Criticality and intermittency in the order parameter space

Contoyiannis, Yiannis; Diakonos, F. Κ.

doi:10.1016/s0375-9601(00)00180-8

Cited by 75 publications

(105 citation statements)

References 9 publications

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“…In Contoyiannis and Diakonos (2000) we investigated how a thermal system at its critical point can be described in terms of dynamical systems. We found that the critical fluctuations of the order parameter φ obey to a dynamical law which is described by the following intermittent map…”

Section: The Methods Of Critical Fluctuationsmentioning

confidence: 99%

Tsallis and Levy statistics in the preparation of an earthquake

Contoyiannis

Eftaxias

2008

Nonlin. Processes Geophys.

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Abstract. Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system.

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Section: The Methods Of Critical Fluctuationsmentioning

confidence: 99%

Tsallis and Levy statistics in the preparation of an earthquake

Contoyiannis

Eftaxias

2008

Nonlin. Processes Geophys.

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“…A less known, but well-established finding is given in Ref. [42], where the authors proved that the fluctuations of a random field at the critical point, which is the order parameter, are described in terms of a Type-I intermittent dynamical map similar to the well-known Manneville map [43]. This is the same as fractal intermittency, essentially defining TC.…”

Section: Structural Vs Temporal Complexity: An Intermittency-mentioning

confidence: 87%

“…A best fit procedure with the functionD(r), Eqs. (42)(43), with respect to the three parameters µ, r p and T can be performed.…”

Section: Proposal For a Novel Scaling Analysis Of Complex Signalsmentioning

confidence: 99%

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

Paradisi

Allegrini

2015

Chaos, Solitons & Fractals

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“…However, power-law size frequency distributions are also typical for critical systems (Bak, 1988;Turcotte, 1997) in which case they are related to the breakdown of scale separation (the dynamical changes reach across spatial and temporal scales). Thus the intermittent behaviour seems to imply the approach of the system to criticality (Contoyiannis and Diakonos, 2000).…”

Section: Intermittency and Criticalitymentioning

confidence: 98%

“…The idea of a connection between criticality, especially in the context of self-organized criticality, and intermittency is not new, and has been discussed in a number of papers (Contoyiannis and Diakonos, 2000;Halley et al, 2004;Murin et al, 1997). The fractal stochastic processes are typically characterized by a power-law size frequency distribution, related to the presence of long term memory in the system.…”

Section: Intermittency and Criticalitymentioning

confidence: 99%

Intermittency of storms and substorms: is it related to the critical behaviour?

Dobias

Wanliss

2009

Ann. Geophys.

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Abstract. Intermittency is one of the possible means of quantifying dynamics of fractal processes. In this paper, the analysis of the intermittency of magnetospheric storms and substorms is presented. The analysis allows for a classification of the processes in terms of the power-law scaling of the magnitude of deviations of the index values from the values at quiet times (normal state), and the relative timings of occurrences of such deviations. These are expressed in terms of the co-dimension and the Fano factor. The relationship between the two is related to the nature of the processes behind the observed storm and substorm dynamics. The results suggest that there is a similarity between the two, and therefore it is possible that there are common dynamical processes behind the storms and substorms. In particular, it appears that both of them behave consistently with what would be expected for critical systems, which is consistent with the conclusions of several previous works.

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Criticality and intermittency in the order parameter space

Cited by 75 publications

References 9 publications

Tsallis and Levy statistics in the preparation of an earthquake

Tsallis and Levy statistics in the preparation of an earthquake

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

Intermittency of storms and substorms: is it related to the critical behaviour?

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