1
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Benzi R, Castaldi I, Toschi F, Trampert J. Self-similar properties of avalanche statistics in a simple turbulent model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210074. [PMID: 35034485 DOI: 10.1098/rsta.2021.0074] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/28/2021] [Indexed: 06/14/2023]
Abstract
In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time [Formula: see text] followed by abrupt avalanche-like energy drops of sizes [Formula: see text] due to strong intermittent fluctuations of energy dissipation. We study the probability distribution [Formula: see text] and [Formula: see text] which both exhibit a quite well-defined scaling behaviour. Although [Formula: see text] and [Formula: see text] are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.
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Affiliation(s)
- Roberto Benzi
- Dipartimento di Fisica, Univ. degli Studi di Roma 'Tor Vergata', via della Ricerca Scientifica 1, Roma 00133, Italy
| | - Ilaria Castaldi
- Dipartimento di Fisica, Univ. degli Studi di Roma 'Tor Vergata', via della Ricerca Scientifica 1, Roma 00133, Italy
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, Eindhoven 5600 MB, The Netherlands
| | - Jeannot Trampert
- Department of Earth Sciences, Utrecht University, Princetonlaan 8a, Utrecht 3594 CB, The Netherlands
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2
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Barés J, Bonamy D. Controlling crackling dynamics by triggering low-intensity avalanches. Phys Rev E 2021; 103:053001. [PMID: 34134297 DOI: 10.1103/physreve.103.053001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 04/23/2021] [Indexed: 11/07/2022]
Abstract
We examine the effect of small, spatially localized excitations applied periodically in different manners, on the crackling dynamics of a brittle crack driven slowly in a heterogeneous solid. When properly adjusted, these excitations are observed to radically modify avalanche statistics and considerably limit the magnitude of the largest events. Surprisingly, this does not require information on the front loading state at the time of excitation; applying it either at a random location or at the most loaded point gives the same results. Subsequently, we unravel how the excitation amplitude, spatial extent, and frequency govern the effect. We find that the excitation efficiency is ruled by a single reduced parameter, namely the injected power per unit front length; the suppression of extreme avalanches is maximum at a well-defined optimal value of this control parameter. analysis opens another way to control the largest events in crackling dynamics. Beyond fracture problems, it may be relevant for crackling systems described by models of the same universality class, such as the wetting of heterogeneous substrates or magnetic walls in amorphous magnets.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, UMR 5508 CNRS-University Montpellier, 34095 Montpellier, France
| | - Daniel Bonamy
- Service de Physique de l'État Condensée, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
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3
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Posadas A, Morales J, Posadas-Garzon A. Earthquakes and entropy: Characterization of occurrence of earthquakes in southern Spain and Alboran Sea. CHAOS (WOODBURY, N.Y.) 2021; 31:043124. [PMID: 34251259 DOI: 10.1063/5.0031844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Accepted: 04/01/2021] [Indexed: 06/13/2023]
Abstract
We propose the use of entropy, H, as an indicator of the equilibrium state of a seismically active region (seismic system). The relationship between an increase in H and the occurrence of a great earthquake in a study area can be predicted by acknowledging the irreversible transition of a system. From this point of view, the seismic system evolves from an unstable initial state (due to external stresses) to another, where the stresses have dropped after the earthquake occurred. It is an irreversible transition that entails an increase in entropy. Five seismic episodes were analyzed in the south of the Iberian Peninsula, the Alboran Sea (Mediterranean Sea), and the North of Morocco: two of them of moderate-high magnitude (Al Hoceima, 2004 and 2016) and three of them of moderate-low magnitude (Adra, 1993-1994; Moron, 2007; and Torreperogil, 2012-2013). The results are remarkably in line with the theoretical forecasts; in other words: an earthquake, understood as an irreversible transition, must suppose an increase in entropy.
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Affiliation(s)
- A Posadas
- Instituto Andaluz de Geofísica, Campus Universitario de Cartuja, Universidad de Granada, 18071 Granada, Spain
| | - J Morales
- Instituto Andaluz de Geofísica, Campus Universitario de Cartuja, Universidad de Granada, 18071 Granada, Spain
| | - A Posadas-Garzon
- Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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4
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Post RAJ, Michels MAJ, Ampuero JP, Candela T, Fokker PA, van Wees JD, Hofstad RWVD, Heuvel ERVD. Interevent-time distribution and aftershock frequency in non-stationary induced seismicity. Sci Rep 2021; 11:3540. [PMID: 33574409 PMCID: PMC7878511 DOI: 10.1038/s41598-021-82803-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 11/17/2020] [Indexed: 11/09/2022] Open
Abstract
The initial footprint of an earthquake can be extended considerably by triggering of clustered aftershocks. Such earthquake-earthquake interactions have been studied extensively for data-rich, stationary natural seismicity. Induced seismicity, however, is intrinsically inhomogeneous in time and space and may have a limited catalog of events; this may hamper the distinction between human-induced background events and triggered aftershocks. Here we introduce a novel Gamma Accelerated-Failure-Time model for efficiently analyzing interevent-time distributions in such cases. It addresses the spatiotemporal variation and quantifies, per event, the probability of each event to have been triggered. Distentangling the obscuring aftershocks from the background events is a crucial step to better understand the causal relationship between operational parameters and non-stationary induced seismicity. Applied to the Groningen gas field in the North of the Netherlands, our model elucidates geological and operational drivers of seismicity and has been used to test for aftershock triggering. We find that the hazard rate in Groningen is indeed enhanced after each event and conclude that aftershock triggering cannot be ignored. In particular we find that the non-stationary interevent-time distribution is well described by our Gamma model. This model suggests that 27.0(± 8.5)% of the recorded events in the Groningen field can be attributed to triggering.
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Affiliation(s)
- Richard A J Post
- Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands.,Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Matthias A J Michels
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Jean-Paul Ampuero
- Université Côte d'Azur, IRD, CNRS, Observatoire de la Côte d'Azur, Géoazur, Nice, France
| | - Thibault Candela
- Applied Geosciences, Netherlands Organisation for Applied Scientific Research (TNO), 3508 TA, Utrecht, The Netherlands
| | - Peter A Fokker
- Applied Geosciences, Netherlands Organisation for Applied Scientific Research (TNO), 3508 TA, Utrecht, The Netherlands.,Department of Geosciences, Utrecht University, 3584 CB, Utrecht, The Netherlands
| | - Jan-Diederik van Wees
- Applied Geosciences, Netherlands Organisation for Applied Scientific Research (TNO), 3508 TA, Utrecht, The Netherlands.,Department of Geosciences, Utrecht University, 3584 CB, Utrecht, The Netherlands
| | - Remco W van der Hofstad
- Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands.,Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Edwin R van den Heuvel
- Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands.
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5
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Unicomb S, Iñiguez G, Gleeson JP, Karsai M. Dynamics of cascades on burstiness-controlled temporal networks. Nat Commun 2021; 12:133. [PMID: 33420016 PMCID: PMC7794342 DOI: 10.1038/s41467-020-20398-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 12/01/2020] [Indexed: 11/16/2022] Open
Abstract
Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.
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Affiliation(s)
- Samuel Unicomb
- Université de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, Lyon, 69364, France.
| | - Gerardo Iñiguez
- Department of Network and Data Science, Central European University, Vienna, A-1100, Austria
- Department of Computer Science, Aalto University School of Science, Aalto, FI-00076, Finland
- Centro de Ciencias de la Complejidad, Universidad Nacional Autonóma de México, CDMX, 04510, Mexico
| | - James P Gleeson
- MACSI and Insight Centre for Data Analytics, University of Limerick, Limerick, V94 T9PX, Ireland
| | - Márton Karsai
- Université de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, Lyon, 69364, France.
- Department of Network and Data Science, Central European University, Vienna, A-1100, Austria.
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6
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Cheng C, Zadeh AA, Kondic L. Correlating the force network evolution and dynamics in slider experiments. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124902007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.
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7
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Kumar P, Korkolis E, Benzi R, Denisov D, Niemeijer A, Schall P, Toschi F, Trampert J. On interevent time distributions of avalanche dynamics. Sci Rep 2020; 10:626. [PMID: 31953412 PMCID: PMC6969144 DOI: 10.1038/s41598-019-56764-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Accepted: 11/29/2019] [Indexed: 11/09/2022] Open
Abstract
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, these interevent time distributions look similar to those for earthquakes and, if different from an exponential, are indirect evidence of non trivial space-time correlations among avalanches. Our results therefore indicate that interevent time statistics are essential to characterise the dynamics of avalanches.
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Affiliation(s)
- Pinaki Kumar
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands
| | - Evangelos Korkolis
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Roberto Benzi
- Dip. di Fisica and INFN, Università "Tor Vergata", Via della Ricerca Scientifica 1, I-00133, Roma, Italy
| | - Dmitry Denisov
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - André Niemeijer
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, 1098, XH, Amsterdam, The Netherlands
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands. .,Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy.
| | - Jeannot Trampert
- Department of Earth Sciences, Utrecht University, P.O. Box 80115, 3508, TC, Utrecht, The Netherlands
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8
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Barés J, Bonamy D, Rosso A. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks. Phys Rev E 2019; 100:023001. [PMID: 31574622 DOI: 10.1103/physreve.100.023001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 11/07/2022]
Abstract
Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Daniel Bonamy
- SPEC/SPHYNX, DSM/IRAMIS CEA Saclay, Bat. 772, F-91191 Gif-sur-Yvette, France
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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9
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Abed Zadeh A, Barés J, Socolar JES, Behringer RP. Seismicity in sheared granular matter. Phys Rev E 2019; 99:052902. [PMID: 31212553 DOI: 10.1103/physreve.99.052902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 06/09/2023]
Abstract
We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.
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Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Joshua E S Socolar
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Robert P Behringer
- Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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10
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Abed Zadeh A, Barés J, Behringer RP. Crackling to periodic dynamics in granular media. Phys Rev E 2019; 99:040901. [PMID: 31108659 DOI: 10.1103/physreve.99.040901] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2018] [Indexed: 06/09/2023]
Abstract
We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.
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Affiliation(s)
- Aghil Abed Zadeh
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
| | - Jonathan Barés
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France
| | - Robert P Behringer
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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11
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Barés J, Bonamy D. Crack growth in heterogeneous brittle solids: intermittency, crackling and induced seismicity. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 377:20170386. [PMID: 30478198 PMCID: PMC6282407 DOI: 10.1098/rsta.2017.0386] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/12/2018] [Indexed: 06/09/2023]
Abstract
Crack growth is the basic mechanism leading to the failure of brittle materials. Engineering addresses this problem within the framework of continuum mechanics, which links deterministically the crack motion to the applied loading. Such an idealization, however, fails in several situations and in particular cannot capture the highly erratic (earthquake-like) dynamics sometimes observed in slowly fracturing heterogeneous solids. Here, we examine this problem by means of innovative experiments of crack growth in artificial rocks of controlled microstructure. The dynamical events are analysed at both global and local scales, from the time fluctuation of the spatially averaged crack speed and the induced acoustic emission, respectively. Their statistics are characterized and compared with the predictions of a recent approach mapping fracture onset to the depinning of an elastic interface. Finally, the overall time-size organization of the events is characterized to shed light on the mechanisms underlying the scaling laws observed in seismology.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.
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Affiliation(s)
- Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, 163 rue Auguste Broussonnet, 34090 Montpellier, France
| | - Daniel Bonamy
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
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12
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Barés J, Dubois A, Hattali L, Dalmas D, Bonamy D. Aftershock sequences and seismic-like organization of acoustic events produced by a single propagating crack. Nat Commun 2018; 9:1253. [PMID: 29593272 PMCID: PMC5871842 DOI: 10.1038/s41467-018-03559-4] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 02/22/2018] [Indexed: 11/28/2022] Open
Abstract
Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology, but also rules the acoustic events produced by a propagating crack. This simpler situation has permitted us to relate these laws to the overall scale-free distribution of inter-event time and energy and to uncover their selection by the crack speed. These results provide a comprehensive picture of how acoustic events are organized upon material failure in the most fundamental of fracture states: single propagating cracks. The multiple microcracking events underlying damage in inhomogeneous brittle materials form characteristic aftershocks sequences obeying similar laws to those in seismology. Here, Barés et al. evidence and explain the same organization in the acoustic noise produced by a single propagating crack.
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Affiliation(s)
- Jonathan Barés
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.,Laboratoire de Mécanique et Génie Civil Université de Montpellier CNRS, 163 rue Auguste Broussonnet, 34090, Montpellier, France
| | - Alizée Dubois
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France
| | - Lamine Hattali
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.,Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France
| | - Davy Dalmas
- Laboratoire de Tribologie et Dynamique des Systemes, CNRS, Ecole Centrale de Lyon, 36, Avenue Guy de Collongue, 69134, Ecully, Cedex, France
| | - Daniel Bonamy
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191, Gif-sur-Yvette, Cedex, France.
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13
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Davidsen J, Kwiatek G, Charalampidou EM, Goebel T, Stanchits S, Rück M, Dresen G. Triggering Processes in Rock Fracture. PHYSICAL REVIEW LETTERS 2017; 119:068501. [PMID: 28949624 DOI: 10.1103/physrevlett.119.068501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Indexed: 06/07/2023]
Abstract
We study triggering processes in triaxial compression experiments under a constant displacement rate on sandstone and granite samples using spatially located acoustic emission events and their focal mechanisms. We present strong evidence that event-event triggering plays an important role in the presence of large-scale or macrocopic imperfections, while such triggering is basically absent if no significant imperfections are present. In the former case, we recover all established empirical relations of aftershock seismicity including the Gutenberg-Richter relation, a modified version of the Omori-Utsu relation and the productivity relation-despite the fact that the activity is dominated by compaction-type events and triggering cascades have a swarmlike topology. For the Gutenberg-Richter relations, we find that the b value is smaller for triggered events compared to background events. Moreover, we show that triggered acoustic emission events have a focal mechanism much more similar to their associated trigger than expected by chance.
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Affiliation(s)
- Jörn Davidsen
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
- GFZ German Research Centre for Geosciences, Section III.2: Geomechanics and Rheology, 14473 Potsdam, Germany
| | - Grzegorz Kwiatek
- GFZ German Research Centre for Geosciences, Section III.2: Geomechanics and Rheology, 14473 Potsdam, Germany
| | | | - Thomas Goebel
- University of California, Santa Cruz, Earth & Planetary Sciences, Santa Cruz, California 95064, USA
| | | | - Marc Rück
- GFZ German Research Centre for Geosciences, Section III.2: Geomechanics and Rheology, 14473 Potsdam, Germany
| | - Georg Dresen
- GFZ German Research Centre for Geosciences, Section III.2: Geomechanics and Rheology, 14473 Potsdam, Germany
- University of Potsdam, 14469 Potsdam, Germany
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14
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Yang C, Wang W, I L. Avalanche structural rearrangement through cracking-healing in weakly stressed cold dusty plasma liquids. Phys Rev E 2016; 93:013202. [PMID: 26871178 DOI: 10.1103/physreve.93.013202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2015] [Indexed: 06/05/2023]
Abstract
We experimentally investigate the spatiotemporal dynamical behaviors of the avalanche structural rearrangement through micro-cracking-healing in weakly stressed cold dusty plasma liquids, and the kinetic origins for their different spatial and temporal classifications. The crystalline ordered domains can be cracked or temporarily sustain and transfer the weak stress to remote regions for cracking-healing. It is found that cracking sites form a fractal network with cluster size following power law distribution in the xyt space. The histograms of the persistent times for sustaining regional ordered and disordered structure, the temporal cracking burst width, and quiescent time between two bursts all follow power law decays with fast descending tails. Cracking can be classified into a single temporal burst with simple line like spatial patterns and the successive cracking fluctuation with densely packed cracking clusters. For an ordered region, whether the Burgers vectors of the incoming dislocations from the boundary allow direct dislocation reduction is the key for the above two classifications through cracking a large ordered domain into medium scale corotating ordered domains or small patches. The low regional structural order at the end of a cracking burst can be regarded as an alarm for predicting the short quiescent period before the next cracking burst.
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Affiliation(s)
- Chi Yang
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 320, Republic of China
| | - Wen Wang
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 320, Republic of China
| | - Lin I
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 320, Republic of China
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Nataf GF, Castillo-Villa PO, Sellappan P, Kriven WM, Vives E, Planes A, Salje EKH. Predicting failure: acoustic emission of berlinite under compression. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:275401. [PMID: 24919038 DOI: 10.1088/0953-8984/26/27/275401] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Acoustic emission has been measured and statistical characteristics analyzed during the stress-induced collapse of porous berlinite, AlPO4, containing up to 50 vol% porosity. Stress collapse occurs in a series of individual events (avalanches), and each avalanche leads to a jerk in sample compression with corresponding acoustic emission (AE) signals. The distribution of AE avalanche energies can be approximately described by a power law p(E)dE = E(-ε)dE (ε ~ 1.8) over a large stress interval. We observed several collapse mechanisms whereby less porous minerals show the superposition of independent jerks, which were not related to the major collapse at the failure stress. In highly porous berlinite (40% and 50%) an increase of energy emission occurred near the failure point. In contrast, the less porous samples did not show such an increase in energy emission. Instead, in the near vicinity of the main failure point they showed a reduction in the energy exponent to ~ 1.4, which is consistent with the value reported for compressed porous systems displaying critical behavior. This suggests that a critical avalanche regime with a lack of precursor events occurs. In this case, all preceding large events were 'false alarms' and unrelated to the main failure event. Our results identify a method to use pico-seismicity detection of foreshocks to warn of mine collapse before the main failure (the collapse) occurs, which can be applied to highly porous materials only.
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Affiliation(s)
- Guillaume F Nataf
- Department d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia. INP Grenoble, 38031 Grenoble Cédex 1, France
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Aragoneses A, Perrone S, Sorrentino T, Torrent MC, Masoller C. Unveiling the complex organization of recurrent patterns in spiking dynamical systems. Sci Rep 2014; 4:4696. [PMID: 24732050 PMCID: PMC3986700 DOI: 10.1038/srep04696] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2014] [Accepted: 03/31/2014] [Indexed: 11/17/2022] Open
Abstract
Complex systems displaying recurrent spike patterns are ubiquitous in nature. Understanding the organization of these patterns is a challenging task. Here we study experimentally the spiking output of a semiconductor laser with feedback. By using symbolic analysis we unveil a nontrivial organization of patterns, revealing serial spike correlations. The probabilities of the patterns display a well-defined, hierarchical and clustered structure that can be understood in terms of a delayed model. Most importantly, we identify a minimal model, a modified circle map, which displays the same symbolic organization. The validity of this minimal model is confirmed by analyzing the output of the forced laser. Since the circle map describes many dynamical systems, including neurons and cardiac cells, our results suggest that similar correlations and hierarchies of patterns can be found in other systems. Our findings also pave the way for optical neurons that could provide a controllable set up to mimic neuronal activity.
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Affiliation(s)
- Andrés Aragoneses
- Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Colom 11, Terrassa, 08222 Barcelona, Spain
| | - Sandro Perrone
- Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Colom 11, Terrassa, 08222 Barcelona, Spain
| | - Taciano Sorrentino
- 1] Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Colom 11, Terrassa, 08222 Barcelona, Spain [2] Departamento de Ciências Exatas e Naturais, Universidade Federal Rural do Semi-Árido, 59625-900 Mossoró, RN, Brazil
| | - M C Torrent
- Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Colom 11, Terrassa, 08222 Barcelona, Spain
| | - Cristina Masoller
- Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Colom 11, Terrassa, 08222 Barcelona, Spain
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Jo HH, Pan RK, Perotti JI, Kaski K. Contextual analysis framework for bursty dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062131. [PMID: 23848651 DOI: 10.1103/physreve.87.062131] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2013] [Indexed: 06/02/2023]
Abstract
To understand the origin of bursty dynamics in natural and social processes we provide a general analysis framework in which the temporal process is decomposed into subprocesses and then the bursts in subprocesses, called contextual bursts, are combined to collective bursts in the original process. For the combination of subprocesses, it is required to consider the distribution of different contexts over the original process. Based on minimal assumptions for interevent time statistics, we present a theoretical analysis for the relationship between contextual and collective interevent time distributions. Our analysis framework helps to exploit contextual information available in decomposable bursty dynamics.
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Affiliation(s)
- Hang-Hyun Jo
- Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P. O. Box 12200, Espoo, Finland.
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