Mechanisms of evolution of avalanches in regular graphs

Handford, T. P.; Pérez‐Reche, Francisco J.; Taraskin, S. N.

doi:10.1103/physreve.87.062122

Cited by 11 publications

(20 citation statements)

References 31 publications

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“…The universality class, however, is not the same since the value κ = 1.1 for our model significantly deviates from the value κ M F = 3/2 in meanfield theories [37,82]. The difference may be associated with the topology of interactions: mean-field models imply a tree-like topology [36,[83][84][85] while our model and other models predicting similar values for κ [86? -88] preserve crucial short interaction loops (while remaining long-range).…”

Section: Universalitymentioning

confidence: 52%

“…15 shows that λ < 0 is associated with a characteristic peak in D(s|τ ) at large avalanche sizes. This indicates the occurrence of snap events analogous to an infinite avalanche in weakly disordered RFMs [5,33,34,36]. Figure 16 illustrates the fitting of a function D(S|τ ) ∼ S −κ e −λS to the avalanche size distribution for heating runs.…”

Section: B Avalanchesmentioning

confidence: 99%

“…Various proposed mechanisms of scaling in such systems which do not require external tuning to a critical point range from depinning, as in the case of disordered ferromagnets [29], to inertia-induced nucleation [7] reminiscent of turbulence. A radically different perspective would be that a classical critical point [32] is involved, however, this scenario in athermal systems requires a particular degree of quenched disorder [33][34][35][36]. * fperez-reche@abdn.ac.ukThe ubiquity of scaling would then mean that either the critical region is sufficiently wide to be routinely crossed in the course of periodic driving [26,37], or that there exists a feedback mechanism fine tuning the system to a critical point.…”

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confidence: 99%

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Origin of scale-free intermittency in structural first-order phase transitions

et al. 2016

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A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to criticality without extrinsic tuning remains unexplained. Here we show that the source of scaling in such systems is an annealed disorder associated with transformationinduced slip which co-evolves with the phase transformation, thus ensuring the crossing of a critical manifold. Our conclusions are based on a model where annealed disorder emerges in the form of a random field induced by the phase transition. Such disorder leads to super-transient chaotic behavior under thermal loading, obeys a heavy-tailed distribution and exhibits long-range spatial correlations. We show that the universality class is affected by the long-range character of elastic interactions. In contrast, it is not influenced by the heavy-tailed distribution and spatial correlations of disorder.The ubiquitous presence of scale-free avalanche behavior during structural transformations in crystals [1][2][3][4] is in an apparent contradiction with the first-order nature of the underlying phase transitions. This question has attracted considerable attention [5-13] not only due to its theoretical interest, but also because of the widespread use of transforming materials, e.g. shape memory alloys, in applications [14,15]. The study of intermittency in such systems is important because the rearrangements of microstructural morphologies associated with avalanches [16] can perilously interfere with material and structural response at sub-micron scale preventing reliable control of the pseudo-plastic deformation [17][18][19].Avalanche dynamics with power-law statistics [20, 21] is an inherent feature of a broad variety of natural systems from neural networks [22] and animal herds [23] to tectonic faults [24] and stellar flares [25]. To explain the mechanism responsible for scale-free regimes in such systems, a number of general paradigms have been proposed, including implicit external tuning [26,27], the involvement of nonlocal restoring fields [28,29], the inherent complexity of the quenched energy landscapes [30], and the multiplicative structure of the endogenous noise [31].Controversy surrounds, in particular, the scale-free intermittent response of solid materials undergoing firstorder phase transitions. Various proposed mechanisms of scaling in such systems which do not require external tuning to a critical point range from depinning, as in the case of disordered ferromagnets [29], to inertia-induced nucleation [7] reminiscent of turbulence. A radically different perspective would be that a classical critical point [32] is involved, however, this scenario in athermal systems requires a particular degree of quenched disorder [33][34][35][36]. * fperez-reche@abdn.ac.ukThe ubiquity of scaling would then mean that either the critical region is sufficiently wide to be routinely crossed in the course of periodic driving [26,37...

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Section: Universalitymentioning

confidence: 52%

Section: B Avalanchesmentioning

confidence: 99%

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confidence: 99%

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Origin of scale-free intermittency in structural first-order phase transitions

et al. 2016

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“…AVALANCHES the interacting spin system described by the random-field Ising model at zero temperature and driven along the hysteresis loop represents a paradigm of complex dynamical behaviour far from the equilibrium [65]. In this example, the spin alignment along the slowly increasing external field is balanced by spin-spin interactions and the local constraints due to the random-filed disorder.…”

Section: The Impact Of Vacancies On Multifractal Spectrum: a Comparismentioning

confidence: 99%

“…These magnetisation changes in time represent the data points in the Barkhausen noise, a complex time series from which then the avalanches can be determined. The scale-invariant behaviour of the Barkhausen avalanches and their dependence on the strength of the random-field disorder has been well understood [65,[68][69][70][71]. Recently, it has been shown [64] that the Barkhausen noise exhibits multifractal structure.…”

Section: The Impact Of Vacancies On Multifractal Spectrum: a Comparismentioning

confidence: 99%

Mechanisms of self-organized criticality in social processes of knowledge creation

2017

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In the online social dynamics, a robust scaling behaviour appears as a key feature of many collaborative efforts that lead to the new social value. The underlying empirical data thus offer a unique opportunity to study the origin of self-organised criticality in social systems. In contrast to physical systems in the laboratory, various human attributes of the actors play an essential role in the process along with the contents (cognitive, emotional) of the communicated artefacts. As a prototypal example, we consider the social endeavour of knowledge creation via Questions & Answers (Q&A). Using a large empirical dataset from one of such Q&A sites and theoretical modelling, we examine the temporal correlations at all scales and the role of cognitive contents to the avalanches of the knowledge creation process. Our analysis shows that the long-range correlations and the event clustering are primarily determined by the universal social dynamics, providing the external driving of the system by the arrival of new users. While the involved cognitive contents (systematically annotated in the data and observed in the model) are crucial for a fine structure of the developing knowledge networks, they only affect the values of the scaling exponents and the geometry of large avalanches and shape the multifractal spectrum. Furthermore, we find that the level of the activity of the communities that share the knowledge correlates with the fluctuations of the innovation rate, implying that the increase of innovation may serve as the active principle of self-organisation. To identify relevant parameters and unravel the role of the network evolution underlying the process in the social system under consideration, we compare the social avalanches to the avalanche sequences occurring in the field-driven physical model of disordered solids, where the factors contributing to the collective dynamics are better understood.

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Modelling Avalanches in Martensites

Pérez‐Reche

2016

Understanding Complex Systems

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Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling. CONTENTS

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Mechanisms of evolution of avalanches in regular graphs

Cited by 11 publications

References 31 publications

Origin of scale-free intermittency in structural first-order phase transitions

Origin of scale-free intermittency in structural first-order phase transitions

Mechanisms of self-organized criticality in social processes of knowledge creation

Modelling Avalanches in Martensites

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