New Bayesian frequency–magnitude distribution model for earthquakes applied in Chile

Sánchez, Ewin; Vega-Jorquera, Pedro

doi:10.1016/j.physa.2018.05.119

Cited by 15 publications

(8 citation statements)

References 10 publications

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“…where α is a system-dependent exponent, and we have set (without loss of generality) E 0 = 0. This form not only includes the ideal gas and systems of classical harmonic oscillators, but sometimes has been used to describe more complex systems [17].…”

Section: Resultsmentioning

confidence: 99%

Fluctuation theorems in nonextensive statistics

Umpierrez¹,

Davis²

2019

Preprint

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Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called q-exponential family of distributions. In this work we present the use of fluctuation theorems for q-canonical ensembles as a powerful tool to readily obtain statistical properties. In particular, we have obtained strong conditions for the possible values of q depending on the density of states of the system.

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Section: Resultsmentioning

confidence: 99%

Fluctuation theorems in nonextensive statistics

Umpierrez¹,

Davis²

2019

Preprint

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“…In this direction, one of the approach currently exercised is the generalization of GR law. Recent works based on generalized logistic equation [11,12], Bayesian statistics [13] and non-extensive statistical mechanics [14] are promising and needs to be explored further.…”

Section: Discussionmentioning

confidence: 99%

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

Burud¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Convergence of the b-value, the exponent of Gutenberg-Richter law, to unity near failure is considered as a universal phenomenon observed in many natural and artificial complex systems. The existence of universality implies that the underlying mechanism in various systems at the critical stage is universal too, irrespective of size, shape, and ingredient (heterogeneity) of the medium. The present work intends to discuss the size effect phenomenon on the b-value and apparent universality through experimental evidences. To study the size effect on the acoustic emission in concrete, geometrically similar, single edge notch beams of three different sizes are tested under three-point bending. The trend exhibited by critical b-value with respect to specimen size confirms its size-dependence which indeed originates from the size dependence of the fracture process zone.

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“…Superstatistics in particular is strongly founded on the rules of probability theory while still being compatible with Jaynes' original maximum entropy principle [7] and is therefore an appealing choice of framework. Moreover, superstatistics is especially suited to the language of Bayesian probability, as has been shown in several different works [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 98%

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

Davis¹

2021

Preprint

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In this work it is shown that the main ensemble of Tsallis nonextensive statistics, namely the χ 2 -superstatistics, can be obtained as a noninformative prior distribution that is singled out by the mathematical structure of superstatistics itself. There are no assumptions involved about the physics of the systems of interest, or regarding their complexity or range of interactions, which supports the thesis that the success of the χ 2 -superstatistics is information-theoretical in its origin, and explainable in terms of Jaynes' original maximum entropy principle.

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New Bayesian frequency–magnitude distribution model for earthquakes applied in Chile

Cited by 15 publications

References 10 publications

Fluctuation theorems in nonextensive statistics

Fluctuation theorems in nonextensive statistics

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

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