or dealing withcompromise solutions: sometimes as simpler as choosing the orderof the authors in a publication. Sometimes much more complex, asdeciding the authors in a publication, or deciding if developing asubject or a collaboration in a delicate situation, for example if thelevel of risks is too high (i.e., probably no results), or ethical issues inconflict with the personal values of someone of the team.

I have many more questions than answers; but the solutions mayalso be personal. For this reason I wrote the Chapter 1: A littlebit of history: to show the origin of the ideas that have driven myresearch projects, the causes (according to my vision) of my needof independence, and the interaction with other researchers in mycareer. Most scientific thesis normally follow the style of the articles,focusing only on results. However, we rarely talk about the processof origin and germination of ideas into projects, and into positiveresults. The interactions between people and the contribution ofdifferent researchers2 (which are also essential in the process) are also 2 High impact journals like Nature in-

clude the contribution of each author inthe article.

normally hidden inside a list of authors and acknowledgments. Ithink that the habilitation thesis is a great frame for discussing thoseissues and giving some hints to future researchers. An overview ofthe current projects is also discussed in this chapter.

The Chapter 2: Scale-Invariant Avalanches is the longest and mostimportant of this habilitation. I have been working on this subjectfor more than a decade, and it is the most relevant subject in mycareer. An introduction discusses a brief state of the art in the field ofscale-invariant avalanches, the impact of the Self-organized criticality(SOC) on the subject, and in particular the confusions provoked by theSOC in the field. I also cite the main questions that have motivatedmy research activities in this subject. Several issues related to the

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classification of scale-invariant avalanches (where earthquakes areoften used as an example) are also discussed. The critical propertiesof avalanches are also studied: first by the analysis of the avalanchesin the Ising model, and second by analyzing how a system loses thecritical properties when dissipation is added. The chapter finisheswith our contributions and projects related to the prediction andcontrol of scale invariant avalanches, before citing the future projectsin this area of research.

In Chapter 3: Other major Risks I discuss two other subjects ofresearch having in common the Physics of risks. The first one corre-sponds to the subcritical fracture, where, by modifying the disorderof a material, we observe that a subcritical crack propagates faster in amore disordered scenario. However, the standard methods analyzingthe materials’ resistance are not sensitive to differences in disorder.As architectural designs are constantly evolving towards thinner andlighter structures, they are often approaching the borders of safetymargins. One main result of our study shows that these marginsmay not be well defined. The presence of aftershocks in subcriticalfracture and the consequences linked to it are also discussed; as wellas future projects to develop in this subject of research. The secondsubject corresponds to the collective behavior of ants, where we havedeveloped experiments showing that, when in panic, ants developthe same herding behavior observed with humans (which can be fatalin a confined space). Some works showing the behavior of the antsin the wild are also discussed, as well as future projects related topedestrians under panic.

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Résumé en français

un début tropical : j’ai commencé ma formation comme chercheuren Physique à l’Université de la Havane sous la direction d’ErnestoAltshuler. Avec très peu de moyens, la solution d’Ernesto pourfaire une Physique expérimentale "de haut facteur d’impact" à Cubaa été de développer une Physique basée sur des expériences trèsoriginales, très simples et dans des multiples domaines. De cette façonet dans la période 1999− 2004, nous avons développé trois expériencesdifférentes. La première (PRL-2001)3 a permis d’étudier l’influence du 3 E. Altshuler, O. Ramos, C. Martínez,

L. E. Flores, and C. Noda. Avalanchesin One-Dimensional Piles with DifferentTypes of Bases. Phys. Rev. Lett., 86:5490–5493, 2001

désordre dans la formation d’une dynamique d’avalanches invariantesd’échelle dans un tas de grains bidimensionnel. Plus le désordre estimportant, plus la distribution des avalanches s’approche d’une loi depuissance. Ces résultats montrent le rôle clé du désordre dans l’auto-organisation d’un système vers une dynamique invariante d’échelle.La deuxième expérience (PRL-2003)4 s’est focalisée sur l’analyse d’un 4 E. Altshuler, O. Ramos, E. Martínez,

A. J. Batista-Leyva, A. Rivera, and K. E.Bassler. Sandpile Formation by Revolv-ing Rivers. Phys. Rev. Lett., 91:014501,2003

type de sable très particulier. Au lieu de produire des avalanchesintermittentes, le sable ajouté sur la cime forme une rivière qui tourneautour du tas. La troisième expérience analyse le comportement defourmis en situation de panique (Am. Nat.-2005)5. Avec deux sorties 5 E. Altshuler, O. Ramos, Y. Nunez, J. Fer-

nández, A. J. Batista-Leyva, and C. Noda.Symmetry Breaking in Escaping Ants.Am. Nat., 166(6):643–649, 2005

symétriques et dans des conditions normales les fourmis s’échappentd’une cellule en utilisant les deux sorties avec la même proportion.Cependant, si les fourmis sont perturbées, la tendance à former etsuivre une horde domine, ce qui produit une rupture de symétrie dansl’utilisation des sorties (un comportement analogue face à la paniquese produit chez les humains). La première expérience m’a donnéles idées que je voulais développer dans le futur : la prédiction desévènements catastrophiques dans des avalanches invariantes d’échelleet sa possible application aux séismes et aux autres phénomènesnaturels, que j’ai commencé à étudier pendant ma thèse.

la thèse : en arrivant à Oslo j’avais déjà de l’expérience commechercheur et deux articles publiés dans Physical Review Letters (PRL),fruits de mes anciens travaux à Cuba. Knut Jørgen m’a fait confianceet m’a laissé la responsabilité de développer mon propre projet dethèse, ayant comme sujet principal la prédiction des avalanches in-variantes d’échelle. Dans la première partie de mes travaux, il s’agitde modifier le modèle de séismes Olami-Feder-Christensen (OFC)afin de le rendre plus réaliste. Les résultats (PRL-2006)6 montrent 6 O. Ramos, E. Altshuler, and K. J. Måløy.

Quasiperiodic Events in an EarthquakeModel. Phys. Rev. Lett., 96:098501, 2006

une périodicité dans la série temporelle des séismes en coexistenceavec la loi de Gutenberg-Richter (loi de puissance dans la distributiondes tailles des évènements). En ajoutant du désordre, la périodicité

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disparaît graduellement tandis que la loi de Gutenberg-Richter estbeaucoup plus robuste. Ces résultats montrent l’importance du dé-sordre dans la génération d’une dynamique invariante d’échelle àpartir d’une situation périodique de type "stick-slip". La deuxièmepartie relève le défi expérimental de prédire des grands évènementsdans ce type de systèmes. La supposée (mais bien ancrée dans lacommunauté) criticalité de ces phénomènes doit rendre impossible laprédiction. Cependant, en étudiant la corrélation entre la structureinterne d’un tas de grains bidimensionnel et ces grandes avalanches,nous sommes parvenus à faire des prédictions sur l’occurrence im-minente de grandes (et très grandes) avalanches (PRL-2009)7. En7 O. Ramos, E. Altshuler, and K. J.

Måløy. Avalanche Prediction in a Self-Organized Pile of Beads. Phys. Rev. Lett.,102:078701, 2009

parallèle de mon projet principal, j’ai collaboré dans un autre projetsur la formation des motifs dynamiques dans l’écoulement de sable(PREr-2007)8 qui fait aussi partie de ma thèse.8 E. Martínez, C. Pérez-Penichet,

O. Sotolongo-Costa, O. Ramos, K. J.Måløy, S. Douady, and E. Altshuler.Uphill solitary waves in granular flows.Phys. Rev. E, 75:031303, 2007

post-docs : après ma thèse, j’ai fait trois années de postdoctoratavant d’obtenir le poste de Maître de Conférences. Les deux premièresannées avec un contrat ANR de Loïc Vanel au Laboratoire de Physiquede l’ENS de Lyon ; et la dernière avec un contrat européen de AnkeLidner et Costantino Creton au Laboratoire PMMH de l’ESPCI, àParis. Pendant la période à Lyon mon projet principal a été l’étude del’influence du désordre sur la dynamique de la fracture sous-critique.Différentes stratégies ont été explorées afin de modifier, d’une façoncontrôlée, la structure d’une feuille de papier à une échelle prochede celle du désordre (taille des fibres). Finalement, deux réseaux dif-férents, composés de trous de 120 microns de diamètre, ont été percéset la fissure s’est propagée plus rapidement dans le système plusdésordonné. Les résultats ont été publiés dans un acte de conférence.Des analyses plus poussées et des mesures complémentaires faitesrécemment ont révélé que l’effet d’accélération trouvé est spécifiqueà la fracture sous-critique (PRL-2013a)9. En parallèle, j’ai conçu et9 O. Ramos, P.-P. Cortet, S. Ciliberto, and

L. Vanel. Experimental Study of theEffect of Disorder on Subcritical CrackGrowth Dynamics. Phys. Rev. Lett., 110:165506, 2013

monté une expérience pour étudier la dynamique de formation desmotifs de fracturation dans une couche granulaire cohésive ; et col-laboré avec J-C Géminard dans une expérience similaire mais avecune géométrie différente. Les résultats montrent une modulationdans la surface de la couche qui augmente avec l’étirement jusqu’àla fracturation du système (PRL-2010)10. À Paris, j’ai analysé la dy-10 H. Alarcón, O. Ramos, L. Vanel, F. Vit-

toz, F. Melo, and J.-C. Géminard. Soft-ening Induced Instability of a StretchedCohesive Granular Layer. Phys. Rev. Lett.,105:208001, 2010

namique de décollement des adhésifs (PDMS avec différents taux deréticulation). Différents types de fracturation (adhésive ou cohésive)ont été trouvés en fonction des paramètres du système ; ainsi quedes lois d’échelles entre l’énergie de décollement et la vitesse de dé-collement, l’épaisseur de l’échantillon et le taux de réticulation (SoftMatter-2010, EPJE-2013)11.

11 J. Nase, C. Creton, O. Ramos, L. Son-nenberg, T. Yamaguchi, and A. Lindner.Measurement of the receding contact an-gle at the interface between a viscoelas-tic material and a rigid surface. SoftMatter, 6:2685–2691, 2010; and J. Nase,O. Ramos, C. Creton, and A. Lindner.Debonding energy of PDMS. A newanalysis of a classic adhesion scenario.Eur. Phys. J. E, 36:103, 2013

maître de conférences : en septembre 2010 j’ai été recrutéau sein de l’équipe "Liquides aux interfaces" du laboratoire LPMCN,[actuel Institut Lumière Matière (ILM)] de l’Université Claude BernardLyon 1. Les deux premières années qui ont suivi ma prise de fonctioncomme Maître de Conférences, ont été consacrées principalementà monter et faire tourner trois expériences. Depuis 2013, nous re-cueillons les fruits de cet investissement : 1 PRL en 2013 (plus deux

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autres issus de collaborations) ; 2 PRLs en 2014, etc. Ces travaux,dans le domaine de la fracture sous-critique et des milieux granu-laires, font partie de mon projet principal sur l’étude des avalanchesinvariantes d’échelle. Je joue aussi un rôle secondaire dans des ex-périences menées avec différents collaborateurs sur la dynamique desmatériaux viscoélastiques (ANR "StickSlip") et la Fractoluminescence(PRL-2013c)12 ; et je continue ma collaboration avec E. Altshuler sur le 12 A. Tantot, S. Santucci, O. Ramos, S. De-

schanel, M.-A. Verdier, E. Mony, Y. Wei,S. Ciliberto, L. Vanel, and P. C. F. Di Ste-fano. Sound and Light from Fractures inScintillators. Phys. Rev. Lett., 111:154301,2013

comportement des fourmis (PRL-2013b)13. Voici les trois expériences

13 S. C. Nicolis, J. Fernández, C. Pérez-Penichet, C. Noda, F. Tejera, O. Ramos,D. J. T. Sumpter, and E. Altshuler. Forag-ing at the Edge of Chaos: Internal Clockversus External Forcing. Phys. Rev. Lett.,110:268104, 2013

développées dans cette période :faille tectonique granulaire : il s’agit d’une monocouche

de disques photoélastiques compressés et cisaillés en continu qui sertde modèle simplifié d’une faille tectonique. Visualisation directe etmesures acoustiques sont appliquées. L’auto-organisation de la dy-namique vers la loi de Gutenberg-Richter, l’influence des paramètresdu système sur la dynamique et l’existence de précurseurs, sont desquestions que l’on se pose dans cette expérience. Ce projet a bénéficiéd’une bourse postdoctorale du Fonds AXA pour la Recherche pourdeux ans (R. Planet) et un étudiant qui a fait un stage de M1 surle projet en 2012 (S. Lherminier) continue sa thèse avec moi. Lespremiers résultats, au travers desquels nous sommes capables derévéler la structure interne du système avec des mesures acoustiques,viennent d’être publiés dans PRL14 et ont fait la couverture de la 14 S. Lherminier, R. Planet, G. Simon,

L. Vanel, and O. Ramos. Revealingthe Structure of a Granular Mediumthrough Ballistic Sound Propagation.Phys. Rev. Lett., 113:098001, 2014

revue.rupture sous-critique : cette expérience a plusieurs points

communs avec les séismes : dynamique lente avec une distributionen loi de puissance de la taille des évènements et distributions destemps de relaxation qui suivent également des lois de puissance (loid’Omori). L’acoustique est la principale source d’informations deséismes et aussi un outil important dans l’analyse de la défaillancedes matériaux. C’est une des raisons pour lesquelles comprendrela relation entre un processus de rupture et sa réponse acoustiqueest une question très pertinente, et deux directions sont en traind’être explorées à ce sujet: (i) la nature des évènements de rupturesimples, et (ii) l’analyse de la dynamique dans le voisinage de larupture critique. Ce projet a bénéficié d’une bourse de la Fédérationde Recherche A. M. Ampère (FRAMA) de Lyon ; et une étudiantequi a fait un stage de M1 sur le projet en 2011 (M. Stojanova) acontinué sa thèse avec nous en 2012. Résultats : 1 PRL publié en2013 sur l’influence du désordre dans la vitesse de propagation de lafissure, 1 PRL15 publié en 2014 et deux actes de colloques à comité de 15 M. Stojanova, S. Santucci, L. Vanel,

and O. Ramos. High Frequency Moni-toring Reveals Aftershocks in Subcriti-cal Crack Growth. Phys. Rev. Lett., 112:115502, 2014

lecture sur les résultats d’une étude comparative entre les mesuresacoustiques et la visualisation directe.

formation des motifs de fracturation dans une couche

granulaire cohésive : quand un matériel se casse en réponse àl’application d’une contrainte isotrope (ce qui est le cas le plus perti-nent en matière de recherche géophysique), généralement deux typesde motifs apparaissent : des réseaux de carrés, résultant d’un proces-sus hiérarchique où de nouvelles fissures rejoignent les anciennes àdes angles droits ; ou des réseaux hexagonaux, qui correspondent à

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la façon la plus efficace de relâcher les contraintes en deux dimen-sions. Le principal objectif de ce projet est de prédire (étant donné unéchantillon particulier dans un environnement particulier) le motif defracture, et la possibilité de transiter d’un motif à l’autre. L’interactionentre fissures dans les différents motifs est un autre des objectifs duprojet. Deux stages (L3 et M1) ont fourni des résultats préliminairesqui sont en cours d’analyse.

Projets actuels

Afin de gagner en clarté, visibilité et attractivité (autant pour lerecrutement des étudiants que pour cibler des sources de financement: "Funds AXA pour la Recherche", "Fondation MAIF", etc.) j’aicommencé à utiliser le label "Physique des Risques" pour décrire mesprincipaux projets (Fig. 1). Ces projets sont les suivants : (A) LesAvalanches Invariantes d’échelle : étude générale de la dynamique,et plus particulièrement l’analyse des évènements extrêmes, dansdes avalanches granulaires, fracture sous-critique et séismes. (B)Comportement collectif : analyse du comportement collectif desfourmis. En particulier dans des conditions de panique. La Formationdes Motifs est l’autre projet de ma recherche actuelle.

Figure 1: Sujets de recherche

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Physique des risques : (A) les avalanches invariantes d’échelle sontle sujet de recherche où j’ai le plus d’expérience. Je m’intéresse à cettedynamique d’un point de vue général : sa génération, l’influence desparamètres physiques (désordre, dissipation, etc) sur l’exposant dela loi de puissance de la distribution des évènements, l’importancede la valeur de l’exposant pour la compréhension de la dynamique,et –le plus important– la prédiction des évènements catastrophiques.L’analyse de données sismiques réelles, ensemble avec les projets"Faille tectonique granulaire" et "Rupture sous-critique", sont mesprojets principaux liés à des avalanches invariantes d’échelle.

Physique des risques : (B) comportement collectif. Dans unesituation de panique, les humains et les fourmis ont le même typede comportement (Am. Nat. 2005) où la tendance à former et suivreune horde domine (ce qui peut s’avérer dangereux dans un espaceconfiné). Récemment des mesures à la sortie du nid ont révélé que lesfourmis opèrent avec une dynamique proche du chaos, ce qui donnela souplesse nécessaire pour s’adapter à des situations changeantesde l’environnement (PRL-2013b). Actuellement, nous essayons decomprendre comment l’information de la panique se propage dansla colonie. Ce projet est une collaboration avec Ernesto Altshuler(Université de la Havane).

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Acknowledgments

It has been a long journey. It is difficult to look back in time, especiallyfor the frustration of not being able to go and save myself. However,the causes and events that drove the chaos16 of my adventure are 16 Chaos theory is a field of study in

mathematics which studies the behav-ior of dynamical systems that are highlysensitive to initial condition –a responsepopularly referred to as the butterfly ef-fect. Small differences in initial condi-tions (such as those due to roundingerrors in numerical computation) yieldwidely diverging outcomes for such dy-namical systems, rendering long-termprediction impossible in general.

there, as well as the intervention of plenty of people essential in myjourney. Without the help of many of these people it would not bepossible to make it until here. Now I would like to thank them.

the basis: the need for learning came very early, from the love forbooks and stories taught by my mother. However, our family was verymodest and the gap between dreams and means was huge. This was akind of solitude that forced the development of my imagination, but thesituation required having the feet on the ground, so I matured veryearly: I was extremely practical solving real problems and a very hardworker. So I consider that it was in my childhood where I grew mybest qualities for becoming a scientist. My parents always supportedme and did enormous sacrifices in order to help me, in particularwhen I went to Havana to study Physics. Having an older brotherthat was always the first in his class was kind of an easy (and oblige)track to follow. They have all my love and gratitude.

I play volleyball since I was ten years old, and I was the captainof a team during the whole high school and university. This taughtme a lot about collaborating in a competitive environment; as wellas inspiring and leading a team, which I consider very valuable in ourcurrent work as a researcher. For these reasons I thank Juan Alexis,my first trainer.

feeding the chaos: the major turning points that have changedmy geographical life: my professor of mathematics at the CentralUniversity of Las Villas (where I studied Pharmacy) convinced me ofgoing to Havana to study Physics; Ernesto helped me to go to Oslo;and Stéphane recommended me coming to Lyon. I thank all of them.

havana: the years in Havana were tough, in particular the firstyear at the school of medicine, which has been the most difficult of mylife17. Many thanks to Lester, Karel and Tamara, and their families,

17 For those that they do not live inHavana, the University provides freehousing and food. The access to theUniversity is through a national com-petition, so it is kind of a scholarship.The conditions are minimal (∼ 6 stu-dents/dormitory), but it is great havingthis opportunity. However, the initialsalary of someone that had just finishedthe university (5 year studies) was 198pesos/month, which is less than 10 USD(notice that a beer was around 0.8 USD).The first 9 months I was homeless, stay-ing at the lab. or at the places of somegood friends that lived in Havana. Then,I got an extra job that allowed me rent-ing a 25 USD room (which was also ille-gal). I lived there until I left to Norway.

Modesto, Luis and Nancy, and Odalys. Without their help I wouldnot make it. Thanks also to Ivette, Orencio, Hermes, Neyda, Luz,Alfo, Aramis, Claro, Etien, Liván, el Gámez, and Iselys for all the helpand the good moments in this difficult period.

Working with Ernesto was a great chance. Besides all the fun andthe value of the work that we have done together, his help went farbeyond the one of a supervisor. Thank you very much Ernesto.

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norway: many thanks also to Knut Jørgen. The opportunity hegave me of following my own project was exceptional. He was anexcellent supervisor and currently a great collaborator.

Thanks to all the good friends I met in Norway. The closest from thelab: Stéphane, Michael, Øistein, Ramon, Renaud; and from outside:Ariel, Yanet, Petra, Pola, Kari Mette, Jorge, Jaclyn, Kamil, Karl Åge,Violeta, Laura. I specially thank Nina and her family for all the yearswe lived together.

france: from my postdoc in Lyon I would like to thank Loïc,Sergio, Jean-Christophe, German, Thibaut, Eric, Valérie, Thierry, Nico-las, Tomasso, Peter, Jean-François; and also Nadine and Laurence(administration) and Frank and Marc (workshop).

During my last postdoc, in Paris, I spent a lot of time preparingauditions and writing projects and articles that were not related tomy main task. Thank you very much to Anke and Costantino for alltheir support, their patience and their consideration; this help wasessential for getting the permanent position. Many thanks also toFrédéric, José Eduardo, Orencio, Benjamin, Ramiro, Vlad, Gastón,Miguel, Rim, Nawal, Hélène.

Thanks also to Ricardo, Francisca, Loredana, Tita, Anthony andSonia and Julien.

university lyon 1: I would like to thank the members of thecommission of recruitment for trusting me five years ago. The peopleof Liquids at interfaces group have always been very welcoming. Thankyou Catherine B, Anne-Laure, Florence, Baptiste, Marie-Geneviève,Lydéric, Nicolas B, Frédéric, Aude, Elisabeth, Antoine, Jean, Cécile,Joseph, Amine, Thomas, Hélène, François, Quentin, Alessandro G,Baudouin, Ludivine, Kerstin, Felix G, Laurent, Simon G, Xixi, Bruno,Loren, Ronan, Henri, Choongyeop, Marie, Coraline, Alexandra, Rod-ney, Alejandro, Luc, Clara, Agnès, Christophe P, Pauline, Stella, Jean-Paul, Charlotte, Pascal, Catherine S, Alessandro S, Vasilica, Elisa,Isaac, Andréa, Richard, Nicolas W, Christophe Y.

Special thanks for those who I have the opportunity to workwith: Felix B, Marie-Julie, Thomas, Stéphanie, Philippe, Sergio, Rémy,Sébastien, Gael, Johan, Ramon, Stéphane, Gilles, Menka, Alexis, Hadil,Loïc, Simon Z. Without the excellent work and major contributions ofMenka and Sébastien this habilitation would not be a reality.

Thank you to the administration (Christelle, Delphine, Dominique)and the electronic workshop (Jean Michel and François). Their sup-port is essential and their work remarkable. The direction of the lab isalways very accessible and efficient: thank you to Alfonso (LPMCN)and Marie-France (ILM).

Without the support of the CNRS chair it would not be possibleto defend the habilitation this year. I also acknowledge the financialsupport of the AXA Research Fund and FRAMA.

Finally I would like to thank the members of the jury (in particularthe reviewers) for accepting my invitation. Many thanks to Sébastien,Stéphane and Catherine for reading the manuscript and making somecorrections.

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I dedicate the habilitation to Ernesto, Menka and Melanie. ToErnesto, for being my first advisor and excellent friend. But also forhis relevant contribution to the Physics in Cuba and the formation ofyoung researchers. To Menka, for the significant work she has doneduring her thesis; and also as an apology, because I have not beingvery accessible in this year, in particular caused by the writing of thishabilitation. To Melanie, my 15 year old niece, which is brilliant anda very hard worker. To congratulate and encourage her.

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Chapter 1: A little bit of history

Figure 2: Ernesto Altshuler, 2000.

the guerrilla, with ernesto: my formation as a researcherstarted at the University of Havana under the direction of ErnestoAltshuler (Fig. 2). At the end of the nineties, Cuba was engaged ina very slow recovery from its worst economic crisis (1993-94), whichwas triggered by the collapse of the Communism in Europe. Drivenalso by the former tied relations with East-Europe, Solid State Physicswas the core of both the formation and the research at the PhysicsFaculty of the University of Havana. However, with zero fundingand old equipment it was impossible to approach the advancing frontof this expensive kind of research. Luckily, the nineties was also aflourishing period for the Physics of Complex Systems worldwide; andprofessors Oscar Sotolongo and Ernesto Altshuler realized that thiswas an opportunity for developing an experimental physics of "highimpact factor" in Cuba. Ernesto, specialist in Superconductivity, hadthe courage of starting to work in something totally new: sandpiles.Soon this became the rule, targeting a new idea or a new phenomenon,and attacking and retreating from the subject, like a guerrilla war18.

18 See recent article in Science "In fromthe cold" commenting the work ofErnesto in Havana.

Figure 3: The "Chicharotron".

I joined Ernesto to work on a sandpile experiment (Fig. 3), relatedto the Self-organized criticality (SOC)19, around 1998: steel beads are

19 The Self-organized criticality (SOC) isa property of dynamical systems thathave a critical point as an attractor. Theirmacroscopic behavior displays spatialand/or temporal scale-invariance (char-acterized by power law distributions).

automatically added, one by one, upon a one-dimensional base, which issandwiched between two glass plates. As a result, a two-dimensional pile isformed and, under certain conditions, the distribution of avalanches (numberof beads that leave the pile after the addition of one grain) follows a powerlaw distribution; which was the signature of the SOC. At the beginningI was not very happy with the subject. We advanced slowly, therewere a lot of work and no publications, while for the students doingSuperconductivity it was much easier getting results and publishing.However, at some point I realized how lucky I was: starting a researchproject from scratch with someone of such experience, but almost atthe same low level as me regarding the knowledge of the new subject,it was an amazing school. I learned a lot; and we also did a little bitof history: publishing the first experimental article in Physical ReviewLetters20 (PRL) having a Cuban university as the only affiliation. This

20 E. Altshuler, O. Ramos, C. Martínez,L. E. Flores, and C. Noda. Avalanchesin One-Dimensional Piles with DifferentTypes of Bases. Phys. Rev. Lett., 86:5490–5493, 2001

work was related to the effect of disorder into the "self-organization"of a system (our two-dimensional pile) towards a scale-invariantdynamics, and the struggle for publication took 20 months. Otherpublications, fruit of the "guerrilla physics" followed this result. Thefirst one was related to granular flows, and motivated by the strangebehavior of a particular sand, which (instead of the usual avalanche

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behavior displayed during a pile formation) it formed a river (Fig. 4)that revolved around the pile21. The phenomenon was discovered21 E. Altshuler, O. Ramos, E. Martínez,

A. J. Batista-Leyva, A. Rivera, and K. E.Bassler. Sandpile Formation by Revolv-ing Rivers. Phys. Rev. Lett., 91:014501,2003

by Ernesto during a demonstration, when trying to illustrate theavalanches in a sandpile that, embarrassing, did not behave in theexpected manner. We also started to work in active matter, trying todemonstrate a theoretical result appeared in Nature [Helbing et al.,2000]. We studied ants to simulate the behavior of pedestrians under

Figure 4: Revolving river.

panic, and we found the same herd behavior observed in humans whensubmitted to similar conditions22.

22 E. Altshuler, O. Ramos, Y. Nunez,J. Fernández, A. J. Batista-Leyva, andC. Noda. Symmetry Breaking in Escap-ing Ants. Am. Nat., 166(6):643–649, 2005

The research process was very democratic and many ideas emergedfrom common discussions. However, Ernesto not only defined theinitial path, but he also worked in the lab with the same intensity,or more, than a student. This totally justified the choice of himbeing first author in all these articles. However, it also pushed me tocreate and develop my own ideas. In addition, I have always been moremotivated for developing something meaningful (or more applied)than something sparkling and new, but with less clear impact inscience or in society. Those were the reasons for deviating from theguerrilla physics into more mainstream (however controversial) issues.I focused my work on three related ideas of my own: one practicalissue, about getting information of the whole dynamics of a SOC system byjust analyzing what happens at the boundaries; the analysis of earthquakesas a SOC-like phenomenon; and the controversial subject of predicting scaleinvariant avalanches. In one hand I had observed regularities in thesandpile experiments that suggested the possibility of prediction. Inthe other hand I had understood that I needed not too many largeevents in order to predict them (reached in the case of a large exponentvalue of the power law distribution of event sizes); and there is anearthquake model were it is possible to modify this exponent value[Olami et al., 1992]. I started developing these subjects during myMSc. thesis, which I was doing in parallel to the work at the Schoolof Medicine.

the school of medicine: I graduated from the Physics Faculty(Licenciatura) in 2000 and worked as a professor in the Latin-AmericanMedical School (ELAM)23 until 2003, which was a beautiful and chal-

23 see TED talk: Where to train theworld’s doctors? Cuba.

lenging experience. The spring semesters I taught preparatory coursesof General Physics to Latin American students starting Medicine thenext semester. The fall semesters I designed and taught an intensiveelective course to students of second year of Medicine. The course,titled "Can We Predict?", used elements of biophysics and generalprinciples of Physics in order to explain the structures developedin organisms during the course of biological evolution. The mainobjective was to achieve a better and more profound understandingof the human physiology.24

24 "...The main problem is that usuallyPhysiology courses show how the organ-ism works, from the molecular level tothe organ level. The information growsand it gets impossible to remember allthe details. One way to really learn andunderstand How the organism works isby understanding that all those detailsare there as solutions to problems thatevolution had to solve. Then, with verybasic concepts of Physics, like elemen-tary Thermodynamics, Symmetry andGeometry, one can try to solve, as naturedid, those problems. For example, it ispossible to choose the type of channelsthat an intestinal cell needs, and whereto put them, in dependence of the gra-dients... or analyze how to increase thearea of absorption, and then "design"microvilli. With this method one doesnot need to remember all the details be-cause they will come out as a necessity.Then one will learn not how a particularstructure works, but why this structure isthere. Thus this zoo of details will showits internal harmony and one will getthe beauty of the solutions that naturefound."

The main part of the fall semesters I worked on a text book for thestudents, together with other professors at the Physics department.The book was published by the ELAM, and is still the students’ textbook. In 2005 it was approved for publication in a national editorial,but the names of the young professors which at that time were abroad,

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independently developing their PhDs, were removed from the list ofauthors.

a new life abroad: Thanks to the advice of Ernesto, which hada collaboration with The University of Oslo, I emigrated to Norwaywith a PhD scholarship in May of 2004.

Figure 5: Knut Jørgen Måløy, 2004.

Norway was the beginning of a new life. I arrived with my projectsrelated to SOC, and Knut Jørgen Måløy (Fig. 5), my PhD supervisor,gave me all the support to develop them. This was possible thanks toboth the huge kindness of Knut Jørgen and the fact that my scholar-ship was not linked to a specific project. Norway was a very happyand naïve period. I benefited from many resources that we did nothave in Havana: access to journals, money for experiments, a decentsalary, etc. In addition, as a PhD student trying to develop my ownprojects, I was isolated and protected from political issues related tomoney, power, positions, authorships, etc, which also play an impor-tant role in the scientific community. I have always been very gratefulto Knut Jørgen for all the great support and the opportunities I got inOslo. However, I guess it was in France where I totally understoodthe exceptional character of my situation in Oslo, driven in one handby my previous scientific results, the hunger for working on my ownideas, as well as some dose of stubbornness; and in the other handsteered by the typical "Lost in Translation" kind of disorientation ofsomeone that has just left Cuba. Knut Jørgen dealt all this wildernesswith great intelligence and generosity and was an excellent directorand collaborator.

Working on my own project was a challenge. I started studying

Figure 6: "Granular tectonic fault" setup.Bottom: side view. Top: Top view, wherethe upper ring compressing the grainshas been removed. Notice the mirrorat 45 degrees. By rotating it and tak-ing photos, the structure of the wholemonolayer of grains can be revealed.

simulations in a more realistic modification of the Olami-Feder-Christensen (OFC) earthquake model. I was convinced of the key roleplayed by the exponent of the power law distribution of avalanche sizes inthese SOC-like systems, and in the OFC model dissipation modifies the valueof the exponent. The publication of the results in PRL25 at the begin-

25 O. Ramos, E. Altshuler, and K. J.Måløy. Quasiperiodic Events in an Earth-quake Model. Phys. Rev. Lett., 96:098501,2006

ning of 2006 gave some assurance to the project. In parallel I designeda granular experiment that mimicked a tectonic fault (Fig. 6).

Figure 7: Bead-pile experiment.

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It consisted of a compressed monolayer of grains with periodic boundaryconditions that is sheared continuously generating avalanches. The ideawas to study the statistics of avalanches both with acoustics and directimaging. However, it seems that the project was too complicated forthe person in charge of building the setup at the workshop of theuniversity. There were many problems at every stage of the makingand the whole process turned extremely slow. After many monthsof struggle I decided to follow a "plan B", designing and buildingmyself (Fig. 7) an improved version of the sandpile experiment Ihad studied in Havana. The main goal was to obtain a power-lawdistribution of uncorrelated avalanches and to focus on the predictionof large events, which was considered impossible in the SOC systems.The results were excellent and for the first time large avalanches werepredicted inside a scale-invariant regime. Some unsuccessful attemptsto explain these results into a more general frame were responsiblefor the rejection of the article from the referees of Nature Physicsand PNAS. The experimental results were finally published in PRL26

26 O. Ramos, E. Altshuler, and K. J.Måløy. Avalanche Prediction in a Self-Organized Pile of Beads. Phys. Rev. Lett.,102:078701, 2009

and featured in NewScientist magazine.27. This article provoked the

27 Beads get ball-rolling on avalancheprediction, NewScientist (2009)

invitations of some editors, one in a scientific journal and another ina broad audience magazine28. Other experiments in the same setup

28 O. Ramos. Criticality in earth-quakes. Good or bad for prediction?Tectonophysics, 485(1-4):321–326, 2010;and O. Ramos. Avalanche! Coming!Now! Close to the borders of unpre-dictability. Significance, 6(2):78–81, 2009

focused on finding the predictions obtained in the OFC model, andexplored the influence of the dissipation and noise reduction in thesystem. The results were nice. However, after the first tour of reviewin PRL, I decided waiting for developing a model that explains theexperimental results, which was an extremely bad decision: the articleis still unpublished. This example, and the two unsuccessful attemptswith the former article, are a clear indication of my lack of experienceconcerning publications during my PhD. In parallel of these mainworks, I continued collaborating with Ernesto in the dynamics ofgranular flows29, which was also a part of my thesis.

29 E. Martínez, C. Pérez-Penichet,O. Sotolongo-Costa, O. Ramos, K. J.Måløy, S. Douady, and E. Altshuler.Uphill solitary waves in granular flows.Phys. Rev. E, 75:031303, 2007

Figure 8: The subcritical crack propa-gated faster in a "more disordered" sce-nario.

la france: I shared the office in Oslo with a French post-doc:Stéphane Santucci, that recommended me coming to Lyon to workwith Loïc Vanel, his PhD advisor, who was offering a postdoctoralposition. In May 2007 I defended my PhD thesis and started apostdoc at the École Normale Supérieure (ENS) in Lyon, France.The Physics Lab at the ENS was a very rich environment, with manyfriendly people always willing to discuss and share ideas. BesidesLoïc, with whom I was working directly, I often discussed with SergioCiliberto and Nicolas Mallick about the thermal activated natureof the subcritical fracture, and with Sergio and Peter Holdsworthabout avalanches and fluctuations in Statistical Physics. I also hadthe opportunity of starting a nice collaboration with Jean-ChristopheGéminard related to fracture patterns in cohesive granular materials.

Subcritical (or slow) fracture was the subject of the postdoc; andthe work focused on trying to control the disorder of a sample inorder to study its influence on the propagation of a subcritical crack.Different strategies were thought and discussed and finally, piercingtwo different arrays of tiny holes in the path of the fracture was thechosen way to tune the interaction between the crack and the structure

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of the system. The experiment were very challenging: both keepingidentical conditions between all different realizations, and extractingthe crack path inside the arrays of holes. The results were very nice(Fig. 8), leading to a publication in PRL30. Besides other issues, the

30 O. Ramos, P.-P. Cortet, S. Ciliberto,and L. Vanel. Experimental Study of theEffect of Disorder on Subcritical CrackGrowth Dynamics. Phys. Rev. Lett., 110:165506, 2013

fact that the results were the opposite to the expected ones, broughtsome delays to the final publication of the article. I also designed adouble periscope (Fig. 9) that increased more than twice the resolutionof the measurement (built by Marc Moulin). Nevertheless, there weresome small problems linked to the mirrors we bought, and finally wedid not use it very much.

I have never felt very comfortable with the (well-accepted) explana-tion that the fluctuations leading to the subcritical crack propagationin a heterogeneous material have a thermal origin. In order to experi-mentally test the effect of the temperature I built a rudimentary

Figure 9: Double periscope.

setup to study the subcritical fracture by the application of a deadweight (instead of a motor), and measuring acoustic emissions whilethe sample is submitted to light pulses. Just a few preliminary experi-ments were done before the end of my contract; however, the setuphas been used later, in the experiments carried out during the PhDthesis of Menka Stojanova.

The idea of the fracture patterns came from Oslo. Ten working daysbefore the PhD defense, the jury announces the title of the trial lecture, whichwill be presented the morning of the PhD defense. The candidate has to passthis test to have the right of defending the PhD in the afternoon.31 The 31 "The trial lectures is an independent

part of the Dr. Philos. examination.The purpose is to test the candidate’sability to acquire knowledge of mattersbeyond the thesis topic, and to impartthis knowledge in a lecture setting."

title of my lecture was "Morphology and dynamics of crack patterns".After intensively studying dozens of articles I realized that there werea few quite interesting and still unsolved questions: under isotropicstress normally two patterns appear: quadrangles or hexagons (Fig. 10).What are the conditions leading to a given pattern, and the existence of apossible transition between them, were the main questions I tried to answer.So, I arrived in Lyon with this project in mind, and started mountingan experiment. This idea resonated quite well with a similar oneof Jean-Christophe Géminard who was interested in a particularpattern formed under uniaxial stress, and we started a collaborationstretching a layer of grains with controlled humidity. The project ofJean-Christophe advanced quite well and gave a publication in

Figure 10: Quadrangles and hexagons.Photo source: http://www.wga.hu

PRL32, mine got stuck due to the grains we used (glass beads) started

32 H. Alarcón, O. Ramos, L. Vanel, F. Vit-toz, F. Melo, and J.-C. Géminard. Soft-ening Induced Instability of a StretchedCohesive Granular Layer. Phys. Rev. Lett.,105:208001, 2010

to react chemically due to the high humidity. At the end of mypostdoc there were just some preliminary results, but nothing verysolid meriting a publication.

In June 2009 I started a post-doc at the ESPCI in Paris. Theproject was a collaboration between Anke Lindner (PMMH Lab) andCostantino Creton (PPMD Lab), and part of a large European project.My choice was based in the qualities of both the place and the peopleinvolved. However, the subject was far from my competences andusual scientific interests. The project was the study of the adhesionproperties of PDMS with different crosslinker percentages. The du-ration was up to four years, so I decided to start the work, but withthe actual focus on trying to obtain a permanent position. In the case

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of not reaching it the first year, to concentrate then all my efforts inthe project. Luckily I got the position in 2010. I participated in twopublications. In the first one33 my contribution was small, and the

33 J. Nase, C. Creton, O. Ramos, L. Son-nenberg, T. Yamaguchi, and A. Lindner.Measurement of the receding contact an-gle at the interface between a viscoelas-tic material and a rigid surface. SoftMatter, 6:2685–2691, 2010

second one34 was the fruit of my experimental work.

34 J. Nase, O. Ramos, C. Creton, andA. Lindner. Debonding energy of PDMS.A new analysis of a classic adhesion sce-nario. Eur. Phys. J. E, 36:103, 2013

One challenging task during my time in Paris was writing a bookchapter for Nova Science Publishers. After getting the invitationand reading about the publisher one understands that it is not anexcellent offer (and most probably an automatic message), but I hadsome material to publish and a book chapter may have an impact(or at least an impression in a jury) larger than a long paper, so Idecided to do it. In order to get some support, I asked Henrik J.Jensen, professor at Imperial College and specialist in the subject, toreview the chapter; and he read it and gave me some comments. Thechapter "Scale-invariant avalanches. A critical confusion" talks aboutseveral aspects of scale-invariant avalanches, and the confusion inthe field35 mainly linked to the interpretations of the Self-organized35 O. Ramos. Scale Invariant Avalanches:

A Critical Confusion. In B. Veress andJ. Szigethy, editors, Horizons in Earth Sci-ence Research. Vol. 3. Nova Science Pub-lishers, 2011

criticality (SOC). Today the number of citations of the book chapter isnot great. However, I consider that it was worth it to write it.

the permanent position: Besides all the attractions linked tothe history, culture and everyday life in France, one major reason forcoming here was the possibility of getting a permanent position inthe academia. I applied to the CNRS (section 5) for the first timein 2009. I was not well prepared and I did not believe much in theproject I presented, so I left a negative impression in the jury. TheFrench community has never been (in general) a supporter of theideas of the SOC. Therefore my works in the subject labeled me as afollower of the theory, a "heretic" position that was heavily criticized.In 2010 I presented a solid project related to SOC that was very muchappreciated by my reviewer and it seems that I arrived to the finalround for one position. I had also applied in other sections of theCNRS and an assistant professor position in Paris, but with actuallyalmost zero chances to get them.

The position I have now did not come easily. As it benefited of aCNRS chair36, it was very attractive. In the auditions we were four36 The Chairs were implemented by the

CNRS between 2009 and 2012. Witha duration of five years, they bring a2/3 reduction of the teaching duties;and –for the "Maître de Conférences"positions– 10K€/year as a research sup-port, and the automatic assignmentof a "bonus of scientific excellence" of6K€/year.

candidates with very similar possibilities: one with already a positionof assistant professor, one postdoc that was recruited by the CNRSthis year, another postdoc recruited by the CNRS in 2011, and myself.The commission in charge of the decision, composed of 12 members(half from the University of Lyon 1 and half externals) voted for meas the first in a list of four classified, so, in principle, I had gottenthe position. However, two weeks later, we were surprised by thefact that the Administrative Council of the University, advised bythe Director of the laboratory, did not respect the decision of therecruiting commission and switched the first and second places ofthe list. Several members of the commission complained, but giventhe recent status of autonomy of the University, the final decisionbelonged to the Administrative Council, so there was nothing illegal inthe procedure. One month later, the researcher declined the positionin Lyon in favor of his CNRS position, so at the end of July 2010,

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the Ministry of Education and Research contacted the second onein the final recruiting list (myself) for offering the position; which Iaccepted.

Nov. 2010

July 2013

a) Pattern formationb) “Granular tectonic fault”c) Subcritical fracture

a b

c

Figure 11: Evolution of the Lab.

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the university of lyon 1: Due to all the delays, I started atthe University of Lyon 1 in November 2010. My position came toreinforce the line of research initiated by Loïc Vanel, who had gottena professor position in the LPMCN laboratory [currently the InstitutLumière Matière (ILM)]. Loïc had focused his main research activitiesin the fracture of polymeric materials (scotch peeling at the Universityand rubber materials at Rodhia).

It was great to have the possibility of recovering the experimentalsetups that I had built during my postdoc in Lyon. The rudimentaryone, for doing acoustic measurements during the subcritical fractureof paper, has already been used by Loïc and it was at the University.The one for stretching and breaking a granular layer (in collaborationwith Jean-Christophe) was also moved to the University in 2012. Ialso contacted Knut Jørgen in order to borrow and bring to Lyon theparts of the granular experiment that mimicked a tectonic fault andwas impossible to properly build during my PhD. He kindly agreed.

My research activities during the first two years after getting theposition (2011-2012) were consecrated to redesigning and mountingseveral experiments (Fig. 11); obtaining some fundings37; recruiting

37120 K€ of a postdoctoral grant for Ra-

mon Planet (March/2012 - March/2014)from the AXA Research Fund; and 30

K€ for equipment, (with S. Santucci)from the A.M. Ampère Federation ofResearch (FRAMA) of Lyon.

students38 and postdocs (Ramon Planet); and getting some results.

38 Menka Stojanova* (M1 in 2011)Sébastien Lherminier* (M1 in 2012)Simon Zugmeyer (L3 in 2012)(*) Both Menka and Sébastien followedtheir PhDs with me in 2012 and 2013

respectively.

Since 2013, we collect the fruits of these investments: 1 PRL in 2013

(two other coming from collaborations39); 2 PRLs in 201440, etc. These

39 A. Tantot, S. Santucci, O. Ramos, S. De-schanel, M.-A. Verdier, E. Mony, Y. Wei,S. Ciliberto, L. Vanel, and P. C. F. Di Ste-fano. Sound and Light from Fractures inScintillators. Phys. Rev. Lett., 111:154301,2013; and S. C. Nicolis, J. Fernández,C. Pérez-Penichet, C. Noda, F. Tejera,O. Ramos, D. J. T. Sumpter, and E. Alt-shuler. Foraging at the Edge of Chaos:Internal Clock versus External Forcing.Phys. Rev. Lett., 110:268104, 2013

40 M. Stojanova, S. Santucci, L. Vanel,and O. Ramos. High Frequency Moni-toring Reveals Aftershocks in Subcrit-ical Crack Growth. Phys. Rev. Lett.,112:115502, 2014; and S. Lherminier,R. Planet, G. Simon, L. Vanel, andO. Ramos. Revealing the Structure ofa Granular Medium through BallisticSound Propagation. Phys. Rev. Lett., 113:098001, 2014

works, in the field of subcritical fracture and granular media, belongto my main project on the study of scale-invariant avalanches. I alsoplay a secondary role in experiences led by various colleagues onthe dynamics of viscoelastic materials (ANR "StickSlip") and photonemissions caused by fracture (PRL-2013a). I have also finished anarticle coming from my last postdoc on the debonding of adhesivematerials (EPJE-2013); and I continue my collaboration with ErnestoAltshuler (University of Havana) on the behavior of ants (PRL-2013b).

Current projects

To gain in clarity, visibility and attractiveness (both for the recruitmentof students as for targeting sources of funding: "AXA Research Fund","MAIF foundation", etc.) I began to use the label "Physics of Risk" todescribe my main projects (Fig. 12). These projects are the followingones: (A) Scale-Invariant Avalanches: general study of the dynamics,and more in particular the analysis of the extreme events, in granularavalanches, subcritical fracture and earthquakes; and (B) CollectiveBehavior: analysis of the collective behavior of ants. In particularin conditions of panic. The other part of my research activities Ihave labeled as Pattern Formation and includes dynamical patterns (ingranular flows) and fracture patterns in different materials.

Physics of Risk: (A) Scale-Invariant Avalanches is the subject of re-search where I have most experience. Earthquakes, granular avalanches,subcritical fracture, solar flares, stock markets, and many other phe-nomena where the energy is accumulated very slowly and liberatedby sudden "avalanches" show a scale-invariant behavior, i.e., the sizes

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!!!!"

Granular Avalanches

Subcritical Fracture

Scale-Invariant Avalanches (extreme events)

Collective Behavior

Panic Risk Physics of

Pattern Formation

Fracture Patterns Dynamical Patterns

Earthquakes

Figure 12: Research Subjects.

of the events distribute following a power law. I create simplified andsmall-scale experiments trying to better understand these phenomena. I aminterested in this dynamics from a general point of view: its gen-eration, the influence of physical parameters (disorder, dissipation,etc.) on the exponent of the power law of the distribution of eventsizes; the relevance of the exponent value for the understanding of thedynamics, and - the most important - the prediction of catastrophicor extreme events. Simple simulations and modeling complement ourexperimental work. Here are our main contributions in this subject:

predictability: An experiment where (challenging the standardidea of unpredictability of scale-invariant avalanches) catastrophicevents are predicted [PRL (2009)41]; simulations transferring these 41 cited in 26

results to an earthquake model [Tectonophysics (2010)42]; and a re- 42 cited in 28

view setting them into the more general framework of avalanchesand critical phenomena [NOVA-Review (2011)43]. The prediction 43 cited in 35

of the internal structure of a granular medium with acoustics [PRL(2014b)44] will allow us reaching new frontiers in the forecasting of 44 cited in 40

catastrophic events.role of disorder: Disorder is a key element that changes the

system from a trivial quasi-periodic state to a power law distributionof avalanches [PRL (2001)45, PRL (2006)46]. An increase of disorder

45 cited in 20

46 cited in 25

can also accelerate the propagation of a subcritical fracture [PRL(2013a)47], bringing an earlier failure of a structure. 47 cited in 30

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others: Photon emissions caused by fracture [PRL (2013c)48]; and48 cited in 39

aftershocks detected only at high frequency measurements, provokinga change in the power-law exponent of the distribution of avalanchesizes [PRL (2014a)49] are other relevant results related to subcritical49 cited in 40

fracture.Currently we are developing two main experimental projects in

this subject, the "Granular tectonic fault" and the study of Subcriticalfracture.

Figure 13: "Granular tectonic fault".

"Granular tectonic fault": Rebuilt from the Oslo experiment, it con-sists of a monolayer of photoelastic disks that is compressed and shearcontinuously, mimicking the behavior of a tectonic fault (Fig. 13). Di-rect visualization and acoustic measurements are applied. The auto-organization of the dynamics towards the Gutenberg-Richter law, theinfluence of the parameters of the system on the dynamics (exponentof the power law, different types of avalanches, etc.), and the existenceof precursors, are questions we are focusing on in this experiment.This project benefited from a two-years postdoctoral grant of the AXAResearch Fund (for Ramon Planet) and the internship (M1 level) ofSébastien Lherminier, who has continued his work with me (now as aPhD student). The first results, where we are capable of revealing theinternal structure of the system with acoustic measures, have beenpublished in PRL50 (in August, 2014) and featured on the cover of the

50 cited in 40

journal (Fig. 14).

Figure 14: PRL Cover, August 2014.

"Subcritical fracture": If a disordered and quasi-fragile material witha crack is submitted to a subcritical load, the crack will grow slowly,by jumps or "avalanches", until it reaches a critical length where thefailure is total and almost instantaneous. This experience has severalpoints in common with the behavior of earthquakes: slow dynamics,with a power law distributions of event sizes (Gutenberg-Richter law),and a distributions of relaxation times which also follow a power law(Omori law). Acoustics is the main source of information concerningearthquakes and also an important tool in the analysis of materialfailure. Therefore, understanding the relation between a ruptureprocess and its acoustical response is of great interest, both fromfundamental and applied perspectives. Two main directions are takenin this project: (i) Analysis of the statistics of events, and a comparisonwith other techniques (visual) and phenomena (earthquakes); and (ii)Understanding the nature of single fracture events. In particular theanalysis of the dynamics in the neighborhood of the critical rupturewith the possible existence of precursors of the catastrophic failure.This project benefited from a grant of the A.M. Ampère Federationof Research (FRAMA) of Lyon; and Menka Stojanova, who madean internship of M1 in 2011, continued her thesis with us in 2012.Results: 1 PRL51 published in 2013 on the influence of the disorder in51 cited in 30

the speed of propagation of the crack. 1 PRL52 published in 2014 and52 cited in 40

two Conference proceedings on the results of a comparative studybetween the acoustic measures and the direct visualization.

Physics of Risk: (B) Collective Behavior. Ants, as social insects, arenot very intelligent at the individual level, but collectively they can be

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quite smart, at least regarding "survival tasks" such as foraging andnest construction. Our experiment (Fig. 15) has shown that, when theyare in panic ants become less smart, behaving in the same way thathumans in panic do. In low panic conditions and two symmetricalexits ants use both of them in the same proportion, but when in panic(after the addition of repellent at the center of the experimental cell),

Figure 15: Symmetry breaking in escap-ing ants.

they tend to "follow-the-crowd" and to use more one exit than theother [Am. Nat. (2004)53], which is the same behavior that humans do

53 cited in 22

when they are in panic (for example in situation of fire in a cinema).Field experiments, where a sensor have been located in the nest

exit, give information about the organization of the colony in relationto external forcing: temperature, light, etc. The results show that antsoperate "at the edge" of chaos, which allows a very flexible responseto external forcing [PRL (2013b)54]. Currently, we are studying how 54 cited in 39

the information of panic propagates in the colony. This work is acollaboration with the University of Havana.

Pattern Formation: The emergence of patterns, with the creationof order and symmetries and well-defined scales, tells a lot aboutthe Physics of a given system. We have been interested in dynami-cal patterns, created with the flow of a peculiar kind of sand [PRL(2003)55, PRE (2007)56]; and different cases of deformation of systems 55 cited in 29

56 cited in 29leading to the creation of fracture patterns, both in PDMS [Soft Matter(2010)57] and in humid granular materials [PRL (2010)58]. We are also 57 cited in 33

58 cited in 32interested in temporal patterns, and currently we are trying to findsigns of "critical slowing down" as precursors of catastrophic eventsin scale-invariant phenomena.

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Chapter 2: Scale-Invariant Avalanches

2.1: Introduction

“But he hasn’t got anything on," a little child said.Hans Christian Andersen in The Emperor’s New Clothes

Scale invariance pervades nature, both in space and time. In space,it is revealed through the ubiquity of fractal structures; and in time,with the presence of scale invariant avalanches. Avalanches can be seenas sudden liberations of energy which has been accumulated very slowly59;

59 A more general definition ofavalanches is introduced in section2.3.1.

and phenomena as diverse as earthquakes [Bak and Tang, 1989, Olamiet al., 1992, Jagla, 2010], granular piles [Held et al., 1990, Frette et al.,1996, Altshuler et al., 2001, Aegerter et al., 2003, Nerone et al., 2003,Aegerter et al., 2004, Lörincz and Wijngaarden, 2007, Ramos et al.,2009], snow avalanches [Birkeland and Landry, 2002], solar flares[Dennis, 1985, Hamon et al., 2002], superconducting vortices [Fieldet al., 1995, Bassler and Paczuski, 1998, Altshuler and Johansen, 2004,Altshuler et al., 2004a,b], sub-critical fracture [Santucci et al., 2004,Stojanova et al., 2014], evolution of species [Sneppen et al., 1995], and

Figure 16: Sandpile growth in a trans-parent cylindrical container.

even stock market crashes [Lee et al., 1998, Gabaix et al., 2003, Preiset al., 2011] have been reported to evolve through scale invariantavalanches. The signature of the scale invariance corresponds to apower law [P(s) ∼ s−b] in the distribution of avalanche sizes. In 1987,Per Bak and co-workers introduced the "Self-organized criticality"(SOC) as the best-known attempt to explain the scale invariance innature [Bak et al., 1987]. The SOC proposed a mapping between scaleinvariant avalanches and critical phenomena, with the key axiomthat the critical state is an attractor of the dynamics, provoking theself-organization60 of the system towards a critical state [Jensen, 1998,

60 The formation of a sandpile is theparadigm of the SOC: the addition ofgrains upon a flat surface leads to a pileformation with a given angle of repose(Fig. 16). The theory suggested the self-organization of the system towards ascale invariant dynamics without anyadjustable parameters. However, theseparation of temporal scales betweenslow addition and sudden liberation ofenergy is required to get a power lawdistribution of avalanches; and in thecase of injecting a continuous flow otherphenomena may appear (see Fig. 4). Ex-periments have shown that not all sand-piles display scale invariant avalanches[Jaeger et al., 1989], and specific condi-tions are needed (type of grains [Fretteet al., 1996], level of disorder [Altshuleret al., 2001], etc.) in order to obtainpower-law distributions of avalanches.

Bak, 1997].Being able to group so many different phenomena into the same

kind of dynamics, where catastrophic events and small events areexplained by the same principles, was a big achievement. However,the axiomatic manner in which the base of the theory was introduced,set SOC as a theory to be proved more than as a theory to develop.Many theoretical studies focused on mapping SOC into the formalismof critical points [Alstrøm, 1988, Pietronero et al., 1994, Vespignaniand Zapperi, 1997]; others, on developing models displaying SOCbehavior [Olami et al., 1992, Bassler and Paczuski, 1998, Sneppenet al., 1995], increasing the members of the SOC family. However, thenumber of experiments was rather small, and they focused mainly

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on validating the theory, where the main goal was finding power-lawdistributions of avalanches [Held et al., 1990, Frette et al., 1996, Alt-shuler et al., 2001, Aegerter et al., 2003]. Besides of the fact that manyof the experimental and numerical results displayed exponent val-ues different than the original Bak-Tang-Wiesenfeld (BTW) model61,

61 The SOC ideas were originally intro-duced in the BTW model [Bak et al.,1987], which is a cellular automatonconsisting of a square lattice with openboundary conditions (Fig. 17). Inte-ger numbers (representing grains) areadded at random positions. If a givencell reaches 4 grains after the additionof one grain, a local and conservativeredistribution happens where 1 grainis added to the four nearest neighbors.If one of the neighbors reach 4 grainsthe process repeats until all sites haveless than 4 grains. Then a new grain isadded. The size of the avalanche corre-sponds to the number of redistributionsthat happen after the addition of onegrain. The distribution of avalanchesfollow a power law with an exponentequal 1.27 (in two dimensions) [Lübeckand Usadel, 1997].

most phenomena displaying scale-invariant avalanches were classi-fied as SOC. This situation brought a lot of confusion to the field ofscale-invariant avalanches [Geller et al., 1997, Main, 1999], to the

1 2 0

0 3 0

1 3 1

1 2 0

0 4 0

1 3 1

1 3 0

1 0 1

1 4 1

1 3 0

1 1 1

2 0 2

1

a b

c d

Figure 17: One avalanche in the BTWmodel implemented in a 3 × 3 lattice.Time runs clockwise, from (a) to (d). Thesize of the avalanche corresponds to 2.

degree of even affecting its reputation62, and is one of the reasons why

62 Several communities remained skepti-cal to the SOC ideas, and scale-invariantavalanches are often linked to the SOC.France is (in general) a good example:having very well established commu-nities in granular matter and statisti-cal physics, but with very little con-tributions related to SOC and to scale-invariant avalanches in general.

many relevant questions concerning the scale invariance of avalancheswere never formulated and consequently never answered: Underwhich conditions does a system organize into a dynamics of scale-invariantavalanches? Which are the relevant parameters (and their roles) driving thisorganization? Which are the critical properties of scale-invariant processes?Is it possible to predict catastrophic events in these systems? How? Thoseare question that have motivated my research activities for more thana decade.

The essential role of the exponent value of the power law in thedynamics is the main subject of the first part of this chapter. Theexponent value controls the ratio of small and large events, the en-ergy balance –required for stationary systems– and the mean valueof the distribution (which may be related to the critical propertiesof the dynamics). However, we will start by analyzing the causesand consequences of logarithmic scales, which is often a source ofconfusion in the community. The second part corresponds to theanalysis of avalanches in a well established critical system: the Isingmodel. By using two different algorithms (Metropolis [Metropoliset al., 1953] and Wolff [Wolff, 1989]) two different dynamics are ob-tained. As expected, the distribution of the time-averaged properties(distributions of fluctuations, magnetization, etc) are the same for thetwo algorithms. However, the distributions of avalanches are verydifferent. In the third part, the study focuses on the critical proper-ties of scale invariant avalanches, where a condition of criticality isintroduced, depending on the exponent value of the avalanche sizedistribution. Our numerical and experimental efforts in order to gainunderstanding of these systems, in particular the predictability ofscale invariant avalanches, are presented in the fourth part of thechapter. I conclude by introducing the main future projects related tothis subject.

2.2: Classification of scale invariant avalanches

2.2.1: Fractals and scale invariant avalanches: the exponent value

The introduction of the fractal dimension by Benoît Mandelbrot in1975 [Mandelbrot, 1975, 1983] changed the way nature is perceived;and self-similar branched and rough structures became more intuitiveand natural than the artificially smooth objects of traditional Euclideangeometry. The self-affine structure of a Romanesco broccoli (Fig.

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18a) is an eloquent example of a natural fractal and if a tiny insecttraverses the vegetable following a straight line, it will surprisinglyfind a very long route. The Koch curve [Koch, 1904] is a goodrepresentation of this path (Fig. 18b), and the distribution of sizes ofits different self-similar parts, resulting from a triangular "bending"of the central part of every line, follows a power-law P(s) ∼ s−b withan exponent b = −β = Log(4)/Log(3) = 1.2619 [Mandelbrot, 1983](Fig. 18c). A similar analysis over a smooth path donates an exponentb = 1. The value of the exponent characterizes the trajectory andprovides its dimension, which is fractal in the case of the broccoli.This fractal dimension is the main concept of the theory introducedby Mandelbrot; and by using the approach of "filling the space",it can be understood rather intuitively: a smooth line "fits" in onedimension, while the rougher the self-affine curve (the higher thefractal dimension), the closer it is to fill a two-dimensional space.For the same reason, self-affine surfaces, as the one of the broccoli,present fractal dimensions between 2 and 3.

Through the fractal dimension, the value of the exponent of thepower-law plays an essential role in the spatial scale invariance; how-ever, in the case of scale invariant avalanches, the relevance of theexponent is much less understood. The earthquake dynamics is thephenomenon that normally comes to people’s minds as the example

Log

[ P

(s) ]

Log (size)

!

a

b

c

Figure 18: (a) Romanesco broccoli. (b)The Koch curve as a representation ofan intersection between a plane and thesurface of the broccoli. (c) Scheme of thesize distribution of the different parts inthe structure of the Koch curve, whichis a power law with an exponent β =−Log(4)/Log(3) = −1.2619.

of scale invariance in the temporal domain. Regardless the valueof the exponent of the power-law distribution, the interpretation ofscale invariance is limited to the absence of characteristic avalanches,and the existence of many small events and a few very large ones.Temporal relations between events are sometimes wrongly added tothe interpretation, considering that there is no correlation between thedifferent avalanches. The logarithmic scale in which the Gutenberg-Richter law was originally introduced [Gutenberg and Richter, 1956]has also created confusion in the value of the exponent for the dis-tribution of earthquakes, and consequently the implications of thisvalue in the dynamics of scale invariant avalanches. Further downtwo examples with different exponents will clarify that, as in the caseof fractal structures, the exponent of the power-law distribution doesplay a central role in the dynamics of scale invariant avalanches. How-ever, first we will analyze how to classify scale invariant phenomena,where the historical use of a logarithmic scale has often added someconfusion to the interpretation of scale invariant avalanches.

2.2.2: The origin of logarithmic scales

All instruments operate with a finite characteristic resolution, whichneed to be considered seriously when analyzing data collected by theinstrument. In a world permeated by scale invariance, how can onemeasure a variable presenting values over several orders of magni-tude? The digital music, propelled by a technological revolution, hasfocused on increasing the resolution of the instruments [Peek et al.,1975]: 16 bits in a CD, 24 bits in a DVD, and up to 64 bits in internal

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processing. Being able to divide a signal into 32 bits (4.294... × 109),or even into 64 bits (1.844... × 1019), is extraordinary; however, naturehad to solve this problem with limited resolution63 and therefore in63 The human eye cannot distinguish be-

tween 256 grey levels [Russ, 2002]. an ingenious manner: by the application of scale transformations. Fig-ure 19 illustrates several functions transforming a phenomenologicalscale of 109 levels of resolution into an instrumental scale of 8 bits ofresolution (256 levels).

The function (I) y = x saturates the instrumental scale in less thanthree decades; while the function (IV) y = c x, although it covers thewhole range of the phenomena, can not differentiate between valuessmaller than 106. In order to find the best function let us introduce ageneric transformation function R(x) and its inverse F(y). R(x) givesthe change in resolution due to the transformation and F(y) providesthe absolute error Eabs and relative error Erel of the measurement:

Eabs ≡ dF(y)/dy ; Erel ≡ Eabs/F(y). (1)

Figure 19: Different scale transformationfrom a phenomenon with 109 levels ofresolution into an instrumental scale of8 bits of resolution.(I) y = x(I I) y = a ln(x)(I I I) y = xb

(IV) y = c xa = 256/ln(109); b = ln(256)/ln(109);c = 256/109.

Two cases are analyzed: (I I I) a power-law transformation and (I I)a logarithmic transformation:

(I I) R(x) = a ln(bx) (2)

F(y) = (1/b) exp(y/a) (3)

Eabs = (1/ab) exp(y/a) ; Erel = 1/a (4)

(I I I) R(x) = axb (5)

F(y) = (y/a)1/b (6)

Eabs = (1/b)(1/a)1b y(

1b −1) ; Erel = (1/b) y−1 (7)

In the case of the power-law transformation, the absolute errordepends on the value of the exponent. For b = 1 (linear case) Eabs

is constant, for b > 1 it decreases with the measured value, thus thelarger the value the more accurate the measurement. For b < 1, theabsolute error increases with the measured value. If a phenomenonoccurs over several orders of magnitude, only the case b < 1 can fulfilan instrumental scale with limited resolution. In the three cases therelative error decreases with the measured value. As a consequence,in the situation of a fractal structure as the one presented in Fig. 18;the larger the measured field, the larger the number of sub-levelsresolved by the measurement. Following this reasoning, if a digitalcamera is used as the instrument of measurement, as the cameramoves apart in order to capture a larger structure, the number ofpixels of the camera have to increase, a situation that is normal andcommon when one uses a measuring tape: in order to measure alarger structure, the tape is enlarged and the number of units ofmeasurement increase; thus the relative error decreases. This effectintroduces a scale during the process of measurement, and allowsknowing the size of the structure through the analysis of the relativeerror; thus, a power-law transformation "breaks" the scale invariance.

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However, the logarithmic transformation keeps constant the relativeerror. By using the same example, the resolution of the cameradoes not change when the camera moves apart, and there are nodifferences between two images taken at different scales. In thissense a logarithmic transformation respects the scale invariance, andthis may be a main reason for using this scale transformation in theclassification of scale invariant phenomena.

Another reason is historical. In 1856 the English astronomer Nor-man R. Pogson proposed the current form of classification of the starsin different magnitudes in relation to the logarithm of their bright-ness [Pogson, 1856]. He based the system on the work of Ptolemy[Ptolemy, 1515], who probably based his work on the writings of theancient Greek astronomer Hipparchus [Toomer, 2011]. In 1860 theexperimental psychologist Gustav T. Fechner proposed a logarithmicrelation between the intensity of the sensation and the stimulus thatcauses it [Fechner, 1860]; so the thought logarithmic response of thehuman eye64 was responsible for the logarithmic nature of the stel- 64 More recent studies have proposed

power-law relations between sensationsand stimuli, experimentally proved in arather narrow range of stimuli [Stevens,1961].

lar scale. In 1935 Charles F. Richter proposed a logarithmic scale todescribe the earthquake’s strength [Richter, 1935]. The name magni-tude for this measurement came from Richter’s childhood interest inAstronomy [Times, 1985]; and the scale matches in some degree theearlier Mercalli intensity scale [Wood and Neumann, 1931], whichquantified the effects of an earthquake based on human perception.

2.2.3: Classifying scale invariant avalanches

Let us analyze now the two examples with different exponents values.Three main variables characterize the dynamics of power-law dis-tributed avalanches: the value of the exponent of the power-law andthe two cut-offs. In general there is one cut-off related to the smallestavalanche size that can be measured. In this study we will considera minimum size Smin = 1. There is also another cut-off limiting themaximum size of the events. In the following, the analysis will be

b = 1

b = 2

Figure 20: Power-law distributions ofavalanche sizes for two different expo-nent values: b = 1 and b = 2. Theavalanches have been classified as small,medium and large following logarith-mic bins. The percentage of each typeof avalanche for the two different expo-nents is also displayed. A circle in eachcurve represents the mean value of theavalanche size 〈s〉.

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simplified in considering a sharp cut-off 65 at a value Smax.65 The shape and behavior of the largecut-off bring a lot of information rel-ative to the dynamics of the system[Bramwell, 2009, Le Doussal and Wiese,2009]: in critical systems with power lawdistributed events, the cut-off is propor-tional to the system size, and the ad-dition of dissipation may provoke the"displacement" of the cut-off to smalleravalanche sizes (breaking the criticality),while the exponent value remains robust[Lauritsen et al., 1996]. Numerical andanalytical studies pay a lot of attentionto the cut-off. However, not all systemsrespond in the same manner to the ad-dition of dissipation, and the change inthe exponent value (with no variationin the cut-offs) is an alternative scenario[Olami et al., 1992]. In addition, it is verydifficult to obtain good-quality large cut-offs in experiments, due to a lack ofstatistics; and sometimes there is no cut-off at all [Ramos et al., 2009], which isalso the case in real earthquakes.

P(s) = As−b (8)

describes the pdf of the avalanches, where 1/A =∫ Smax

Smin=1 s−bds fulfill

the condition of normalization∫ Smax

Smin=1 P(s)ds = 1. Figure 20 showsthe pdfs of two distributions of avalanche sizes with Smax = 109

and exponents b = 1 and b = 2. The distributions are representedin a log-log plot, and the avalanches are classified considering alogarithmic resolution: a "magnitude" m of the avalanches is definedas the logarithm of the avalanche size [m = Log(s)]; and the graphis divided into n equally spaced zones of m. For n = 3, avalanchessmaller than m = 3 are considered small (S), those lying betweenm = 3 and m = 6 are medium (M), and those greater than m = 6 arelarge (L).

2.2.4: Integrated probability

One main confusion related to logarithmic scales is a consequenceof the fact that during the measurement, an integration has beenalready performed, which is well described through the integratedprobability: PInt(s, k) =

∫ kss As′−bds calculates the probability of hav-

ing an avalanche with size in the interval between s and ks. Dueto the properties of the integral, the integrated probability is also apower-law with an exponent −b + 1.

PInt(s, k) =ln(ks)− ln(s)

ln(Smax)=

ln(k)ln(Smax)

, b = 1 (9)

PInt(s, k) =(k−b+1 − 1)s−b+1

(S−b+1max − 1)

' (1− k−b+1)s−b+1 , 1 < b ≤ 2 (10)

The calculations performed with a value of k = 103 give the proba-bilities of the S, M and L avalanches shown in the graph of Fig. 20.For b = 1 the integrated probability is constant and equal to 1/n, sothe three types of avalanches have the same probability equal to 1/3.In the same manner, considering k = 10, the graph can be dividedinto decades: 9 zones equispaced in m that can be denominated as S1,S2, S3, M1, M2, M3, and L1, L2, L3 (shown in the graph), all of themwith equal probability 1/9. This situation, which evidently resultsfrom the logarithmic scale of the measurement, is very far from thecommon interpretation of many small events and only a few very largeones. For b = 2, PInt(s, k) = (1− k−1)/s. Every decade the probabilitydecreases by a factor 10. As a consequence, the probabilities of havinga small avalanche is 0.999; 9.99× 10−5 for a medium size avalanche;and only 9.99× 10−7 for a large event (Fig. 20).

2.2.5: Mean value of avalanche size

Another relevant quantity signaling the key role of the exponent ofthe power-law, corresponds to the mean value of the size distributionof the avalanches 〈s〉 =

∫ SmaxSmin=1 sP(s)ds.

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〈s〉 = Smax − 1ln(Smax)

, b = 1 (11)

〈s〉 = (−b + 1)(−b + 2)

S(−b+2)max − 1

S(−b+1)max − 1

, 1 < b < 2 (12)

〈s〉 = ln(Smax)

1− S−1max

, b = 2 (13)

The mean value of the avalanche size is related to both the responseof the system to a perturbation, and the energy balance in the dynam-ics. In the Fig. 20, where Smax = 109, the values of 〈s〉 correspond to4.8× 107 and 20.7 for b = 1 and b = 2 respectively. These values arerepresented by a circle in each curve.

The value 〈s〉 corresponds to the average response of the system toa perturbation, under the consideration that small perturbations canprovoke the overcoming of local thresholds and thus the triggeringof avalanches. In average, the system is delivering an avalanche ofsize 〈s〉; so in terms of avalanche production, this is equivalent togenerate an avalanche of size 〈s〉 in every event of the dynamics. Inthe particular case of 〈s〉 proportional to the system size, the situationcan be interpreted as critical66: in average a perturbation provokes 66 Criticality in scale-invariant

avalanches is normally associatedto the behavior of the cut-off, whichis somehow equivalent to define acorrelation length proportional tothe linear size of the characteristicavalanche size presenting in the cut-off:ξ ∼ s1/dA

max in our case, where dA is thefractal dimension of the avalanche.However the analysis of this sectionsuggests instead ξ ∼ 〈s〉1/dA . (see morein section 2.4).

a response proportional to the system size. However, the fact thatthe dimension of the avalanche is smaller than the dimension of thesystem, adds some complexity to the analysis of the criticality throughthe avalanche size distribution, which will be discussed in section 2.4.

2.2.6: Energy balance in slowly driven systems

As mentioned in the introduction, avalanches are defined as suddenliberation of energy that has been accumulated very slowly. Thisindicates that the energy is injected in small portions, and that there isa separation between the drive of the system (slow) and the avalancheduration (fast). At every single time interval, it is possible to definean injected energy, an avalanche of a particular size, and a dissipatedenergy. If the system is in a stationary state, the average energyinjected to the system in every time interval has to be equal to theaverage dissipated energy. Consequently, the average dissipatedenergy has to be small,

〈Einjected〉 = 〈Edissip〉. (14)

Many of the models dealing with scale invariant avalanches arenon-dissipative in the bulk, and the energy is liberated through theboundaries of the system [Bak et al., 1987]. However, they still referto avalanches as the local processes related to rearrangements in thebulk of the system, with no energy cost. As the avalanche productionis not directly related to the dissipation of energy, these systems canhave a large value of 〈s〉 and still present a small average value of thedissipated energy 〈Edissip〉.

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However, the vast majority of real phenomena are dissipative.Considering that 〈Einjected〉 ∼ Smin << Smax, and 〈Edissip〉 = α〈s〉,where α is a dissipation coefficient,

α〈s〉 << Smax. (15)

From eq. 12,

〈s〉 ∼ S(−b+2)max (∀ b �= 1; �= 2) (16)

α << Smax/〈s〉 ∼ S(b−1)max . (17)

As a result, large values of 〈s〉, obtained from b values close to 1, areforbidden for dissipative slowly driven system. The previous analysis didnot consider the existence of avalanches of size zero (let us call themzero avalanches), where the addition of energy to the system provokesno response in terms of avalanches (s < Smin). In order to compensatethe energy lost for an average non-zero avalanche 〈s〉, the system needsa number nS0 of zero avalanches proportional to α〈s〉/Smin. For largeb values, and thus small α〈s〉, nS0 can be the consequence of a lack ofresolution in the measurement.

2.2.7: The distribution of earthquakes

Figure 21a shows the statistics of earthquake occurrence in the wholeplanet and in four zones with different sizes and activities. The datahas been extracted from the U.S. Geological Survey (USGS). It

4 5 6 7 8 9 10

10−1

100

101

102

103

104

Magnitude

Nu

mb

er

of

Ea

rth

qu

ake

s /

yea

r

Worldwide

Australia

Japan

South America

California

1 1.2 1.4 1.6 1.8 2

10−2

100

102

104

106

108

1010

b

Nu

mb

er

of

Ea

rth

qu

ake

s /

yea

r

−1.1

−0.9

M 0−1

M 3−4

M 1−2

M 8−9

M 4−5

M 4-5

M 5-6

M 6-7

M 7-8

M 8-10

a

b c

Figure 21: Distributions of earthquakes.(a) Earthquake world map, with fourselected zones with different sizes andactivities. (b) Distributions of earth-quake’s magnitude worldwide and ineach selected zone. The red line, withan slope −1 is the best fit, while thedashed lines indicate that the error ofthe slope is around ±0.1. (c) Number ofearthquakes of a given magnitude peryear considering different exponent val-ues. The vertical lines indicate the criti-cal value of the exponent in the conserva-tive case of the Olami-Feder-Christensen(OFC) earthquake model [Olami et al.,1992] (1.27), the value of the exponentfor critical systems in the Mean-Fieldcase (3/2) and the exponent for realearthquakes (5/3).

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covers a 40 years period, from 1973-01-01 00:00:00 to 2013-12-31

23:59:59. In order to guarantee the completitude of the catalog, onlythe events with magnitude M ≥ 4.0 have been considered. We findthe well-known Gutenberg-Richter law (Fig. 21b):

Log[Pint(M)] ∼ kM (18)

where M corresponds to the magnitude and Pint indicates that themeasurements involve the integration of the values in a given intervalof magnitudes. The solid red line and the dashed ones in Fig. 21bshow that k = −1± 0.1 (provided a large statistics). By substitutingM into the definitions

M ≡ Log(A) + const ; M ≡ 2/3 Log(E) + const, (19)

where A is the wave amplitude, according to the work of Richter[Richter, 1935], and E the energy released by a quake [Hanks andKanamori, 1979], one gets Pint(A) ∼ A−1 and Pint(E) ∼ E−2/3. Aftertaking their derivatives we obtain the distributions of earthquakes interms of A and E:

P(A) ∼ A−2 ; P(E) ∼ E−5/3 (20)

After many pages insisting on the relevance of the exponent value,we arrive to a situation where two power laws, with two different exponentvalues, describe the same phenomenon. Is there a "right" one? Whichone?67 In the light of critical phenomena, the correlation length ξ

67 Which is the "right" variable to mea-sure? Let us consider a power lawP(s) = 1

N s−b, where N is a normal-ization constant. The variable s can bewritten as s = sDA

l (the most commoncase is E ∼ A2, where E and A are theenergy and the amplitude respectively).

P(s)ds = P(sl)dsl (21)

1N

s−bDAl DAsDA−1

l dsl = P(sl)dsl (22)

P(sl) =DA

Ns−β

l (23)

with β = (b− 1)DA + 1 (24)

As a result, we have two power laws,with two different exponents, describingthe same process. In the case of criticalphenomena, the standard manner to de-fine the size of an event is by measuringits volume [Stauffer and Aharony, 2003](in a n-dimensional space). Therefore,in order to analyze the critical proper-ties of a given process, the variable tochoose is the one proportional to thevolume. In the case of earthquakes,we introduced the energy and the am-plitude: P(E) ∼ E−5/3, P(A) ∼ A−2;and it is the energy the one propor-tional to the area of the two-dimensionalevent. Notice that the relation betweenthe two is given by E ∼ ADA withDA = (2− 1)/(5/3− 1) = 3/2 (insteadof the common E ∼ A2).

is a key variable describing the nature of the system. In order tocompare the results of scale-invariant avalanches with those fromcritical phenomena, the avalanche size has to be proportional to thevolume of the avalanche. In this case, the equation ξ ∼ 〈s〉1/dA willhave units of length (which are the adequate ones for the correlationlength). Therefore, s must be proportional to the area "involved"in the earthquake. In a first approximation (considering only thespherical spreading loss) E should be proportional to 1/r2, where ris the distance hypocenter-sensor. This makes the energy E the rightmeasurement to analyze the critical properties of earthquakes. Inprinciple, the amplitude must decay as 1/r. However, notice that therelation between the two measurements corresponds to E ∼ A3/2,instead of the commonly used E ∼ A2 .

By considering that one earthquake with magnitude M between0 and 10 happens every 0.028 s, the distribution P(E) ∼ E−b withb = 5/3 reproduces the red line of Fig. 21b. In order to illustratethe relevance of the exponent value, the behavior of earthquakesworldwide is analyzed supposing different exponents. The numberof earthquakes per year of a given magnitude as a function of bappears in Fig. 21c. In the real case of b = 5/3 there is 1 catastrophicearthquake with magnitude between 8 and 9 per year (blue line).However, by keeping the total number of events, and redistributingthem with b = 1.5 (Mean-Field), there would be 162 (almost oneevery second day); and 138,000 (∼ one every 4 minutes) in the criticalsituation of b = 1.27 (OFC model [Olami et al., 1992]).

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2.3: Avalanches in critical phenomena

The original motivation of this section was to study the propertiesof the scale invariant avalanches in well established critical systems;in order to compare them with the SOC avalanches. As discussed inthe introduction, the SOC borrowed the concept of critical point ofequilibrium phase transitions in order to describe their uncorrelatedpower-law distributed avalanches. The term critical in the avalanchecontext has been presented through the fact that at any moment aminor perturbation can trigger a response (avalanche) of any size andduration, a behavior that is linked to a divergence of the correlationlength in the original numerical model of SOC: the BTW model[Bak et al., 1987]. Many dissipative phenomena involving avalanchesdistributed according to power-laws have been treated as criticalsystems [Jensen, 1998, Bak, 1997]; however, recent studies have showndifferent systems evolving through power-law distributed avalanchesin a non-critical behavior [Ramos et al., 2009, Ramos, 2010, Pruessnerand Peters, 2006], which has motivated this analysis of the avalanchedynamics in a well established critical scenario: a second order phasetransition.

In Physics, the classical scenario of critical phenomena takes placeduring a second order phase transition [Stanley, 1987]. The text-book example is the transition where a permanent magnet loses itsmagnetism: its magnetic properties cease when the temperature is

d

b

a

c

m !

T

Figure 22: Ising model simulated in a128 × 128 lattice. Snapshots of the dy-namics at (a) T = 2.1, (b) T = 2.3 and(c) T = 2.7. Magnetization m and Cor-relation length ξ as a function of thetemperature T.

increased above a certain critical temperature Tc. Below this tem-perature (Fig. 22a), a majority of spins point in the same direction,creating a magnetic field. Large fluctuations in spins do not occur atlow temperatures, thus the system will remain unchanged. Above thecritical temperature the spins’ directions are random and change di-rection randomly, frequently and individually (Fig. 22c). The systemis already disordered, therefore, no large-scale changes will happen;there is no overall magnetic field. However, at the critical temperatureitself, large fluctuations occur and different snapshots of the systemshow different patterns - but all of the patterns will be statisticallysimilar, in that clusters of aligned spins are surrounded by areas withspins oriented in the opposite direction (Fig. 22b). The clusters are ofall sizes and their distribution follows a power-law [Clusel et al., 2004].Four characteristic of this critical state will be used in our analysisalong this chapter:

a) Divergence of the correlation length (ξ): The temporal averageof the spatial autocorrelation function

〈CAs(d, t)〉t =

⟨∑ f (x, y) f (x′, y′)− 〈 f (x, y)〉2

∑( f (x, y)− 〈 f (x, y)〉)2

t

(25)

where f (x, y) represents the structure of the system (in two dimen-sions) and d corresponds to the distance between (x, y) and (x′, y′),can generally be fitted (∀T �= Tc) as an exponential decay in the form

〈CAs(d, t)〉t ∼ exp(−d/ξ). (26)

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At the critical point, the correlation length ξ is proportional tothe linear size of the system L (diverging in an infinite system). Thetemporal average is necessary because the calculus is performed in asnapshot of the dynamics (a microstate), and any physical measureimplies an average over many different microstates, which is equiv-alent to a temporal average if the system is ergodic [Newman andBarkema, 1999].

b) Divergence of the correlation time (τ): The temporal autocorre-lation function

CAt(t) = ∑ f (ti) f (ti + t)− 〈 f (ti)〉2∑( f (ti)− 〈 f (ti)〉)2 (27)

can be fitted as an exponential decay in the form

CAt(t) ∼ exp(−t/τ). (28)

Far from the critical point, the correlation time τ is small, sothe system will quickly recover from a perturbation. At the criticalpoint, τ diverges due to the fact that the system hesitates betweenthe two states, and perturbations can move the system away fromits equilibrium state during long periods of time. As a result, thedynamics turns slow, a phenomenon which is known as critical slowingdown (CSD) [Newman and Barkema, 1999].

c) Both ξ and τ present power-law dependencies with the reducedtemperature Tr = (T − Tc)/Tc in the way ξ ∼ |Tr|−ν and τ ∼ |Tr|−zν;and thus they relate to each other through τ ∼ ξz. ν is called a criticalexponent and is an attribute of the Ising model. Phenomena with thesame critical exponents belong to the same universality class. Theexponent z is often called the dynamic exponent. It gives a way toquantify the CSD and it depends on the algorithm, i.e., it depends onthe type of dynamics [Newman and Barkema, 1999].

d) As the size of the system increases, the transition between thetwo states becomes sharper, and it is infinitely sharp in an infinitesystem [Newman and Barkema, 1999].

2.3.1: Avalanches & fluctuations in the Ising model

In this subsection, the dynamics of avalanches is studied in a wellestablished critical system: the Ising model, which is certainly themost thoroughly researched model in the whole of Statistical Physics.It is a model of a magnet, and consists of a lattice where every siterepresents a spin of unit magnitude taking two values ±1 as an indi-cation of the only two possible directions to point: “up" or “down".The spins interact with their nearest neighbors and the magnetizationM is the sum over all the spins. For two or more dimensions thesystem shows a second order phase transition at a critical temperatureTc (Tc = 2.269 in two dimensions) from a ferromagnetic to a paramag-netic state when the temperature is increased, and in two dimensionsthe model is analytically solved [Onsager, 1944]. The behavior ofthe average fluctuations of the magnetization is well known, and it

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defines the magnetic susceptibility, as well as its relation with thecorrelation function. The fluctuations of the magnetization (M− 〈M〉)have also been studied [Stauffer, 1998], and their pdf is reported tobe universal [Bramwell et al., 2000]. It presents an exponential tailon one side, and a rapid falloff on the other side. However, in thescenario of SOC systems, instead of analyzing the fluctuations of themagnitudes, the standard is to define avalanches68, corresponding to68 Avalanches 6= Fluctuations. Fluctua-

tions account for how far it is a valuefrom the mean value of an ensemble,while avalanches relate to the differ-ences in value between two consecutiveevents.

relative differences between consecutive states. Therefore, the defi-nition of avalanches presented in the introduction, which is relativeto slowly driven system, has been extended to differences between eq-uispaced values in the time series of the measured variable. In the caseof the Ising model, they corresponds to jumps in the magnetizationbetween two consecutive microstates. Small simulations, both in sizeand in running time, will be sufficient to illustrate the dynamics ofavalanches in this critical scenario.

The simulations take place in a 128 × 128 lattice with periodicboundary conditions (Fig. 22), and compute 106 Monte Carlo steps(MCS) after 105 thermalization steps. Both Metropolis [Metropoliset al., 1953] and Wolff [Wolff, 1989] algorithms are implementedconsidering no external magnetic field. Thus the energy of the systemreads as E = −J ∑N

〈i,j〉 sisj where J = 1 is a coupling constant and〈i, j〉 indicates that the sum is over nearest neighbors only. In theMetropolis algorithm one MCS consists of N = (128)2 events whereone random spin is selected, and flipped (si = −si) if exp(−∆E/KT)is larger or equal to a random number between 0 and 1. ∆E is thechange in energy due to the flip of the spin, and K is considered equalto 1, so the temperature T is presented as an adimensional magnitude.In the Wolff algorithm, one MCS consists of building up a cluster offlipped spins. Starting from flipping one spin at a random position,its neighbors will become part of the growing cluster if exp(−2J/KT)is smaller than a random number between 0 and 1.

The average of the absolute value of the magnetization per spinm, and the value of the correlation length ξ for the Metropolis algo-rithm are shown in Fig. 22d (Identical results are found for the Wolffalgorithm). The correlation length has been extracted following theeqs. 25 and 26:

〈C(r)〉t =⟨

∑Nd(i,j)=r(sisj)−m2

∑Nd(i,j)=r(si|sj| −m)2

⟩t

(29)

〈C(r)〉t ∼ exp(−r/ξ). (30)

The correlation function has been calculated by using periodicboundary conditions, through an average of values taken every 1000MCS, and the sum is over those sites that are separated from eachother by a distance equal to r. Both algorithms give the same results onthe averages of the physical magnitudes, with a peak in the correlationlength coinciding with the phase transition.

The behavior of the fluctuations for the Wolf algorithm is presentedin Fig. 23. For very low temperatures two symmetric Gaussian dis-

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tributions (GDs) in the pdf of the magnetization indicate the twosymmetric ordered states in the system (not shown in the graph). Asthe temperature increases, the two GDs approach each other (Fig. 23a)and a small asymmetry starts to be noticed at the low frequencies inthe pdf of the fluctuations of the absolute value of the magnetization(Fig. 23d). At the critical point, the two GDs start to merge formingthe universal Gumbel distribution reporter by Bramwell et. al. inthe pdf of the fluctuations of the absolute value of the magnetization[Bramwell et al., 2000] (Fig. 23e). This Gumbel distribution of thefluctuations has been used by different experiments as an indicationof the criticality of the system [Joubaud et al., 2008, Planet et al.,2009]. For high temperatures we can consider that the two GDs haveperfectly merged, and there is a Gaussian behavior of the fluctuation

Figure 23: (a-c) Distribution of the mag-netization for the Wolff algorithm at dif-ferent temperatures. At the critical point,the distribution for the Metropolis algo-rithm is also displayed (b), presentingan asymmetric behavior (in red). (d, e)Distribution of the fluctuations of the ab-solute value of the magnetization for theWolf algorithm at different temperatures.(f) Distribution of the fluctuations of themagnetization for the Wolf algorithm atT = 2.6.

of the magnetization (Fig. 23f). In the case of the Metropolis algorithmonly one side of the graph (a) will be explored by the system in a finitetime (either positive or negative magnetization). The asymmetry dis-played by the Metropolis algorithm in the graph (b) is a consequenceof its slow dynamics, as it will be discussed further down. 106 MCSare not enough for the system to spend on average the same "time" insymmetrical areas of the phase space (with 107 MCS both algorithmsgive the same result). The other graphs (c − f ) are the same for bothalgorithms; consequently, they give the same results concerning thefluctuations of the absolute value of the magnetization.

The distributions of the jumps of M (avalanches) and the distribu-tions of flips for the Metropolis algorithm are displayed in Fig. 24.The avalanches follow a Gaussian for every measured T, and thedistributions widen as T increases (Fig. 24a). The distributions of flips

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(Fig. 24b) also follow Gaussian distributions, with their mean valuesincreasing with T and standard deviations having a maximum at thecritical value Tc = 2.269.

Figure 24: (a) Distribution of the jumpsin the magnetization (avalanches) fordifferent temperatures (T) with theMetropolis algorithm. The curves corre-spond to T values between 1.8 and 2.7with spacings of 0.1, and also the criticalpoint: Tc = 2.269. b) Distributions offlips for different temperatures.

The jumps of M in the Wolff algorithm (avalanches) are displayedin Fig. 25. The way that clusters build-up makes the absolute valueof the jumps of M equal to the number of flipped spins, so onlythe distributions of avalanches are presented. As T decreases fromthe critical point the distributions display an increasing number ofevents that involve the whole system, which is an artefact. They havebeen removed from the graph and will not be taken into accountin the analysis. At the critical temperature the avalanches follow apower-law distribution with an exponent β = 1.1. The distributionsdeviate from power-laws as the temperature moves away from Tc.

Figure 25: Distributions of the jumpsof the magnetization (avalanches) forthe Wolff algorithm at different temper-atures. The analysis of the simulations has demonstrated that power-law

distributed avalanches are not a necessary condition in order to clas-sify a system as critical, but different kinds of distributions can rulethe avalanche behavior of an equilibrium system at the critical point.The Metropolis dynamics at Tc is ruled by avalanches whose sizesare distributed following a Gaussian with standard deviation much

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smaller than the system size. It is a local dynamics happening on(and slowly re-shaping) a globally correlated landscape. Small jumpswill move the system slowly around the phase space, so in a realsituation a fast enough measurement can get the system "trapped" ona fluctuation, even far from the equilibrium value (calculated after along enough averaging). This slow dynamics is directly linked to thecritical slowing down, situation which has been artificially eliminatedin the Wolff algorithm. The Wolff dynamics at Tc is the one thatpeople working with SOC models are accustomed to: avalanchesthat follow the landscape in an "invasion" mode, cascading throughthe system and resembling the properties of the globally correlatedlandscape. This direct relation between structure and avalanches isthe key that allows analyzing the critical properties of a system fromthe characteristics of its scale invariant distribution of avalanches.

Two questions emanate from this analysis. The first: Is there an"algorithm" (a dynamics) chosen by nature? And the second: Is therecritical slowing down in real critical systems evolving through scaleinvariant avalanches? Let us discuss some experimental results.

2.3.2: Experiments: from the micro to the macro-world

The Wolff algorithm is much faster than the Metropolis one around Tc.This was a big achievement in 1989, where the computing capabilitieswhere rather limited. However, it is well known that Metropolisrepresents better the dynamics of the second order phase transitionaround the Curie temperature69 [Dunlavy and Venus, 2005]. Recent 69 The reason for this is the fact that

many other less stronger interactionshave not been considered in the anal-ysis. They are included in somethingdenominated thermal bath which tries toequilibrate the dynamics.

experiments have focused on the non-gaussian (Gumbel) distributionof fluctuations close to the Fréedericksz transition, a second orderphase transition in a liquid crystal [Joubaud et al., 2008], and theyhave also confirmed the Gaussian character of the avalanche distributionsclose to the critical point70. However, if a ferromagnetic system is 70 S. Ciliberto, Private Communication.

kept at a low temperature (below Tc) and an external magnetic fieldis applied, the spins try to align themselves with the external field,and a reorganization of the magnetics domains takes place. Thisreorganization is not a smooth process, but is composed of smallbursts or avalanches distributed following a power-law; a phenomenonwhich has been widely studied from the avalanche context [Sethnaet al., 2001, Zapperi et al., 1998] and is known as the Barkhauseneffect [Barkhausen, 1919].

Moving towards the macro-world, a turbulent flow is anotherphenomenon where non-gaussian fluctuations have been reported[Bramwell et al., 1998, R. Labbé et al., 1996]: two coaxial disks counter-rotate at a fixed velocity generating a swirling flow in the gap betweenthem. The power required to keep a constant velocity of the disks(through a feedback loop) is measured and the fluctuations of thepower correspond to the variable of analysis. If the experiment isperformed inside a cylinder coaxial with the disks but with a diame-ter much larger than the disks’ diameter, the fluctuations of the totalpower follow a Gaussian distribution. However, if the diameter of

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the cylinder is only slightly larger than the disks’ diameter, the fluc-tuations of the total power follow a Gumbel distribution [Bramwellet al., 1998]. The data of the experiment have been reanalyzed71 and71 Courtesy of J.-F. Pinton

avalanches have been defined as relative differences between twopoints separated a time interval τ in the time series of total power.While the fluctuations of the total power display a Gumbel distribu-tion, interpreted as a signature of a critical scenario; the avalanchesfollow a Gaussian distribution for all the different τ values [Ramos,2011].

Recently an experiment has been reported where both avalanchesand fluctuations have been measured in an imbibition front [Planetet al., 2009]. A viscous liquid is injected into a Hele-Shaw cell wherea random distribution of well controlled patches guaranties a specificlevel of disorder. The competition between viscous and capillaryforces creates a jerky dynamics where the global velocity of the frontdisplays avalanches that follow a scale invariant distribution fitted to anexponent −1. The average of the avalanche size increases with thedecrease of the injection rate (v → 0) and as a consequence, thecutoff of the power-law moves to higher values of avalanche size,approaching a pure power-law in the limit (v = 0). The distributionof fluctuations also change from a Gaussian to a Gumbel as v → 0,indicating the critical properties of the system around v = 0. Theauthors have been able to relate the asymmetry of the Gumbel to thereduction of the degrees of freedom in the system as the velocity ofthe dynamics is reduced.

The main message of this part consists in revealing that power-law distributed avalanches are not a necessary condition in order toclassify a system as critical, but different kinds of distributions can rulethe avalanche behavior of an equilibrium system at the critical point.The question about the dynamics chosen by nature has been answeredin the way that different dynamics have been observed in diversephenomena; nevertheless, a general formalism capable of predictingthe kind of dynamics for a particular phenomenon is still lacking.Concerning the question about critical slowing down, although in boththe Barkhausen and the imbibition experiments the critical point of thepinning-depinning transition is reached at a limit (v→ 0), the fact thatthe velocity of the dynamics is externally imposed leaves some doubtsabout the existence of critical slowing down in real critical systemsevolving through scale invariant avalanches. A stronger argumentin favor of its existence comes from percolation, which shares manydifferent points with a second order phase transition (including criticalslowing down) at the percolation threshold, and where the avalanchesare power-law distributed [Stauffer and Aharony, 2003]. Anotherthing to retain from this part is the value of the exponent of thepower-law displayed by this well established critical system in twodimensions.

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2.4: Criticality in scale invariant avalanches

2.4.1: Models without spatial structure

After the introduction in 1987 of the SOC [Bak et al., 1987], manydifferent approaches have been used in order to describe its dynamics.The first one corresponded to the critical branching process [Alstrøm,1988].

The schema in figure 26 represents a branching process where eachbranch has a probability Pn of having n subbranches, n ∈ [0, nmax].The different probabilities can be calculated by the following equa-tions:

nmax

∑0

nPn = 1 + G (31)

nmax

∑0

Pn = 1 (32)

P0

P1P2

Figure 26: Branching process withnmax = 2.

where G corresponds to the average growth. Criticality is reachedin the situation where the process barely "survives" [Alstrøm, 1988],which corresponds to G = 0; i.e., it is the minimum probability ableto develop branches proportional to the system size L; where L isthe length where the process is artificially stopped. For nmax = 2,P0 = P2 = (1 − P1)/2. If avalanches are defined as the number ofgenerated branches, and the process is repeated a large number oftimes, the avalanche size distribution corresponds to a power-lawwith an exponent equal 3/2 and an exponential cut-off in the form

P(s) ∼ s−3/2exp(−s/λ) (33)

where λ ∼ L [Harris, 1963]. This result is in perfect agreement withthe mean-field theory [Vespignani and Zapperi, 1997], with percolationin a Bethe lattice [Stauffer and Aharony, 2003]; and also with recentworks using functional renormalization group [Le Doussal and Wiese,2009]. In the first two approaches there is no spatial structure. How-ever, the same result appears if the processes take place in a reallattice, but only above a critical dimension dc.

Unfortunately, dc = 4 for the branching process [Obukhov, 1989,Díaz-Guilera, 1994], and for the functional renormalization group[Le Doussal and Wiese, 2009]. For percolation dc = 6 [Stauffer andAharony, 2003]. However, in real situations of two and three dimen-sions the results are different, and we will find values smaller than3/2 for the critical exponents.

2.4.2: Avalanches in two and three dimensions

Percolation gives the clearest example about the relation between theexponent of the avalanche size distribution and the dimension of thesystem (black circles in Fig. 27). The exponents go from 187/91 − 1 =

1.05 in two dimensions, to 3/2 in six dimensions (dc = 6). Fordimension six (or larger) the fractal dimension of the avalanche is 4

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[Stauffer and Aharony, 2003]. In these conditions, the avalanche frontdoes not make loops. Thus, it behaves in the same way as avalanchesin the Bethe lattice. As the dimension of the system decreases, thedifference between the fractal dimension of the avalanche and thedimension of the system reduces, and the exponent of the avalanchesize distributions moves towards the value b=1. Similar results areobtained from different models of slowly driven phenomena, wherethe exponent values go from 3/2 in four dimensions (dc = 4), to 1.27

in two dimensions (open triangles in Fig. 27). In the case of MeanField models and avalanches in a Bette Lattice, which are equivalentto an infinite dimension, the exponent value corresponds also to3/2. These results strongly suggest that the critical exponents valuescorresponding to avalanche size distributions are bounded between1 and 3/2. However, both in many real systems and in models it ispossible to find exponent values far beyond 3/2 (see green zone inFig. 27). How to explain this contradiction?

2.4.3: Losing criticality

By setting a negative value to G in eq. 31 it is possible to simulatethe effect of the dissipation during the branching process: At everybranching occasion, the probability is lower than the critical one; andas a result the average length of the branches decreases. The solutionof the avalanche size distribution has the same shape (eq. 33). Theexponent 3/2 is robust but λ decreases with the dissipation. Thecut-off does not scale with L, but it presents smaller values related to

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Figure 27: Exponents of the powerlaw distribution of avalanche sizes fordifferent phenomena. Two universal-ity classes of critical systems are rep-resented: one containing Percolation[Stauffer and Aharony, 2003] and theIsing model [Ramos, 2011, Hu, 1984],and another with different examples ofslowly driven phenomena (OFC, BTW[Tang and Bak, 1988, Lübeck and Us-adel, 1997, Chessa et al., 1999] andManna models [Chessa et al., 1999]).Notice that 3/2 is the maximum valueof the exponent for critical systems inboth situations, obtained also in thecase of an equivalent infinite dimension(Mean Field [Vespignani and Zapperi,1997] and Bethe Lattices [Stauffer andAharony, 2003, Alstrøm, 1988]). How-ever, several actual two-dimensionalslowly driven systems (Solar Flares[Dennis, 1985], Earthquakes, Granularpiles [Ramos et al., 2009], Superconduct-ing vortices [Altshuler and Johansen,2004], Subcritical fracture [Stojanovaet al., 2014]) show exponent valueslarger than their critical value (∼ 1.27)and often also larger than 3/2.

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the dissipation. As a consequence, avalanches do not reach the systemsize L and criticality is lost. The same behavior (robust exponentvalue with cut-off moving to smaller avalanche sizes with dissipation)has been obtained in other models [Lauritsen et al., 1996], and it isthe standard criterium to define a scale-invariant process as critical.This definition is based on the assumption that if the linear size ofthe largest avalanches in the system s1/dA

max (where dA is the fractaldimension of the avalanche) are proportional to the system size L,then the correlation length ξ is proportional to L, diverging if L→ ∞.In other words, this definition associates ξ ∼ s1/dA

max72. 72 Notice that with this definition (which

is the one accepted by the community), allproceses with scale-invariant avalanchesand cut-offs (or s1/dA

max ) proportional to Lare defined as critical, without consid-ering the value of the exponent of thedistribution.

Under the assumption of ξ ∼ s1/dAmax , all the phenomena considered

in the green zone of Fig. 27 would be critical. Also both processesdisplayed in Fig. 20 with exponent values 1 and 2, and 〈s〉 equal to4.8× 107 and 20.7 respectively, would also be critical. Following theanalysis started in section 2.2.5, let us associate the correlation lengthto the linear size of the mean value of the avalanche sizes ξ ∼ 〈s〉1/dA .In this case the criticality of the system will depend on the value ofthe exponent b of the power law distribution of avalanche sizes.

In order to simplify the analysis, let us consider a sharp cut-offat smax that is associated to the system size. The mean value of theavalanche size 〈s〉 ∼

∫ smaxsmin=1

ss−bds, in the limit of smax >> 1 and in

the interval b ∈ (1, 2), corresponds to 〈s〉 ∼ s −b+2max .

In the hypothetical case where the fractal dimension of the avalanchedA would correspond to the dimension of the system d, ξ ∼ 〈s〉1/d ∼s −b+2/d

max . In this case only bc = 1 will fulfill a diverging correlationlength (ξ ∼ s1/d

max). As mentioned at the beginning of the previ-ous section, referring to percolation [Stauffer and Aharony, 2003],bc → 1 when dA → d. As the difference between dA and d increases,avalanches become more "direct", percolating through the system forlinear sizes of avalanches smaller than s1/d

max and therefore reachingcriticality with larger exponent values (bc > 1). This growing of bc

stops when the difference between dA and d reaches the point wherethe avalanche front does not make loops anymore, which happens atthe critical dimension dc, where bc = 3/2.

In this new approach, the exponent value plays an essential role inthe critical properties of the dynamics, and the critical exponents bc arebounded between 1 and 3/2. Therefore the phenomena considered inthe green zone of Fig. 27 (with exponent values larger than 3/2) cannotbe critical. As mentioned earlier, the best-known effect of dissipationin scale-invariant processes is the shifting of the cut-off to smalleravalanche sizes (while the exponent value remains robust). However,an alternative scenario is possible, where dissipation may increase theexponent value of the avalanche size distribution: The Olami-Feder-Christensen (OFC) model of earthquakes is a nonconservative modelthat mimics the behavior of two tectonic plates, and is able to tune theexponent of the power-law distribution of avalanches by modifyingthe degree of dissipation in the system [Olami et al., 1992] 73. In this

73 Recent and still unpublished resultsin granular piles (the continuation of[Ramos et al., 2009]) have shown thesame tendency displayed by the OFCmodel: an increase in the value of the ex-ponent of the power-law distribution ofavalanche sizes as dissipation increases.

model (see Fig. 29a, b) we can clearly define a critical exponent valuebc = 1.27, which corresponds to the case with no dissipation, and

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many other exponent values related to different values of dissipation.In a critical scenario, reached in a situation where the exponent bcorresponds to the critical one bc, the correlation length should beproportional to the linear size of the system, ξc ∼ L. Followingthe same analysis as before we obtain a critical mean avalanche size〈sc〉 ∼ s −bc+2

max , and the correlation length can be written as

ξ(b) ∼( 〈s〉〈sc〉

)1/dA

L. (34)

In the standard scenario of b = bc with a cut-off (at scuto f f ) sensitive tothe dissipation [Lauritsen et al., 1996], ξ ∼ (scuto f f /smax)−(bc−2)/dA L,

which is qualitatively similar to the standard definition (ξ ∼ s 1/dAcuto f f ).

However, for b > bc, the new definition brings the following conditionof criticality:

ξ(b)/L ∼ s−(b−bc)/dAmax ∼ 1, (35)

showing that the correlation length will decrease exponentially as theexponent value b gets larger than the critical value bc.

simulations: The analysis of the classical OFC earthquake model[Olami et al., 1992] will allow the validation of the condition ofcriticality. This model is a mapping of the Burridge-Knopoff spring-block model of earthquakes [Burridge and Knopoff, 1967] into acellular automaton (Fig. 28). The spring-block model considers anarray of blocks placed on a flat and fixed plate. Springs connect eachblock to its nearest neighbors and to a moving plate. Due to themovement of the plate the stress in each block increases. Eventually,the static friction between one block and the fixed plate is overcome,and a block slips. This may also provoke (or not) the sliding ofneighboring blocks, generating an avalanche with a size equal to thenumber of blocks involved in the process.

moving plate

fixed plate

f (x,y) Th (x,y)

Figure 28: Mapping of the Burridge-Knopoff spring-block model into theOFC model.Main rules of the OFC model:∀x, y fi(x, y) = fi−1(x, y) + δFi f [ fi(x, y) > Th(x, y)] thenfi(x, y ± 1) = fi(x, y ± 1) + α fi(x, y)/4fi(x ± 1, y) = fi(x ± 1, y) + α fi(x, y)/4fi(x, y) = 0

In a more realistic modification of the OFC model [Ramos et al.,2006] each site (corresponding to one block) stores the force value,f (x, y), that grows continuously until overcoming a local frictionthreshold Th(x, y) at a given site. Some portion α of the released forceis equally added to the nearest neighbors (provoking, or not, theirrelaxation) and some amount is lost (dissipation of energy). The force

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is then set to zero and a new friction threshold is attributed to the site.The size of an avalanche (earthquake) is the number of sites involvedin energy release events at a given time (between two consecutiveincreases of the global force). Simulations take place in a square latticeof side L = 256 sites, with open boundary conditions. The rules of thesimulations and the analysis of the correlation functions are detailedin [Ramos, 2010].

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101

102

-1

LDissipation

b = 5/3T

bcDlow

a b c

(<s>/<sc>)1/2LξDM

Dhigh 1Dhigh 2

Figure 29: Simulations in the OFC earth-quake model. Dissipation values gofrom 0% (critical scenario) to 44% in in-tervals of 4%, plus 1% and 2%. (a) Dis-tributions of avalanche sizes for differ-ent dissipation values. The critical value(1.27) and the one coinciding with theone of actual earthquakes (5/3) are indi-cated. The data is divided in four differ-ent zones (Dlow, T, Dhigh 1, Dhigh 2). (b)Exponent values as a function of the dis-sipation. (c) Correlation length both cal-culated through ξ(b) ∼ (〈s〉/〈sc〉)1/dA Land directly measured (ξDM) by theanalysis of the spatial autocorrelationfunction through equations (25) and(26).

The distributions of avalanche sizes for different dissipation val-ues [Dissipation = (1 − α) × 100%] appear in Fig. 29a, while theexponent values extracted from them are plotted in Fig. 29b. In theconservative case (critical scenario) the pdf is a power law with anexponent b = bc = 1.27. For very low dissipation values (1% and2%), denominated zone Dlow, the system has a standard behavior[Lauritsen et al., 1996, Le Doussal and Wiese, 2009], characterizedby a constant exponent value (actually b decreases a little) and acut-off that moves to smaller avalanche sizes as dissipation increases.However, for higher dissipation values (4% and 8%), zone T, a fasttransition occurs where the exponent value increases and the cut-offdisappears. Between 12% and 28%, (zone Dhigh 1), clear power lawsshow up with exponent values varying linearly with the dissipation(for much larger statistics a cut-off, associated to the size of the sys-tem, must appear [Ramos et al., 2006]). For high dissipation valuesbetween 32% and 44%, (zone Dhigh 2), the pdfs are still clear powerlaws with exponent values that increase with dissipation. Figure 29ccompares two different procedures to obtain the correlation length ξ.The first one uses the equation (34). The values of ξ as a function ofb − bc decay exponentially, with the exception of zone Dhigh 2, wherethe high exponent values provoke very low values of 〈s〉. The sec-ond method is the direct one: averaging the spatial autocorrelationfunctions during the whole simulations and fitting the results to ex-ponential decays (equations (25) and (26)). The obtained ξ values aresimilar to those from the first procedure, which vote in favor of thenew relation between correlation length and mean value of avalanche

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size (equation 34). The results of this section are still unpublished.Currently longer and more accurate simulations are under analysis inorder to validate the proposed approach. Understanding the criticalproperties of slowly-driven systems evolving through uncorrelatedand scale-invariant avalanches has a strong relevance, because a largepart of the scientific community considers that it is inherently impos-sible to predict large avalanches in those systems due to their criticalproperties [Main, 1999, Geller et al., 1997].

2.5: Towards prediction and Control

Several works have claimed the unpredictable character of phenomenaevolving through scale invariant avalanches as a consequence oftheir classification as critical systems [Main, 1999, Geller et al., 1997].However, in the last section it has been suggested that many ofthose systems may not be critical, which is a consequence of the largeexponent values of their power-laws compared to the critical exponentat their respective dimensions. If they are not critical, they may be,in principle, predictable; a fact that has been recently proved in bothexperiments and simulations.

Figure 30: (a) Distribution of avalanchesize for the granular experiment (circles).These points have been averaged witha logarithmic binning (diamonds) andthey follow a power-law with an expo-nent b = 1.6. Avalanches have been clas-sified as small (S), medium (M), large(L) and extra-large (XL). The percentageof occurrence of each type of avalancheis also displayed. (b) The average of theavalanche size around a large event (L)presents weak signs of foreshocks andaftershocks.

2.5.1: Predicting scale invariant avalanches

The first experiment where large avalanches were forecasted insidea regime of uncorrelated and power-law distributed events was per-formed during my PhD. in Oslo (see Fig. 7) and published in PRL in2009 [Ramos et al., 2009].

The experiment studies the dynamics of avalanches in a quasi-two-dimensional granular pile. It consists of a base of 60 cm rowof randomly spaced 4 mm steel spheres, sandwiched between two

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a b

Figure 31: (a) Portion of the granularpile where the color of each voronoi cellrepresents the value of the shape fac-tor. (b) Temporal cross-correlation be-tween the large avalanches and the aver-age shape factor.

parallel vertical glass plates 4.5 mm apart. The same steel beads aredelivered one by one from a height of 28 cm above the base andat its center, resulting in the formation of a quasi-two-dimensionalpile. The extremes of the base are open, leaving the beads free toabandon the pile. After a bead is delivered, the pile is recordedwith a digital camera at a resolution of 21 pixels/bead-diameter,followed by the dropping of a new bead. One experiment containsmore than 55000 dropping events with a total duration of more than310 hours. The first 4500 events before the pile reaches a stationarystate are not included in the statistics. The average number of beadsin the pile is 3315. The centers of all the particles for each imageare found, and the size of an avalanche is defined as the numberof beads that has moved between two consecutive dropping events.The distribution of avalanches follows a power-law with an exponentb = 1.6 (Fig. 30a). Avalanches are classified as small, medium, largeand extra-large; and the study focuses on predicting large and extra-large events. Foreshocks and aftershocks take place around largeavalanches (Fig. 30b). However, these signs are rather weak, andall the efforts to predict when a large avalanche is going to happendid not succeed: the analysis of the time series does not allow theprediction of large events.

As the position of the centers of each particle at every step of theexperiment is known, different structural variables can be definedand their evolution followed during all the experiment, particularlyin the neighborhood of a large avalanche. The shape factor ζ =

C2/4πS, where C is the perimeter and S the area of each voronoicell in which the structure has been divided (Fig. 31a), has beencomputed at each step of the experiment. ζ is equivalent to the localdisorder and inversely proportional to the packing fraction of the pile.The temporal cross-correlation between the shape factor (spatiallyaveraged) and the large avalanches read as:

C(t) = ∑ sb(ti)ζ(ti + t)− 〈sb(ti)〉〈ζ(ti)〉√∑(sb(ti)− 〈sb(ti)〉)2 ∑(ζ(ti)− 〈ζ(ti)〉)2

(36)

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where sb corresponds to the binary series of large (extra-large) events,i.e., 1 (one) if the avalanche is large (extra-large) and 0 (zero) otherwise.The results are shown in Fig. 31b. The continuous variation displayedby the average disorder of the pile before a large avalanche is veryclear74 and approximately fifty steps before a large event, the average74 Very similar results have been ob-

tained in a more realistic modificationof the OFC model [Ramos, 2010]. Inthis case the structural disorder corre-sponded to the standard deviation ofthe average force in the whole cell.

disorder continuously increases until the avalanche takes place. Thenthe pile reorganizes itself, but it gets trapped in an intermediatelevel of disorder. In the aftershocks zone, the disorder increases, andafter that, the pile slowly evolves into more organized states. Byusing the information relative to the average disorder and the helpof an extremely simple algorithm, it has been possible to reach up to62% and 64% of success in the predictability of large and extra-largeavalanches respectively. By changing the algorithm and adding moreinformation these odds can be improved.

These results broke the myth about the inherently unpredictabilityof large (catastrophic) events inside a regime of uncorrelated andpower-law distributed avalanches. However, the fact that the forecast-ing was based on the analysis of the internal structure, limited theapplication of these findings. Given the relevance of earthquakes, Idecided building an experiment trying to mimic the dynamic of atectonic fault, and where acoustics will be the main source of infor-mation.

the earthquake machine: Many different tabletop experimentshave already tried to simulate the dynamics of earthquakes. Theseexperiences are typically friction experiments or fracture experiments.In the case of subcritical fracture [Stojanova et al., 2014, Barò et al.,2013], different analogies to earthquakes have been found (Gutenberg-Richter law, Omori law, etc.). However, fracture experiments are,in general, non-stationary and they accelerate towards the total fail-ure of the material. In the case of shear experiences, some workshave studied the friction between two solid blocks [Ben-David et al.,2010, Rubinstein et al., 2007]. In this case the study generally focuseson one single event. Other experiments have sheared a granularlayer, trying to simulate the behavior of a tectonic fault. However,it has been difficult to obtain a distribution of events that resem-bles the Gutenberg-Richer law [Richter, 1935]. Sometimes becausethe intrinsic response of the system is a regular stick-slip with all"earthquakes" having approximately the same size [Johnson et al.,2008], and sometimes because of insufficient statistical sets of data[Daniels and Hayman, 2008, Walker et al., 2014]. Most of the recentshear experiments have a linear geometry. Consequently, the relativemotion between the two sliders is limited to a fraction of the length ofthe system, which is responsible for the insufficient data collection. Inorder to solve this problem, we have a shear experiment with periodicboundary conditions75 , allowing the system to run continuously and

75 Earlier experiments in granular sys-tems have also used cylindrical contain-ers in order to obtain periodic boundaryconditions and thus, a continuous shear[Miller et al., 1996, Howell et al., 1999,Tsai and Gollub, 2004]. However, theydid not pay attention to the statistics ofavalanches.

therefore capturing a very rich statistics.The experimental setup consists on two fixed, transparent, and

concentric cylinders, with a gap between them, so that a monolayerof birefringent disks can be introduced into the gap (see Fig. 32). The

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c d

Figure 32: The earthquake machine.

birefringent nature of the grains allows visualization of the internalforce chains in our granular material (close-up in Fig. 32). Two ringscontaining fixed grains will constrain the pack from upper and bottomboundaries (the yellow arrow in Fig. 32 indicate the force between theplates, controlled by a dead load). As the rings rotate in relation toeach other at a controlled and very low speed (blue arrow in Fig. 32),shear stresses build up on the packed beads, and eventually they areliberated through a sudden avalanche.

We use cylindrical grains of 4 mm thickness and 6.4 mm and7.0 mm diameter (in equal proportion) to avoid crystallization. Thesedisks are made of Durus White 430 and have been generated in aObjet30 3D printer. The translucent and photoelastic character of thegrains allows the visualization of the stress inside the disks whenplacing the experimental setup between two circular polarizers. TheYoung’s modulus of Durus material is E � 100 MPa. This contrastswith the classical experiments using photoelastic disks with a Young’smodulus E = 4 MPa [Walker et al., 2014, Miller et al., 1996, Howellet al., 1999, Majmudar et al., 2007, Zhang et al., 2010, Daniels andHayman, 2008, Owens and Daniels, 2011]. Our grains can hold amuch larger stress without a considerable deformation, which favorsboth the acoustic propagation and image analysis [Lherminier et al.,2014].

10−1

101

103

105

107

10−2 10−1 100 101β = −1.64

Figure 33: Distribution of avalanches,measured as torque variations and ex-pressed in arbitrary units (a. u).

Acoustic will be the main source of information in the experi-ment. However, the internal structure of the system (position ofthe grains and force networks) and the global applied torque willbe also monitored. Preliminary results focus on the analysis of thetorque, measured thanks to a steel lever and a force sensor SML-900

from Interface (of range 900 N) sampled at 10 Hz. The distribution

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!"

b b b #" 1

3

2

4

Figure 34: (a) Experimental setup. (b)Four different configurations.

of avalanches (measured as torque variations) follows a power lawwith an exponent b = 1.64 (Fig. 33) [Planet et al., 2015] . By increas-ing the load between the plates, the exponent value remains robustwhile the cut-off moves to larger avalanche sizes. The waiting timesbetween large events (size > 0.5 (in Fig. 33), which correspond to3% of the total of the events) distribute following an exponentialdecay, indicating no correlation between events (which is the casein real earthquakes). The waiting time between events of all sizesfollow a generalized gamma distribution: τ−γ exp

[− (τ/τ0)

δ]

withγ = 0.30 ± 0.05, τ0 = 9.5 ± 0.5 s and δ = 0.80 ± 0.04, which is alsoconsistent with the behavior extracted from real earthquakes data[Corral, 2004].

In the sandpile experiment [Ramos et al., 2009], the variationsin structural disorder were used to forecast the occurrence of largeavalanches. In the earthquake machine we expect having similarresults, but also detecting those variations76 with acoustic measure-

76 The existence of very low frequencymodes (denominated "Soft modes")[Wyart et al., 2005, Tanguy et al., 2010,Goodrich et al., 2013] in the vicin-ity of the transition where the systemloses its stability (unjamming event oravalanche), may serve as a precursor ofthe avalanche. ments. In order to analyze the structure of the system with acoustic

measurements, I designed a simple experiment to study the prop-agation of acoustic waves across a monolayer of the same granularmaterial as the earthquake machine. No shear was applied in this case,and the acoustic wave was generated by a loudspeaker connected toa metallic rod that hits one grain at the bottom of the system (see theexperimental setup in Fig. 34a). The confining force F was varied andthe speed of sound c measured in different structural configurations

Figure 35: c vs. F relation for a disor-dered structure.

(Fig. 34b). The relation c vs. F is a power law where the exponentvalue depends on the number of coordination number of the grains,being around 1/2 or 1/6 for 2 or 4 contacts/grain respectively. Themost interesting case is the disordered system (Fig. 34b4) where atcertain force value the system transits from an average configurationof 2 contacts/grain to 4 contacts/grain (Fig. 35) [Lherminier et al.,2014]. By analyzing the ratios between the vertical and horizontalvelocities cv/ch, it was possible to calculate the anisotropy of the

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structure and therefore differentiate between the structures 1 and 2 inFig. 34b (both with 4 contacts/grain). Thanks to the analysis of theacoustic signal it was possible to predict the internal structure of thesystem (either disordered or a particular crystalline structure). Wehave been able to link the c vs. F relations, measured globally, to theForce − de f ormation relation of a single grain when submitted to 2

points (or 4 points) deformation [Lherminier et al., 2014].unjamming: To understand (in order to predict) large avalanches

in scale-invariant phenomena, it is essential to focus first in the occur-rence of simple events. "Single avalanches" in granular media havebeen carefully analyzed by the community of "jamming" [Liu andNagel, 1998, Majmudar et al., 2007, Kolb et al., 2004], which has foundvery strong similarities between the dynamical behavior of granularmaterials close to the "jamming transition" and that of liquids closeto the glass transition [Liu and Nagel, 1998]. Indeed, granular mediaclose to jamming display a similar dramatic slowing down of thedynamics [Knight et al., 1995, D’Anna and Gremaud, 2001, Ovarlezand Clément, 2003], dynamical heterogeneities [Dauchot et al., 2005],as well as other glassy features such as aging [Ovarlez and Clément,2003] and memory effects [Josserand et al., 2000]. The existence ofvery low frequency modes (denominated "Soft modes") [Wyart et al.,2005, Tanguy et al., 2010, Goodrich et al., 2013] in the vicinity ofthe transition where the system loses its stability (unjamming eventor avalanche), may serve as a precursor of the avalanche. We willpay a special attention to this effect as a possible way to predict theemergence of catastrophic events in our system.

2.5.2: Origin & Control

Gaussian Gaussian Gaussian

Power law Power law Power law

Quasi-periodic Quasi-periodic Quasi-periodic Dis

ord

er

Figure 36: Disorder is able to modifythe distribution of avalanche sizes in asystem with an energy gap.

influence of the disorder: We have performed experiments [Alt-shuler et al., 2001] and simulations [Ramos et al., 2006] showing thekey role of the structural disorder in achieving power-law distributionsof avalanche sizes. In the granular pile, two angles define the en-ergy gap: the subcritical angle and the supercritical angle [Daerrand Douady, 1999]. In ideal conditions (little disorder and largefriction) a trivial periodic behavior rules the dynamics [Jaeger et al.,1989, Rosendahl et al., 1993], charging and discharging the energygap. In the earthquake model [Olami et al., 1992, Ramos et al., 2006]there is some elastic energy increasing continuously in every site ofa given lattice, which is limited by local thresholds related to a localstatic friction coefficient. In that case, the largest possible avalanchehappens when all the sites have reached their thresholds at the sametime and, with the trivial condition of a flat distribution of thresholds,a trivial periodic behavior also rules the dynamics.

If the structural disorder in the granular pile is large enough, theperiodicity is broken and avalanches become temporally uncorrelatedwith sizes distributed following a power-law [Frette et al., 1996, Alt-shuler et al., 2001, Ramos et al., 2009]. In the case of the earthquakemodel, a more realistic Gaussian distribution of static friction thresh-

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olds will be sufficient in order to obtain a power-law distributionof events [Ramos et al., 2006]; however, some signs of periodicity(proportional to the dissipation) are still present in the dynamics. Byintroducing more disorder (a Gaussian distribution of the values ofthe dissipation), the periodicity is broken while the avalanche size dis-tribution remains as a power-law. Nevertheless, increasing even morethe values of the standard deviation of the Gaussian distribution willlead to the removal of the power-law behavior [Ramos et al., 2006]. Inthe limit of a very high disorder, the accumulation of energy in largequantities must be very instable, spatial correlations must have veryshort range and the system may show a Gaussian behavior (Fig. 36).

controlling scale-invariant avalanches: We have dis-cussed both the influence of the dissipation and disorder in thedynamics of scale-invariant avalanches. Dissipation may change theexponent value of the power-law distribution, while our results indi-cate that the scale-invariant behavior takes places in a given windowof disorder. Besides the scientific interest of gaining a better under-standing of the dynamics of scale-invariant avalanches, the obtainedknowledge may offer strategies in order to control this dynamics [Noëlet al., 2013, Cajueiro and Andrade, 2010], with the main objective ofavoiding the generation of catastrophic events. A classical exampleis the controlled early triggering in snow avalanches, which aimsavoiding the occurrence of large avalanches in ski resorts. After theeconomical crisis of 2008, introducing more regulation in the financesin order to avoid financial bubbles is often a subject of discussion[Holt, 2009, Rothkopf, 2013]. In the case of earthquakes, the fact thathumans can generate earthquakes (currently unwanted) [Ellsworth,2013, Parsons et al., 2008] may be eventually a way to control therelease of energy in the faults, in a similar manner that today’s snowavalanches.

2.6: Future projetcs

Continuing the "earthquake machine" project is the main immediatetask concerning scale-invariant avalanches. The eventually applicationof the obtained results to real earthquake data may be a project toexplore in the future, in a similar way we are currently doing in thecase of subcritical fracture (see section 3.1.3).

The relation of the exponent value of the power law distribution ofavalanche sizes with dissipation, and with the critical properties ofthe dynamics, is the other immediate task already being developed inthis subject.

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Chapter 3: Other major Risks

Buildings must support considerable stress during many decades.However, in the pursuit of both artistic expression and wide openspaces, designs are constantly evolving towards thinner, lighter andmore challenging structures (Fig. 37), pushing sometimes architectsand engineers to approach the borders of safety margins (Fig. 38).

Figure 37: Modern architecture:Nord/LB, Hannover. Photo source:Roel Hemkes (c.c.)

We have analyzed the subcritical propagation of a crack inside adisordered medium. By adding two different spatial distributionsof micro-defects into the material, we have noticed that the crackpropagates faster in a more disordered scenario, which is a conse-quence of the accumulation of micro-defects in the structure of thesystem. However, the standard methods testing material’s resistancedo not notice any difference between the two configurations, whichsuggest that these safety margins may not be very well defined [Ramoset al., 2013]. We have also monitored the propagation of the crackby using acoustic measurement, detecting the occurrence of very fastaftershocks (not noticed in earlier works in the same system due to aslower data acquisition). By changing the number ratio between largeand small events, these aftershocks modify the statistics of avalanchesizes [Stojanova et al., 2014]. Currently we are analyzing the sameissue in real earthquakes, and the results are very similar to thoseobtained in subcritical fracture.

Another safety issue related to modern buildings is the evacuationof people in case of an emergency (a fire, a terrorist attack, etc.).We have performed experiments (using ants as model pedestrians)proving that when individuals under panic try to escape from a roomwith two symmetrically located exits, one exit is more used than the

Figure 38: On 23 May 2004, 11 monthsafter its inauguration, a portion of Ter-minal 2E at Charles de Gaulle airport inParis, collapsed early in the day, killingfour people. "The 750m-euro buildingwas not designed to support the stress itwas put under, and the concrete used inits shell weakened gradually to a pointthat pillars pierced through it, the re-port said" (BBC news). Photo source:civildigital.com.

other one [Altshuler et al., 2005]. This is related to a "follow-the-crowd" effect, and may have grave consequences. Field studies havealso shown that, in nature, ants operate "at-the-edge of chaos", whichprovides a required flexibility in the case of changing the environ-mental conditions [Nicolis et al., 2013]. Currently we are analyzinghow the information of panic propagates in the colony.

3.1: Fracturing slowly

It is intuitive that, beyond a certain critical value, applying a loadto a material will bring a sudden failure of the structure. However,even a subcritical load can provoke the breaking of the structure, butin a time dependent manner; by the intermittent (in the case of an

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heterogeneous material) and slow growth of an initial crack until itreaches a length where the whole sample rapidly breaks apart. Thisprocess is known as subcritical fracture [Måløy et al., 2006, Vanel et al.,2009].

3.1.1: Where are the safety margins in subcritical fracture?

In order to improve our understanding of this phenomenon, we havebeen able to introduce defects in the structure of a disordered system(a sheet of paper). Artificial disorder was created by adding twodifferent patterns of holes of 120 µm diameter along the crack path(see Fig. 8): one with holes distributed regularly (unimodal), andanother alternating short and long distances (bimodal), while keepingthe same hole density. The samples, containing an initial crack of 3 cmlength, were submitted to a constant force, resulting in a subcriticalpropagation of the crack. Rupture dynamics turns out to be fasterin the bimodal distribution (Fig. 39a), provoked by the accelerationof the crack in the short inter-hole distances. This effect shows theconsequences of the accumulation of micro-defects in the structure ofthe system: the acceleration of the crack [Ramos et al., 2013].

L (mm)

Tim

e (s

) Fo

rce

(N)

d (mm)

a

b

Figure 39: a) time vs.crack length from(red) unimodal and (blue) bimodal dis-tributions of holes. The shadowed areascorrespond to the standard deviation ofthe data. They are limited by a thinsolid line. b) Force vs elongation for 18

samples [nine unimodals (red) and ninebimodals (blue)] submitted to a loadingrate of 45 µm/s.

More striking is the fact that, instead of applying a constant load,if a deformation ramp is imposed leading to the failure of the sam-ples, no difference is noticed between the two different configurations(Fig. 39b). This test is much more common for analyzing materi-als’ properties. However, the results of this work indicate that it isarguably not the best way to test a structure built for supporting aconstant load [Ramos et al., 2013].

3.1.2: When very long processes require very fast measurements

As discussed in the first chapter, earthquakes, snow avalanches, sub-critical fracture, and many other phenomena where the energy isaccumulated very slowly and liberated by sudden episodes, havepower law distributions of "avalanche" sizes. Our work in subcriti-cal fracture [Stojanova et al., 2014] has shown that the existence oftime correlations between events in form of aftershocks modifies theexponent of the power law distribution of avalanche sizes when the

498,2 498,25 498,3−2

−1

0

1

2x 10

4

time (s)

bits

F

F

5 mm

Figure 40: Schema of the experimen-tal setup with typical examples of bothan acoustic signal, recorded by a piezo-electric transducer, and an image. Theimage also shows the paths resultingfrom adding consecutive crack advancesdefined as sl , ss, and s (from top to bot-tom).

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events are analyzed at larger time scales than the typical correlationtime.

This main result was understood during the study of a subcriti-cal crack growth in a sheet of paper containing an initial crack andsubmitted to a constant force. Both acoustics and imaging techniqueshave been used to follow the crack propagation (Fig. 40). Both meth-ods result in a similar intermittent dynamics, with a larger number ofevents for the acoustic measurements. The time distributions betweensuccessive events are the same for both measurement. However, thedistributions of avalanche energies, which are both power law distri-butions, present different exponent values: 1.51± 0.06 for the acousticmeasurement (at 2 MHz) and 1.3 ± 0.1 for the visual measurements:ss and sl (at 10 Hz). ss corresponds to the size of the "jump", definedas the distance between the crack tip of two successive images; and sl

is defined as the projection of ss on the initial direction of the crack.Although the whole rupture process may last for more than half anhour, there are aftershocks associated to large energy events with atypical correlation time around 1ms. Image analysis operating at 10Hz, unable to resolve these aftershocks, delivers a misleading expo-nent value. By integrating the acoustic signal (measured at 2 MHz)in larger time windows, we find a dependence of the exponent valuewith the time window (recovering the value obtained by the images at10 Hz). This dependence disappears when time correlations betweenevents are artificially removed (Fig. 41). Similar results have beenfound by simulation in a fiber bundle model [Danku and Kun, 2013].

Figure 41: (Red) The exponent valuechanges with the window of analysis,which is a consequence of aftershockshaving a time correlation around 10−3s. (Green) After artificially removingthe time correlations between events, theexponent remains constant. (Grey) Timezone of the image analysis.

An important consequence of this effect is the fact that a lowfrequency acquisition (or analysis) of power law distributed events,may lead to a misleading exponent value. This exponent, whichrelates the number of catastrophic events to the number of smallones, is the most relevant variable in the characterization of a scaleinvariant dynamics. Currently we are doing the same analysis in thetime series of real earthquakes, obtaining similar results and trying toestablish relations between the two most relevant laws in seismicity:the Gutenberg-Richter (power-law distribution of earthquakes size)and the Omori law (aftershocks’ statistics).

3.1.3: Future projects: fracturing at the micro-scales

Besides trying to apply the results obtained in subcritical fracture toearthquakes, the continuation of these projects will focus on what hap-pens at the micro-scales. So far, in all the experiments performed inour group, the stress is applied globally, at the scale of the whole sam-ple (typically 21cm [Santucci et al., 2004, Ramos et al., 2013, Stojanovaet al., 2014], and both direct imaging and acoustic measurementshave been used to analyze the fracture process, which consists ofa succession of failures at the fibre level. A future project will aimstudying the rupture process of single fibers, which have diametersbetween a few microns and a few hundreds of nanometers.

The breaking of individual fibers will be a great step in the under-

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standing of the subcritical fracture in heterogeneous materials. Hereare some examples of relevant questions that may be answered by thisproject: The global process follows a power law distribution of events’energy; is this a consequence of a wide distribution of fibre diametersonly, or also of an avalanche process where a few fibers break veryclose in time? Is the rupture of a fibre a simple process or is it acomplex one, with substructures that may also break subcritically?What are the characteristics of the typical acoustic emission linkedto a fibre failure? And how does this compare to the acoustic eventsrecorded globally [Stojanova et al., 2014]? What is the influence ofthe temperature (in particular its fluctuations) during the fractureprocess? These questions may also help understanding the energybudged during the fracture, as well as directly validating the thermalactivated nature of the subcritical fracture in heterogeneous materials.

3.2: Pedestrians in Panic

Figure 42: Symmetry breaking in escap-ing ants.

It is not possible to overestimate the importance of the study of crowdstampede induced by panic, such as that taking place when peopletry to escape from a burning room. In these situations the "follow-the-crowd" effect associated with imitation may have grave consequences.In the year 2000 a theoretical article [Helbing et al., 2000] made an im-portant step forward in this subject, where simulations of individualsescaping from a closed room were presented. That work has beenrapidly followed by further theoretical models and by experimentsin rats [Saloma et al., 2003] and humans [Helbing et al., 2003, 2007],with no control in the panic level. One of the most unexpectedphenomena predicted in the article [Helbing et al., 2000] is the panic-induced symmetry breaking in the escape from a room with two exits.When individuals under panic try to escape from a room with twosymmetrically located exits, one of them is more used than the otherone.

a

b

Figure 43: Histograms showing the per-centage difference in the use of the twodoors for (a) low-panic and (b) high-panic conditions.

We have performed experiments [Altshuler et al., 2005] that demon-strate the correctness of such prediction. We have been able to exam-ine low- and high-panic scenarios, using ants as model pedestrians.In addition, we have reported the details of the temporal evolutionin their escape in low- and high-panic conditions and show that itcan be described by a simple computer model inspired by that re-ported by [Helbing et al., 2000]. Our experiments show that escapebehavior under panic can be amazingly similar from invertebrates tovertebrates.

The experimental setup consisted of a cell of 8 cm diameter, 0.5cm height, and two symmetrical exits 1 cm wide (Fig. 42). In a firstexperiment (1), 66 ants77 were introduced in the cell and at the time77 Atta insularis (common name Bibi-

jagua). t0 = 0 both exits were simultaneously open. Under these (low-panic)conditions, ants leave the cell by using both exits with (statistically)the same proportion (Fig. 43a). In a second experiment (2), everythingtook place as in experiment 1, with the important difference beingthat a few seconds before opening the doors, a dose of 50 mL of

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an insect-repelling liquid (citronella, Labiofam, Cuba) was rapidlyinjected into the cell through the hole in the cover glass, producing adisk- shaped spot of the substance at the center of the filtering paperon which the whole setup rested. Under these (high-panic) conditions,a symmetry-breaking takes place: Fig. 43b shows that ants (statistically)use one exit more than the other (however there is no distinctionfor a particular exit)78. With simple simulations having as main

78 Experiments 1 and 2 were repeated 30

times. In each repetition, a new groupof ants collected from a single nest wasused.ingredient the "follow-the-crowd" effect it was possible to perfectly

fit the escaping dynamic of the ants in both experimental situations[Altshuler et al., 2005]. The effect was illustrated by a modificationof the direction of the trajectory �ek of each ant in the next time step(k + 1) through:

�ek+1 =(1 − p)�ek + p〈�e herd

k 〉‖(1 − p)�ek + p〈�e herd

k 〉‖ (37)

Time (days)

Temperature (0C)

Activity (number of ants)

403530

40302010

0 1 2 3 4 5 6 7

Figure 44: Activity and temperature,measured at 2 Hz, at the nest exit.

where p ∈ [0, 1] correspond to the "panic parameter" (equal to 0 inexperiment 1 and fitted to 0.8 in experiment 2). p determines thetendency of an ant to "follow the crowd" (the extreme cases are p = 0,where the ant acts "individualistically" and keeps moving in theprevious direction and p = 1, where it reorients to follow the crowd).〈�e herd

k 〉 is the average unit vector of the velocities of neighboring antsinside the cell located within a radius Rh = 3.5 cm from the ant understudy at computer step k. This work was performed at the Universityof Havana, under the direction of Ernesto Altshuler.

Ernesto’s group focused then on field experiments. A customizedsensor was created and set on the nest exit [Noda et al., 2006], count-ing the number of ants passing through it (a variable denominatedactivity). Temperature and light were also measured (Fig. 44). I partic-ipated in the analysis of the data. The activity shows a quasi-periodicbehavior (period ∼ 24 hours) having a time shift with respect to thetemperature. Nonlinear differential equations were used to modelthe coupling between the self-excitatory interactions of individualsand external forcing (the temperature). At the transition betweenquasiperiodic and chaotic regimes, activity cycles are asymmetrical,with rapid activity increases and slower decreases and a phase shiftbetween external forcing and activity [Nicolis et al., 2013]. We find

Figure 45: Two cells in contact througha window with thins bars, allowing an-tenna contacts between ants. Insect-repelling liquid has been added at thecenter of one cell (top) provoking thepanic of the ants in the cell. The analysisfocuses on the behavior of the ants inthe other cell (bottom).

similar activity patterns in ant colonies in response to varying temper-ature during the day, indicating that foraging ants operate in a regionof quasiperiodicity close to a cascade of transitions leading to chaos.This "at-the-edge of chaos" dynamics allows a very flexible responseto external forcing, and may be an evolutive advantage for the colony[Nicolis et al., 2013].

Currently, we are studying how the information of panic prop-agates in the colony. By building two adjacent cells with different"semipermeable" walls separating them, we try to find under whichconditions the information of panic propagates from the ants of onecell to the ants in the adjacent cell. One wall, consisting of a glasswindow, allows passing just visual information; a second wall con-sists of thick bars, lets passing more information, but does not allow

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antenna contact between the ants of different cells; and a third wallconsists of thin bars (Fig. 45), allowing antenna contacts. Preliminaryresults indicates that the information of panic propagates through theantenna contacts.

3.2.1: Future projects: jamming under panic

The first future project is the continuation of "how the informationof panic propagates in the colony", which is a collaboration with theUniversity of Havana. Besides that, I would also like to start studyingdifferent strategies in order to maximize the escaping of people inpanic from a confined space, where jamming can be fatal. Somestudies have suggested putting an obstacle (column) in front of theexit, in order to reduce the clogging, which has given positive resultsboth in granular hoppers [Zuriguel et al., 2011] and in a sheep herdpassing through a bottleneck [Zuriguel et al., 2014, Garcimartín et al.,2015]. Others works present a more efficient evacuation if doors areset in the corner of a room (however, their simulations have foundless efficient the use of an obstacle in front of the exit) [Shiwakotiet al., 2011].

Due to the scarcity of data of humans under panic, it is difficultto validate the results of the simulations [Shiwakoti and Sarvi, 2013],and many of the results obtained in other species (ants, sheep, rats)may not be directly mapped into a possible human behavior [Soriaet al., 2012, Shiwakoti and Sarvi, 2013]. Developing more realisticsimulations, controlled experiments and analysis of the available data[Helbing et al., 2007, Moussaïd et al., 2011, Silverberg et al., 2013,Karamouzas et al., 2014] is essential to a better understanding ofpedestrians, and in a more general frame, traffic [Helbing, 2001] andhuman nature [Alnabulsi and Drury, 2014].

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Bibliography

C. M. Aegerter, R. Günther, and R. J. Wijngaarden. Avalanche dynam-ics, surface roughening, and self-organized criticality: Experimentson a three-dimensional pile of rice. Phys. Rev. E, 67:051306, 2003.

C. M. Aegerter, K. A. Lörincz, M. S. Welling, and R. J. Wijngaarden.Extremal dynamics and the approach to the critical state: Experi-ments on a three dimensional pile of rice. Phys. Rev. Lett., 92:058702,2004.

H. Alarcón, O. Ramos, L. Vanel, F. Vittoz, F. Melo, and J.-C. Gémi-nard. Softening Induced Instability of a Stretched Cohesive GranularLayer. Phys. Rev. Lett., 105:208001, 2010.

Hani Alnabulsi and John Drury. Social identification moderatesthe effect of crowd density on safety at the hajj. Proceedings of theNational Academy of Sciences, 111(25):9091–9096, 2014.

Preben Alstrøm. Mean-field exponents for self-organized criticalphenomena. Phys. Rev. A, 38:4905–4906, 1988.

E. Altshuler and T. H. Johansen. Colloquium : Experiments in vortexavalanches. Rev. Mod. Phys., 76:471–487, 2004.

E. Altshuler, O. Ramos, C. Martínez, L. E. Flores, and C. Noda.Avalanches in One-Dimensional Piles with Different Types of Bases.Phys. Rev. Lett., 86:5490–5493, 2001.

E. Altshuler, O. Ramos, E. Martínez, A. J. Batista-Leyva, A. Rivera,and K. E. Bassler. Sandpile Formation by Revolving Rivers. Phys.Rev. Lett., 91:014501, 2003.

E. Altshuler, T. H. Johansen, Y. Paltiel, P. Jin, K. E. Bassler, O. Ramos,G. F. Reiter, E. Zeldov, and C. W. Chu. Experiments in superconduct-ing vortex avalanches. Physica C, 410:501–504, 2004a.

E. Altshuler, T. H. Johansen, Y. Paltiel, Peng Jin, K. E. Bassler,O. Ramos, Q. Y. Chen, G. F. Reiter, E. Zeldov, and C. W. Chu. Vor-tex avalanches with robust statistics observed in superconductingniobium. Phys. Rev. B, 70:140505, 2004b.

E. Altshuler, O. Ramos, Y. Nunez, J. Fernández, A. J. Batista-Leyva,and C. Noda. Symmetry Breaking in Escaping Ants. Am. Nat., 166

(6):643–649, 2005.

Page 66: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

66

P. Bak. How Nature works-The Science of Self-organized Criticality.Oxford Univ. Press, Oxford, 1997.

Per Bak and Chao Tang. Earthquakes as a self-organized criticalphenomenon. Journal of Geophysical Research: Solid Earth, 94(B11):15635–15637, 1989.

Per Bak, Chao Tang, and Kurt Wiesenfeld. Self-organized criticality:An explanation of the 1/ f noise. Phys. Rev. Lett., 59:381–384, 1987.

H. Barkhausen. Zwei mit hilfe der neuen verstärker entdeckte er-scheinugen. Physik Z, 20:401–403, 1919. (Two phenomena, discoveredwith the help of the new amplifiers).

Jordi Barò, Álvaro Corral, Xavier Illa, Antoni Planes, Ekhard K. H.Salje, Wilfried Schranz, Daniel E. Soto-Parra, and Eduard Vives.Statistical similarity between the compression of a porous materialand earthquakes. Physical Review Letters, 110:088702, 2013.

Kevin E. Bassler and Maya Paczuski. Simple model of superconduct-ing vortex avalanches. Phys. Rev. Lett., 81:3761–3764, 1998.

O. Ben-David, G. Cohen, and J. Fineberg. The dynamics of the onsetof frictional slip. Science, 330:211, 2010.

K. W. Birkeland and C. C. Landry. Power-laws and snow avalanches.Geophysical Research Letters, 29(11):49–1–49–3, 2002.

S. T. Bramwell, P. C. W. Holdsworth, and J.-F. Pinton. Universalityof rare fluctuations in turbulence and critical phenomena. Nature,396:552–554, 1998.

S. T. Bramwell, K. Christensen, J.-Y. Fortin, P. C. W. Holdsworth,H. J. Jensen, S. Lise, J. M. López, M. Nicodemi, J.-F. Pinton, andM. Sellitto. Universal fluctuations in correlated systems. Phys. Rev.Lett., 84:3744–3747, 2000.

Steven T. Bramwell. The distribution of spatially averaged criticalproperties. Nat Phys, 5:443–447, 2009.

R. Burridge and L. Knopoff. Model and theoretical seismicity. Bull.Seismol. Soc. Am., 57:341–371, 1967.

Daniel O. Cajueiro and R. F. S. Andrade. Controlling self-organizedcriticality in sandpile models. Phys. Rev. E, 81:015102, 2010.

Alessandro Chessa, H. Eugene Stanley, Alessandro Vespignani, andStefano Zapperi. Universality in sandpiles. Phys. Rev. E, 59:R12–R15,1999.

Maxime Clusel, Jean-Yves Fortin, and Peter C. W. Holdsworth. Crite-rion for universality-class-independent critical fluctuations: Exampleof the two-dimensional ising model. Phys. Rev. E, 70:046112, 2004.

Álvaro Corral. Long-term clustering, scaling, and universality in thetemporal occurrence of earthquakes. Phys. Rev. Lett., 92:108501, 2004.

Page 67: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

67

A. Daerr and Douady. Two types of avalanche behaviour in granularmedia. Nature, 399:241, 1999.

Karen E. Daniels and Nicholas W. Hayman. Force chains in seismo-genic faults visualized with photoelastic granular shear experiments.Journal of Geophysical Research: Solid Earth, 113(B11):2156–2202, 2008.

Zsuzsa Danku and Ferenc Kun. Creep rupture as a non-homogeneous poissonian process. Sci. Rep., 3:2688, 2013.

G. D’Anna and G. Gremaud. The jamming route to the glass statein weakly perturbed granular media. Nature, 413:407–409, 2001.

O. Dauchot, G. Marty, and G. Biroli. Dynamical heterogeneity closeto the jamming transition in a sheared granular material. Phys. Rev.Lett., 95:265701, 2005.

Brian R. Dennis. Solar hard x-ray bursts. Solar Physics, 100(1-2):465–490, 1985.

A. Díaz-Guilera. Dynamic renormalization group approach to self-organized critical phenomena. EPL (Europhysics Letters), 26(3):177,1994.

M. J. Dunlavy and D. Venus. Critical slowing down in the two-dimensional ising model measured using ferromagnetic ultrathinfilms. Phys. Rev. B, 71:144406, 2005.

William L. Ellsworth. Injection-induced earthquakes. Science, 341

(6142):1225942, 2013.

G. T. Fechner. Elemente der Psychophysik. Breitkopf und Härtel,Leipzig, 1860.

Stuart Field, Jeff Witt, Franco Nori, and Xinsheng Ling. Supercon-ducting vortex avalanches. Phys. Rev. Lett., 74:1206–1209, 1995.

Vidar Frette, Kim Christensen, Anders Malthe-Sørenssen, Jens Fed-ers, Torstein Jøssang, and Paul Meakin. Avalanche dynamics in apile of rice. Nature, 379:49–52, 1996.

Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, andH. Eugene Stanley. A theory of power-law distributions in financialmarket fluctuations. Nature, 423:267–270, 2003.

A. Garcimartín, J. M. Pastor, L. M. Ferrer, J. J. Ramos, C. Martín-Gómez, and I. Zuriguel. Flow and clogging of a sheep herd passingthrough a bottleneck. Phys. Rev. E, 91:022808, 2015.

Robert J. Geller, David D. Jackson, Yan Y. Kagan, and FrancescoMulargia. Earthquakes cannot be predicted. Science, 275(5306):1616,1997.

Carl P. Goodrich, Wouter G. Ellenbroek, and Andrea J. Liu. Stabilityof jammed packings i: the rigidity length scale. Soft Matter, 9:10993–10999, 2013.

Page 68: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

68

Beno Gutenberg and Charles F. Richter. Magnitude and energy ofearthquakes. Annali di Geofisica, 9:1–15, 1956.

D. Hamon, M. Nicodemi, and H. J. Jensen. Continuously driven ofc:A simple model of solar flare statistics. Astronomy and Astrophysics,387(1):326–334, 2002.

Thomas C. Hanks and Hiroo Kanamori. A moment magnitude scale.Journal of Geophysical Research: Solid Earth, 84(B5):2348–2350, 1979.

T. E. Harris. The theory of branching processes. Springer-Verlag, Berlin,1963.

D. Helbing, I. Farkas, and T. Vicsek. Simulating dynamical featuresof escape panic. Nature, 407:487 – 490, 2000.

Dirk Helbing. Traffic and related self-driven many-particle systems.Rev. Mod. Phys., 73:1067–1141, 2001.

Dirk Helbing, Motonari Isobe, Takashi Nagatani, and Kouhei Taki-moto. Lattice gas simulation of experimentally studied evacuationdynamics. Phys. Rev. E, 67:067101, 2003.

Dirk Helbing, Anders Johansson, and Habib Zein Al-Abideen. Dy-namics of crowd disasters: An empirical study. Phys. Rev. E, 75:046109, 2007.

G. A. Held, D. H. Solina, H. Solina, D. T. Keane, W. J. Haag, P. M.Horn, and G. Grinstein. Experimental study of critical-mass fluctua-tions in an evolving sandpile. Phys. Rev. Lett., 65:1120–1123, 1990.

Jeft Holt. A summary of the primary causes of the housing bubbleand the resulting credit crisis: A non-technical paper. The Journal ofBusiness Inquiry, 8:120–129, 2009.

Daniel Howell, R. P. Behringer, and Christian Veje. Stress fluctuationsin a 2d granular couette experiment: A continuous transition. Phys.Rev. Lett., 82:5241–5244, 1999.

Chin-Kun Hu. Percolation, clusters, and phase transitions in spinmodels. Phys. Rev. B, 29:5103–5108, 1984.

H. M. Jaeger, Chu-heng Liu, and Sidney R. Nagel. Relaxation at theangle of repose. Phys. Rev. Lett., 62:40–43, 1989.

E. A. Jagla. Realistic spatial and temporal earthquake distributionsin a modified olami-feder-christensen model. Phys. Rev. E, 81:046117,2010.

H. J. Jensen. Self-organized Criticality, Emergent Complex Behavior inPhysical and Biological Systems. Cambridge Univ. Press, Cambridge,1998.

Paul A. Johnson, Heather Savage, Matt Knuth, Joan Gomberg, andChris Marone. Effects of acoustic waves on stick-slip in granularmedia and implications for earthquakes. Nature, 451:57, 2008.

Page 69: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

69

Christophe Josserand, Alexei V. Tkachenko, Daniel M. Mueth, andHeinrich M. Jaeger. Memory effects in granular materials. Phys. Rev.Lett., 85:3632–3635, 2000.

S. Joubaud, A. Petrosyan, S. Ciliberto, and N. B. Garnier. Experimen-tal evidence of non-gaussian fluctuations near a critical point. Phys.Rev. Lett., 100:180601, 2008.

Ioannis Karamouzas, Brian Skinner, and Stephen J. Guy. Universalpower law governing pedestrian interactions. Phys. Rev. Lett., 113:238701, 2014.

James B. Knight, Christopher G. Fandrich, Chun Ning Lau, Hein-rich M. Jaeger, and Sidney R. Nagel. Density relaxation in a vibratedgranular material. Phys. Rev. E, 51:3957–3963, 1995.

H. V. Koch. Sur une courbe continue sans tangente, obtenue par uneconstruction géométrique élémentaire. Arkiv för matematik, astronomioch fysik, 1:681–704, 1904.

Évelyne Kolb, Jean Cviklinski, José Lanuza, Philippe Claudin, andÉric Clément. Reorganization of a dense granular assembly: Theunjamming response function. Phys. Rev. E, 69:031306, 2004.

Kent Bækgaard Lauritsen, Stefano Zapperi, and H. Eugene Stan-ley. Self-organized branching processes: Avalanche models withdissipation. Phys. Rev. E, 54:2483–2488, 1996.

Pierre Le Doussal and Kay Jörg Wiese. Size distributions of shocksand static avalanches from the functional renormalization group.Phys. Rev. E, 79:051106, 2009.

Youngki Lee, Luis A. Nunes Amaral, David Canning, Martin Meyer,and H. Eugene Stanley. Universal features in the growth dynamicsof complex organizations. Phys. Rev. Lett., 81:3275–3278, 1998.

S. Lherminier, R. Planet, G. Simon, L. Vanel, and O. Ramos. Reveal-ing the Structure of a Granular Medium through Ballistic SoundPropagation. Phys. Rev. Lett., 113:098001, 2014.

Andrea J. Liu and Sidney R. Nagel. Nonlinear dynamics: Jammingis not just cool any more. Nature, 396:21–22, 1998.

S. Lübeck and K. D. Usadel. Bak-tang-wiesenfeld sandpile modelaround the upper critical dimension. Phys. Rev. E, 56:5138–5143,1997.

Kinga A. Lörincz and Rinke J. Wijngaarden. Edge effect on thepower law distribution of granular avalanches. Phys. Rev. E, 76:040301, 2007.

Knut Jørgen Måløy, Stéphane Santucci, Jean Schmittbuhl, and Re-naud Toussaint. Local waiting time fluctuations along a randomlypinned crack front. Phys. Rev. Lett., 96:045501, 2006.

Page 70: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

70

Ian Main. Is the reliable prediction of individual earthquakes arealistic scientific goal? Nature, 1999. URL http://www.nature.com/

nature/debates/earthquake/.

T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer. Jammingtransition in granular systems. Phys. Rev. Lett., 98:058001, 2007.

Benoît B. Mandelbrot. Les Objets fractals, forme, hasard et dimension.Flammarion, Paris, 1975.

Benoît B. Mandelbrot. The fractal geometry of nature. W. H. Freemanand Co. cop., New York, 1983.

E. Martínez, C. Pérez-Penichet, O. Sotolongo-Costa, O. Ramos, K. J.Måløy, S. Douady, and E. Altshuler. Uphill solitary waves in granularflows. Phys. Rev. E, 75:031303, 2007.

Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosen-bluth, Augusta H. Teller, and Edward Teller. Equation of statecalculations by fast computing machines. The Journal of ChemicalPhysics, 21(6):1087–1092, 1953.

Brian Miller, Corey O’Hern, and R. P. Behringer. Stress fluctuationsfor continuously sheared granular materials. Phys. Rev. Lett., 77:3110–3113, 1996.

Mehdi Moussaïd, Dirk Helbing, and Guy Theraulaz. How simplerules determine pedestrian behavior and crowd disasters. Proceedingsof the National Academy of Sciences, 108(17):6884–6888, 2011.

J. Nase, C. Creton, O. Ramos, L. Sonnenberg, T. Yamaguchi, andA. Lindner. Measurement of the receding contact angle at the inter-face between a viscoelastic material and a rigid surface. Soft Matter,6:2685–2691, 2010.

J. Nase, O. Ramos, C. Creton, and A. Lindner. Debonding energy ofPDMS. A new analysis of a classic adhesion scenario. Eur. Phys. J. E,36:103, 2013.

N. Nerone, M. A. Aguirre, A. Calvo, D. Bideau, and I. Ippolito.Instabilities in slowly driven granular packing. Phys. Rev. E, 67:011302, 2003.

M. E. J. Newman and G. T. Barkema. Monte Carlo Methods in StatisticalPhysics. Oxford Univ. Press, New York, 1999.

S. C. Nicolis, J. Fernández, C. Pérez-Penichet, C. Noda, F. Tejera,O. Ramos, D. J. T. Sumpter, and E. Altshuler. Foraging at the Edgeof Chaos: Internal Clock versus External Forcing. Phys. Rev. Lett.,110:268104, 2013.

C. Noda, J. Fernández, C. Pérez-Penichet, and E. Altshuler. Measur-ing activity in ant colonies. Review of Scientific Instruments, 77(12):126102, 2006.

Page 71: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

71

Pierre-André Noël, Charles D. Brummitt, and Raissa M. D’Souza.Controlling self-organizing dynamics on networks using modelsthat self-organize. Phys. Rev. Lett., 111:078701, 2013.

S. P. Obukhov. The upper critical dimension and -expansion forself-organized critical phenomena. In E. Stanley and N. Ostrowsky,editors, Random Fluctuations and Pattern Growth, pages 336–344. Klu-ver Academic, Dordrecht, 1989.

Zeev Olami, Hans Jacob S. Feder, and Kim Christensen. Self-organized criticality in a continuous, nonconservative cellular au-tomaton modeling earthquakes. Phys. Rev. Lett., 68:1244–1247, 1992.

Lars Onsager. Crystal statistics. i. a two-dimensional model with anorder-disorder transition. Phys. Rev., 65:117–149, 1944.

G. Ovarlez and E. Clément. Slow dynamics and aging of a confinedgranular flow. Phys. Rev. E, 68:031302, 2003.

E. T. Owens and K. E. Daniels. Sound propagation and force chainsin granular materials. EPL (Europhysics Letters), 94(5):54005, 2011.

Tom Parsons, Chen Ji, and Eric Kirby. Stress changes from the 2008

wenchuan earthquake and increased hazard in the sichuan basin.Nature, 454:509–510, 2008.

J. B. H. Peek, J. W. M. Bergmans, J. A. M. M. Haaren, F. Toolenaar,and S. G. Stan. Origins and Successors of the Compact Disc. PhilipsResearch Book Series, Vol. 11, Eindhoven, 1975.

L. Pietronero, A. Vespignani, and S. Zapperi. Renormalizationscheme for self-organized criticality in sandpile models. Phys. Rev.Lett., 72:1690–1693, 1994.

R. Planet, S. Lherminier, G. Simon, K. J. Måløy, L. Vanel, andO. Ramos. Mimicking earthquakes with granular media. Proceedingsof the Congrès Français de Mécanique, 2015.

Ramon Planet, Stéphane Santucci, and Jordi Ortín. Avalanches andnon-gaussian fluctuations of the global velocity of imbibition fronts.Phys. Rev. Lett., 102:094502, 2009.

N. R. Pogson. Magnitudes of thirty-six of the minor planets for thefirst day of each month of the year 1857. Mon. Not. Roy. Astron. Soc,17:12–15, 1856.

Tobias Preis, Johannes J. Schneider, and H. Eugene Stanley. Switch-ing processes in financial markets. Proceedings of the National Academyof Sciences, 108(19):7674–7678, 2011.

Gunnar Pruessner and Ole Peters. Self-organized criticality andabsorbing states: Lessons from the ising model. Phys. Rev. E, 73:025106, 2006.

C. Ptolemy. Almagestum. Petrus Lichtenstein, Venice, 1515.

Page 72: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

72

R. Labbé, J.-F. Pinton, and S. Fauve. Power fluctuations in turbulentswirling flows. J. Phys. II France, 6(7):1099–1110, 1996.

O. Ramos. Avalanche! Coming! Now! Close to the borders ofunpredictability. Significance, 6(2):78–81, 2009.

O. Ramos. Criticality in earthquakes. Good or bad for prediction?Tectonophysics, 485(1-4):321–326, 2010.

O. Ramos. Scale Invariant Avalanches: A Critical Confusion. InB. Veress and J. Szigethy, editors, Horizons in Earth Science Research.Vol. 3. Nova Science Publishers, 2011.

O. Ramos, E. Altshuler, and K. J. Måløy. Quasiperiodic Events in anEarthquake Model. Phys. Rev. Lett., 96:098501, 2006.

O. Ramos, E. Altshuler, and K. J. Måløy. Avalanche Prediction in aSelf-Organized Pile of Beads. Phys. Rev. Lett., 102:078701, 2009.

O. Ramos, P.-P. Cortet, S. Ciliberto, and L. Vanel. Experimental Studyof the Effect of Disorder on Subcritical Crack Growth Dynamics.Phys. Rev. Lett., 110:165506, 2013.

Charles F. Richter. An instrumental earthquake magnitude scale.Bull. Seismol. Soc. Am., 25:1–32, 1935.

J. Rosendahl, M. Vekic, and J. Kelley. Persistent self-organization ofsandpiles. Phys. Rev. E, 47:1401–1404, 1993.

David Rothkopf. Power, Inc.: The Epic Rivalry Between Big Businessand Government–and the Reckoning That Lies Ahead. Farrar, Straus andGiroux, New York, 2013.

S. M. Rubinstein, G. Cohen, and J. Fineberg. Dynamics of precursorsto frictional sliding. Phys. Rev. Lett., 98:226103, 2007.

J. C. Russ. The image processing handbook. CRS Press, Boca Raton, FL,2002.

Caesar Saloma, Gay Jane Perez, Giovanni Tapang, May Lim, andCynthia Palmes-Saloma. Self-organized queuing and scale-free be-havior in real escape panic. Proceedings of the National Academy ofSciences of the United States of America, 100(21):pp. 11947–11952, 2003.

Stéphane Santucci, Loïc Vanel, and Sergio Ciliberto. Subcriticalstatistics in rupture of fibrous materials: Experiments and model.Phys. Rev. Lett., 93:095505, 2004.

J. P. Sethna, K. A. Dahmen, and C. R. Myers. Crackling noise. Nature,410:242–250, 2001.

Nirajan Shiwakoti and Majid Sarvi. Understanding pedestrian crowdpanic: a review on model organisms approach. Journal of TransportGeography, 26:12 – 17, 2013.

Page 73: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

73

Nirajan Shiwakoti, Majid Sarvi, Geoff Rose, and Martin Burd. Ani-mal dynamics based approach for modeling pedestrian crowd egressunder panic conditions. Transportation Research Part B: Methodological,45(9):1433 – 1449, 2011.

Jesse L. Silverberg, Matthew Bierbaum, James P. Sethna, and ItaiCohen. Collective motion of humans in mosh and circle pits at heavymetal concerts. Phys. Rev. Lett., 110:228701, 2013.

K Sneppen, P Bak, H Flyvbjerg, and M H Jensen. Evolution as a self-organized critical phenomenon. Proceedings of the National Academyof Sciences, 92(11):5209–5213, 1995.

S.A. Soria, R. Josens, and D.R. Parisi. Experimental evidence of the"faster is slower" effect in the evacuation of ants. Safety Science, 50(7):1584 – 1588, 2012.

H. E. Stanley. Introduction to Phase Transitions and Critical Phenomena.Oxford Univ. Press, New York, 1987.

D. Stauffer. Monte carlo investigation of rare magnetization fluctu-ations in ising models. International Journal of Modern Physics C, 09

(04):625–631, 1998.

D. Stauffer and A. Aharony. Introduction To Percolation Theory. CRCPress, 2003.

S. S. Stevens. To honor fechner and repeal his law: A power function,not a log function, describes the operating characteristic of a sensorysystem. Science, 133(3446):80–86, 1961.

M. Stojanova, S. Santucci, L. Vanel, and O. Ramos. High FrequencyMonitoring Reveals Aftershocks in Subcritical Crack Growth. Phys.Rev. Lett., 112:115502, 2014.

Chao Tang and Per Bak. Critical exponents and scaling relationsfor self-organized critical phenomena. Phys. Rev. Lett., 60:2347–2350,1988.

A. Tanguy, B. Mantisi, and M. Tsamados. Vibrational modes as apredictor for plasticity in a model glass. EPL (Europhysics Letters), 90

(1):16004, 2010.

A. Tantot, S. Santucci, O. Ramos, S. Deschanel, M.-A. Verdier,E. Mony, Y. Wei, S. Ciliberto, L. Vanel, and P. C. F. Di Stefano.Sound and Light from Fractures in Scintillators. Phys. Rev. Lett., 111:154301, 2013.

Los Angeles Times. Charles f. richter dies; earthquake scale pioneer.October 01 1985. URL http://articles.latimes.com/1985-10-01/

news/mn-19126_1_richter-scale.

G. T. Toomer. Hipparchus. In C. C. Gillespie, editor, Dictionary ofScientific Biography. Charles Scribner, New York, 2011.

Page 74: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

74

J.-C. Tsai and J. P. Gollub. Slowly sheared dense granular flows:Crystallization and nonunique final states. Phys. Rev. E, 70:031303,2004.

L. Vanel, S. Ciliberto, P.-P. Cortet, and S. Santucci. Time-dependentrupture and slow crack growth: elastic and viscoplastic dynamics.Journal of Physics D: Applied Physics, 42(21):214007, 2009.

Alessandro Vespignani and Stefano Zapperi. Order parameter andscaling fields in self-organized criticality. Phys. Rev. Lett., 78:4793–4796, 1997.

David M. Walker, Antoinette Tordesillas, Michael Small, Robert P.Behringer, and Chi K. Tse. A complex systems analysis of stick-slipdynamics of a laboratory fault. Chaos: An Interdisciplinary Journal ofNonlinear Science, 24(1):013132, 2014.

Ulli Wolff. Collective monte carlo updating for spin systems. Phys.Rev. Lett., 62:361–364, 1989.

H. O. Wood and F. Neumann. Modified mercalli intensity scale of1931. Bull. Seismol. Soc. Am., 21:277–283, 1931.

Matthieu Wyart, Leonardo E. Silbert, Sidney R. Nagel, andThomas A. Witten. Effects of compression on the vibrational modesof marginally jammed solids. Phys. Rev. E, 72:051306, 2005.

Stefano Zapperi, Pierre Cizeau, Gianfranco Durin, and H. EugeneStanley. Dynamics of a ferromagnetic domain wall: Avalanches,depinning transition, and the barkhausen effect. Phys. Rev. B, 58:6353–6366, 1998.

Jie Zhang, T. S. Majmudar, M. Sperl, and R. P. Behringer. Jammingfor a 2d granular material. Soft Matter, 6:2982–2991, 2010.

Iker Zuriguel, Alvaro Janda, Angel Garcimartín, Celia Lozano,Roberto Arévalo, and Diego Maza. Silo clogging reduction by thepresence of an obstacle. Phys. Rev. Lett., 107:278001, 2011.

Iker Zuriguel, Daniel Ricardo Parisi, Raúl Cruz Hidalgo, CeliaLozano, Alvaro Janda, Paula Alejandra Gago, Juan Pablo Peralta,Luis Miguel Ferrer, Luis Ariel Pugnaloni, Eric Clément, Diego Maza,Ignacio Pagonabarraga, and Angel Garcimartín. Clogging transitionof many-particle systems flowing through bottlenecks. Sci. Rep., 4:7324, 2014.

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Appendix: Curriculum Vitae

Osvanny Ramos, 39 years old. Nationality: Cuban & French.Position: Associate professor (Maître de Conférences, chaire CNRS)Address: Institut Lumière Matière (ILM), UMR5306 CNRSUniversité Claude Bernard Lyon 1, Domaine Scientifique de La DouaBâtiment Brillouin, 6 rue Ada Byron, 69622 Villeurbanne cedex, FranceEmail: [email protected]: http://ilm-perso.univ-lyon1.fr/ oramos/

- Education and Experience:

2014.01: Invited Professor at the Physics Department of CatholicUniversity of Valparaiso, Chile.

2013.10: Invited Researcher at the University of Oslo, Norway.2010.09 – : Associated professor (Maître de Conférences, Chaire

CNRS) Institut Lumière Matière (LPMCN until Dec. 2012),Lyon, France.

2009.06 – 2010.08: Postdoc at PMMH Laboratory, ESPCI, Paris, France.2007.06 – 2009.05: Postdoc at the Physics Laboratory of the ENS de

Lyon, France.2004.05 – 2007.05: PhD in Physics: "Complex" group, Physics

Department of the University of Oslo, Norway.2003.05: Master in Physics. University of Havana, Cuba.2000.09 – 2003.02: Junior professor at the Physics department of the

Latin-American School of Medicine (ELAM), Havana, Cuba.2000.07: Licenciatura in Physics. University of Havana, Cuba.1998 – 2004.04: Junior researcher at the Superconductivity Laboratory,

IMRE, University of Havana, Cuba.

- Current research areas:

Physics of Risks, Scale-invariant avalanches, Avalanche dynamicsin granular systems, Earthquake dynamics, Fracture of heterogeneousmaterials, Patter formation, Active matter.

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- Main awards, grants and contracts:

2012.09 – 2015.09: Project ANR: "StickSlip" (9 researchers, 4 laborato-ries, project leader: L. Vanel (ILM) – 409 k€).

2012.01: Postdoctoral grant (for R. Planet) from the AXA ResearchFund (with R. Planet. 2 years – 120 k€).

2011.10: Grant from Fédération de Recherche A. M. Ampère (FRAMA)of Lyon (with S. Santucci. – 30 k€).

2006, 2005, 2002: Annual Award from the Cuban Academy of Sci-ences.

2006, 2003, 2001: Annual Award from the University of Havana (bestarticle).

- Publications (26):

– 18 articles in international peer-reviewed journals (including 11 Phys-ical Review Letters and 1 Am. Naturalist), with several presentationsin "broad audience" journals: New Scientist, Discover, Significance,Physics Synopsis, etc.– 1 book chapter (NOVA Science Publishers).– 4 conference proceedings (peer-reviewed).– 1 textbook (in Spanish, 15 authors).– 1 invited article for a "broad audience" journal (Significance Maga-zine).– 1 articles submitted to international peer-reviewed journals.

- Communications:

– 16 oral presentations in international conferences (5 invited, 1

keynote, 2 chairs).– 1 invited course (Invited professor, Chile 2014).– 6 poster presentations in international conferences.– 19 seminars.– 1 invited conference to come: Southern Workshop on Granular Ma-terials 2015 (Chile).

- Organization of Conferences:

- "Mini-Workshop in Complex Systems" (in collaboration with KnutJørgen Måløy), University of Oslo, Feb. 4-5, 2014, Oslo, Norway.

- Reviewer:

- Physical Review Letters, Physical Review E, JSTAT, Journal of Geo-physical Research (Solid Earth), Tectonophysics, Nonlinear Processesin Geophysics, Revista Cubana de Fisica, Frontiers in Physics.- Project labex PALM (2015).

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- Postdoc and students’ supervision:

- 2 postdocs: R. Planet, AXA, 2012.03 – 2014.03; G. Pallares (co-directed), ANR, 2012.09 – 2014.07

- 2 PhD students, ongoing (S. Lherminier, since 3013.09; M. Stojanova(co-directed), since 2012.10.- 7 students in internships (level: L3, M1).

- Teaching:

- Since 2010.09 - General Physics (Mechanics and Optics) to first yearstudents. TD & TP (problems & laboratory classes). (64 hours/year).University Lyon 1, France.- 2014.01: Invited course, Physics Department of the Catholic Uni-versity of Valparaiso, Chile: "Avalanche dynamics in scale-invariantphenomena" (4h).- 2000-2003: General Physics (216 hours/year) and Biophysics (42

hours/year). Physics department of the Latin-American School ofMedicine (ELAM), Havana, Cuba.

- Other responsibilities:

2014.03 – : Elected member of the Local Committee of Hygiene andSecurity of ILM.2013.01 – : In charge of the organization of the "soft-matter" seminarsat the ILM.2012.01-12: In charge of the organization of the seminars of the lab.(LPMCN).2012.06: Jury of "2012 European BEST Engineering Competition" (na-tional level). INSA de Lyon, France.

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List of publications

- Book chapters:

– O. Ramos, Scale invariant avalanches: a critical confusion, inHorizons in Earth Science Research. Vol. 3 (Nova Science Publishers)pp 157-188 (2011). (arXiv:1104.4991v1). [pdf]

- Articles in refereed journals:

– M-J. Dalbe, J. Koivisto, L. Vanel, A. Miksic, O. Ramos, M. Alava,and S. Santucci, Repulsion and attraction between a pair of cracks ina plastic sheet, Phys. Rev. Lett. 114, 205501 (2015). [pdf]

– S. Lherminier, R. Planet, G. Simon, L. Vanel and O. Ramos, Re-vealing the structure of a granular medium through ballistic soundpropagation, Phys. Rev. Lett. 113, 098001 (2014). [pdf]

– M. Stojanova, S. Santucci, L. Vanel, and O. Ramos, High Fre-quency Monitoring Reveals Aftershocks in Subcritical Crack Growth,Phys. Rev. Lett. 112, 115502 (2014). [pdf]

– A. Tantot, S. Santucci, O. Ramos, S. Deschnel, M.-A. Verdier, E.Mony, Y. Wei, S. Ciliberto, L. Vanel, P.C.F. Di Stefano, Sound and Lightfrom Fractures in Scintillators, Phys. Rev. Lett. 111, 154301 (2013).[pdf]

– J. Nase, O. Ramos, C. Creton, and A. Lindner, Debonding energyof PDMS. A new analysis of a classic adhesion scenario, Eur. Phys. J.E 36, 103 (2013). [pdf]

– S. C. Nicolis, J. Fernández, C. Pérez-Penichet, C. Noda, F. Tejera,O. Ramos, D. J. T. Sumpter, and E. Altshuler, Foraging at the Edge ofChaos: Internal Clock versus External Forcing, Phys. Rev. Lett. 110,268104 (2013). [pdf]

– O. Ramos, P-P. Cortet, S. Ciliberto, and L. Vanel, ExperimentalStudy of the Effect of Disorder on Subcritical Crack Growth Dynamics,Phys. Rev. Lett. 110, 165506 (2013). [pdf]

– H. Alarcón, O. Ramos, L. Vanel, F. Vittoz, F. Melo, and J-C Gémi-nard, Softening Induced Instability of a Stretched Cohesive GranularLayer, Phys. Rev. Lett. 105, 208001 (2010). [pdf]

– J. Nase, C. Creton, O. Ramos, L. Sonnenberg and T. Yamaguchi,and A. Lindner, Measurement of the receding contact angle at theinterface between a viscoelastic material and a rigid surface, SoftMatter 6, 2685-2691 (2010). [pdf]

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– O. Ramos, Criticality in earthquakes. Good or bad for prediction?,Tectonophysics 485 321-326 (2010). [pdf]

– O. Ramos, E. Altshuler, and K. J. Måløy, Avalanche Prediction in aSelf-organized Pile of Beads, Phys. Rev. Lett. 102, 078701 (2009). [pdf]

– E. Martínez, C. Perez, O. Sotolongo, O. Ramos, K. J. Måløy, S.Douady, and E. Altshuler, Uphill solitary waves in granular flows,Phys. Rev. E 75, 031303 (2007). [pdf]

– O. Ramos, E. Altshuler, and K. J. Måløy, Quasiperiodic Events inan Earthquake Model, Phys. Rev. Lett. 96, 098501 (2006). [pdf]

– E. Altshuler, O. Ramos, Y. Nuñez, J. Fernández, A. J. Batista-Leyvaand C. Noda, Symmetry breaking in escaping ants, Am. Naturalist,166, 643-649 (2005). [pdf]

– E. Altshuler, T.H. Johansen, Y. Paltiel, Peng Jin, K. E. Bassler, O.Ramos, G. F. Reiter, E. Zeldov, and C. W. Chu, Vortex avalanches withrobust statistics observed in superconducting niobium, Phys. Rev. B70, 140505(R) (2004). [pdf]

– E. Altshuler, T.H. Johansen, Y. Paltiel, Peng Jin, K. E. Bassler,O. Ramos, G. F. Reiter, E. Zeldov, and C. W. Chu, Experiments insuperconducting vortex avalanches, Physica C, 501, 408-410, (2004).[pdf]

– E. Altshuler, O. Ramos, A. J. Batista-Leyva, A. Rivera, and K. E.Bassler, Sandpile Formation by Revolving Rivers, Phys. Rev. Lett. 91,014501 (2003). [pdf]

– E. Altshuler, O. Ramos, C. Martínez, L. E. Flores, and C. Noda,Avalanches in One-Dimensional Piles with Different Types of Bases,Phys. Rev. Lett. 86, 5490 (2001). [pdf]

- Conference proceedings (peer reviewed):

– R. Planet, S. Lherminier, G. Simon, K. J. Måløy, L. Vanel andO. Ramos, Mimicking earthquakes with granular media, CongrèsFrançais de Mécanique 2015, Lyon, France (August 24-28, 2015).

– M. Stojanova, S. Santucci, L. Vanel, and O. Ramos, Acoustic emis-sions in fracturing paper, 13th International Conference on Fracture,Beijing, China (June 16-21, 2013).

– M. Stojanova, S. Santucci, L. Vanel, and O. Ramos, The effects oftime correlations in subcritical fracture. An acoustic analysis, CongrèsFrançais de Mécanique 2013, Bordeaux, France (August 26-30, 2013).

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– O. Ramos, P-P. Cortet, G. Huillard, L. Vanel, and S. Ciliberto,Probing the effect of disorder and interactions on crack growth dy-namics. 12th International Conference on Fracture, Ottawa, Canada(July 12-17, 2009).

- Submitted:

– O. Ramos, When scale-invariant avalanches depart from critical-ity.

- Broad audience articles:

– O. Ramos, Avalanche! Coming! Now! Close to the borders ofunpredictability, Significance 6 (2), 78-81 (2009).

- Others:

– M. Capote, J. Torres, M. Alfonso, G. Pérez, N. Santos, L. Fornaris,M. Rodríguez, R. Acosta, E.L. del Castillo, L. Hernández, L. Kudelia,E. Portuondo, J. Martínez, O. Ramos, and O. Durán Física. CursoPremédico. Libro de texto (ELAM, 2003) (in spanish).

- O. Ramos, Avalanches in self-organized systems. Earthquakemodel and Sandpile experiments, Ph.D. Thesis. (University of Oslo,2007).

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Page 82: AVALANCHES & other major RISKSilm-perso.univ-lyon1.fr/~oramos/documents/HDR_Osvanny.pdf · 8 classification of scale-invariant avalanches (where earthquakes are often used as an

Earthquakes, granular avalanches, subcritical fracture, and many other phenomena where the energy is accumulated very slowly and liberated by sudden “avalanches” show a scale-invariant behavior, i.e., the sizes of the events distribute following a power law. Very large avalanches are in general quite rare; however, they strike with no warning and today it is still not possible to predict when and where the next catastrophic earthquake will happen. Osvanny Ramos* has studied these processes for more than a decade, mainly by creating simplified and small-scale experiments trying to better understand these phenomena; in particular, the development of extreme events. Simple simulations and modeling have complemented his experimental work.The main projects and contributions of his work are presented here. They concern the influence of disorder and dissipation on the dynamics of scale-invariant avalanches, as well as showing the possibility of predicting catastrophic events in these systems. Currently an experiment that mimics the behavior of earthquakes has been built, and the main goals are the prediction and eventually control of catastrophic events.Avalanches have been analyzed both in granular materials and during the subcritical fracture in heterogeneous materials. The existence of fast aftershocks in the latter one, and their relation with the distribution of events is a major result that may have implications in the analysis of the statistics of real earthquakes. The collective behavior of ants has also been studied. In their natural habitat they show a dynamics close to a chaotic behavior, which allows a flexible response to changes in the environment. However, when under panic, they show a follow-the-crowd behavior (also found in humans) that may be quite dangerous in a confined situation. Both studies, extreme avalanches and collective behavior under panic, have been grouped into the PHYSICS OF RISKS.

* Osvanny Ramos is an Associate Professor of Physics (Maître de Conférences)

at the Institut Lumière Matière, University Lyon 1, France.

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