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Lebyodkin MA, Shashkov IV, Lebedkina TA, Gornakov VS. Experimental investigation of the effect of thresholding on temporal statistics of avalanches. Phys Rev E 2017; 95:032910. [PMID: 28415359 DOI: 10.1103/physreve.95.032910] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2016] [Indexed: 06/07/2023]
Abstract
Avalanchelike behavior reflected in power-law statistics is a ubiquitous property of extended systems addressed in a number of generic models. The paper presents an experimental investigation of the effect of thresholding on the statistics of durations and waiting times between avalanches using acoustic emission accompanying unstable plastic deformation. It is found that durations of acoustic events obey power-law statistical distributions robust against thresholding. The quiescent time distributions follow the Poisson law for low threshold values. Both these results corroborate the hypothesis that plastic deformation is akin to the phenomena associated with self-organized criticality (SOC), often advanced on the basis of power-law amplitude statistics. Increasing the threshold height enforces deviation from the Poisson distributions toward apparent power-law behavior. Such a thresholding effect may hinder the experimental determination of SOC-like dynamics because of the inevitable noise.
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Affiliation(s)
- M A Lebyodkin
- Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux, UMR 7239, CNRS/Université de Lorraine, Ile du Saulcy, 57045 Metz, France
| | - I V Shashkov
- Institute of Solid State Physics RAS, 142432 Chernogolovka, Russia
| | - T A Lebedkina
- Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux, UMR 7239, CNRS/Université de Lorraine, Ile du Saulcy, 57045 Metz, France
| | - V S Gornakov
- Institute of Solid State Physics RAS, 142432 Chernogolovka, Russia
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2
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Sattin F, Baiesi M. Self-organized-criticality model consistent with statistical properties of edge turbulence in a fusion plasma. PHYSICAL REVIEW LETTERS 2006; 96:105005. [PMID: 16605745 DOI: 10.1103/physrevlett.96.105005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2005] [Indexed: 05/08/2023]
Abstract
The statistical properties of the intermittent signal generated by a recent model for self-organized criticality are examined. A successful comparison is made with previously published results of the equivalent quantities measured in the electrostatic turbulence at the edge of a fusion plasma. This result reestablishes self-organized criticality as a potential paradigm for transport in magnetic fusion devices, overriding shortcomings pointed out in earlier works [E. Spada, Phys. Rev. Lett. 86, 3032 (2001)10.1103/PhysRevLett.86.3032; V. Antoni, Phys. Rev. Lett. 87, 045001 (2001)10.1103/PhysRevLett.87.045001].
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Affiliation(s)
- Fabio Sattin
- Consorzio RFX, ENEA-Euratom Association, Corso Stati Uniti 4, 35127 Padova, Italy.
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3
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Paczuski M, Boettcher S, Baiesi M. Interoccurrence times in the Bak-Tang-Wiesenfeld sandpile model: a comparison with the observed statistics of solar flares. PHYSICAL REVIEW LETTERS 2005; 95:181102. [PMID: 16383890 DOI: 10.1103/physrevlett.95.181102] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2005] [Indexed: 05/05/2023]
Abstract
A sequence of bursts observed in an intermittent time series may be caused by a single avalanche, even though these bursts appear as distinct events when noise and/or instrument resolution impose a detection threshold. In the Bak-Tang-Wiesenfeld sandpile, the statistics of quiet times between bursts switches from Poissonian to scale invariant on raising the threshold for detecting instantaneous activity, since each zero-threshold avalanche breaks into a hierarchy of correlated bursts. Calibrating the model with the time resolution of GOES data, qualitative agreement with the interoccurrence time statistics of solar flares at different intensity thresholds is found.
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Affiliation(s)
- Maya Paczuski
- Perimeter Institute for Theoretical Physics, Waterloo, Canada
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Sattin F, Vianello N. Statistical model for intermittent plasma edge turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016407. [PMID: 16090099 DOI: 10.1103/physreve.72.016407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2004] [Revised: 04/07/2005] [Indexed: 05/03/2023]
Abstract
The probability distribution function of plasma density fluctuations at the edge of fusion devices is known to be skewed and strongly non-Gaussian. The causes of this peculiar behavior are, up to now, largely unexplored. On the other hand, understanding the origin and the properties of edge turbulence is a key issue in magnetic fusion research. In this paper we show that a stochastic fragmentation model, already successfully applied to fluid turbulence, is able to predict an asymmetric distribution that closely matches experimental data. The asymmetry is found to be a direct consequence of intermittency. A discussion of our results in terms of recently suggested Bramwell-Holdsworth-Pinton universal curve [S. T. Bramwell, P. C. W. Holdsworth, and J.-F. Pinton, Nature (London) 396, 552 (1998)], that should hold for strongly correlated and critical systems, is also proposed.
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Affiliation(s)
- F Sattin
- Consorzio RFX, Corso Stati Uniti 4, 35127 Padova, Italy
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5
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Steinbrecher G, Weyssow B. Generalized randomly amplified linear system driven by gaussian noises: extreme heavy tail and algebraic correlation decay in plasma turbulence. PHYSICAL REVIEW LETTERS 2004; 92:125003. [PMID: 15089681 DOI: 10.1103/physrevlett.92.125003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2003] [Indexed: 05/24/2023]
Abstract
The extreme heavy tail and the power-law decay of the turbulent flux correlation observed in hot magnetically confined plasmas are modeled by a system of coupled Langevin equations describing a continuous time linear randomly amplified stochastic process where the amplification factor is driven by a superposition of colored noises which, in a suitable limit, generate a fractional Brownian motion. An exact analytical formula for the power-law tail exponent beta is derived. The extremely small value of the heavy tail exponent and the power-law distribution of laminar times also found experimentally are obtained, in a robust manner, for a wide range of input values, as a consequence of the (asymptotic) self-similarity property of the noise spectrum. As a by-product, a new representation of the persistent fractional Brownian motion is obtained.
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Affiliation(s)
- György Steinbrecher
- Association EURATOM-MEC, Physics Faculty, University of Craiova, Craiova, Romania
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Alava MJ, Chattopadhyay AK. Fluctuations and correlations in sandpiles and interfaces with boundary pinning. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:016104. [PMID: 14995664 DOI: 10.1103/physreve.69.016104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2003] [Indexed: 05/24/2023]
Abstract
Interfaces are studied in an inhomogeneous critical state where boundary pinning is compensated with a ramped force. Sandpiles driven off the self-organized critical point provide an example of this ensemble in the Edwards-Wilkinson (EW) model of kinetic roughening. A crossover from quenched to thermal noise violates spatial and temporal translational invariances. The bulk temporal correlation functions have the effective exponents beta(1D) approximately 0.88+/-0.03 and beta(2D) approximately 0.52+/-0.05, while at the boundaries beta(b,1D/2D) approximately 0.47+/-0.05. The bulk beta(1D) is shown to be reproduced in a randomly kicked thermal EW model.
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Affiliation(s)
- Mikko J Alava
- Laboratory of Physics, Helsinki University of Technology, FIN-02015 HUT, Finland
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7
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Sánchez R, van Milligen BP, Newman DE, Carreras BA. Quiet-time statistics of electrostatic turbulent fluxes from the JET tokamak and the W7-AS and TJ-II stellarators. PHYSICAL REVIEW LETTERS 2003; 90:185005. [PMID: 12786015 DOI: 10.1103/physrevlett.90.185005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2002] [Indexed: 05/24/2023]
Abstract
The statistics of the quiet times between successive turbulent flux bursts measured at the edge of the JET tokamak and the W7-AS and TJ-II stellarators are analyzed in search for evidence of self-organized critical behavior. The results obtained are consistent with what would be expected in the situation where the underlying plasma is indeed in a near critical state.
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Affiliation(s)
- R Sánchez
- Departamento de Física, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain.
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Isliker H, Vlahos L. Random walk through fractal environments. PHYSICAL REVIEW E 2003; 67:026413. [PMID: 12636828 DOI: 10.1103/physreve.67.026413] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2002] [Indexed: 11/07/2022]
Abstract
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D(F) of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D(F)< or =2 can thus be considered as defective Levy walks. The distribution of jump increments for D(F)>2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D(F)<2, the diffusion is dominated by the finite escape rate. Diffusion for D(F)>2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations.
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Affiliation(s)
- H Isliker
- Association Euratom-Hellenic Republic, Section of Astrophysics, Astronomy and Mechanics Department of Physics, University of Thessaloniki, GR 54006 Thessaloniki, Greece.
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Gruzinov I, Diamond PH, Rosenbluth MN. Sandpiles with bistable automata rules: towards a minimal model of pedestal formation and structure. PHYSICAL REVIEW LETTERS 2002; 89:255001. [PMID: 12484893 DOI: 10.1103/physrevlett.89.255001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2002] [Indexed: 05/24/2023]
Abstract
A sandpile with two stable and two unstable ranges of slopes is presented as a minimal model for the study of H-mode pedestal formation and dynamics. Pedestals are observed to form and expand inward with increasing deposition. Transport bifurcation is not critical to pedestal formation, though the pedestal structure obtained with a second, hard stability boundary is qualitatively different from that found in standard sandpiles. Nonperiodic particle ejection events are observed, but do not initiate pedestal collapse. Pedestal formation alters the spectrum of transport avalanches.
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Affiliation(s)
- I Gruzinov
- University of California, San Diego, La Jolla 92093-0319, USA
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Sánchez R, Newman DE, Carreras BA. Waiting-time statistics of self-organized-criticality systems. PHYSICAL REVIEW LETTERS 2002; 88:068302. [PMID: 11863861 DOI: 10.1103/physrevlett.88.068302] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2001] [Revised: 10/15/2001] [Indexed: 05/23/2023]
Abstract
It is argued that a system governed by self-organized-criticality (SOC) dynamics can lack Poisson waiting-time statistics not only when the experimental resolution lies within the self-similar scale range but also if the system is slowly driven in a correlated way. This result thus suggests that waiting time statistics cannot be used as a necessary test for SOC behavior in real physical systems.
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Affiliation(s)
- R Sánchez
- Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain.
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Antoni V, Carbone V, Cavazzana R, Regnoli G, Vianello N, Spada E, Fattorini L, Martines E, Serianni G, Spolaore M, Tramontin L, Veltri P. Transport processes in reversed-field-pinch plasmas: inconsistency with the self-organized-criticality paradigm. PHYSICAL REVIEW LETTERS 2001; 87:045001. [PMID: 11461623 DOI: 10.1103/physrevlett.87.045001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2001] [Indexed: 05/23/2023]
Abstract
A statistical analysis of the anomalous particle flux in the edge region of the RFX experiment has revealed that laminar times between bursts, which account for more than 50% of the losses, have a power law distribution and that flux fluctuations are not self-similar. These properties are found in contrast with a wide class of self-organized-criticality models so that it is concluded that there is no experimental evidence of avalanchelike process occurrence in the plasma of RFX.
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Affiliation(s)
- V Antoni
- Consorzio RFX, Associazione EURATOM-ENEA per la fusione, corso Stati Uniti 4, 35127 Padova, Italy
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