Domain growth morphology in curvature-driven two-dimensional coarsening

Sicilia, Alberto; Arenzon, Jeferson J.; Bray, A. J.; Cugliandolo, Leticia F.

doi:10.1103/physreve.76.061116

Cited by 76 publications

(201 citation statements)

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“…When the system approaches the critical state, clusters of the new phase are formed by enhanced fluctuations and their size increases as does the correlation length. But this happens not instantly, because long range correlations develop gradually leading to the so-called dynamic phase transition (critical transition) (Bray 1994;Stanley 1999;Sicilia et al 2007;Varotsos et al 2011b, c). Thus, the time series emitted in such a nonequilibrium process will be nonstationary and p k , or the corresponding probability density function p(v) will no longer be independent of v.…”

Section: Discussionmentioning

confidence: 99%

“…364-365 of Varotsos et al 2011c). According to the dynamic scaling hypothesis (see Bray (1994); Sicilia et al (2007) and references therein), the time-dependent correlation length n at dynamic phase transitions scales as n µ t 1/z , where z is as mentioned above the so-called dynamic critical exponent. The time t is usually measured in Monte Carlo steps.…”

Section: Discussionmentioning

confidence: 99%

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Identifying the occurrence time of an impending major earthquake: a review

2017

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Identifying the occurrence time of an impending major earthquake: a review

2017

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“…The pre-asymptotic dynamics leading to this regime have not been discussed in detail in the literature. It was noticed in [19] that the low-temperature evolution of a bidimensional 50:50 binary mixture after a quench from infinite temperature shares many points in common with the one generated by Glauber single spin-flip stochastic dynamics satisfying detailed balance [20,21]. On the one hand, an early approach to critical percolation was noticed, although the time needed to reach this state was not studied in detail.…”

mentioning

confidence: 99%

“…A discussion of the scaling properties of the first term in terms of A/ 2 d (t), and the crossover of the scaling function from the regime in which the scaling variable varies from being much smaller to being much larger than one was presented in [19]. In the second regime the first term approaches the algebraic finite-size clusters distribution [19,21,36].…”

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confidence: 99%

Phase separation and critical percolation in bidimensional spin-exchange models

Tartaglia¹,

Cugliandolo²,

Picco³

2016

EPL

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-Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phaseseparate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first take a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.Phase separation is the process whereby a binary mixture of components A and B, initially in a homogeneous phase, demix. This process leads to the coexistence of two phases: one rich in A and the other in B [1][2][3][4][5][6]. The system, initially in an unstable spatially uniform state, progressively coarsens to approach its thermodynamically stable phase-separated state. Such phenomena arise in binary alloys, fluid mixtures, and polymer blends. Recently, the dynamics of phase separation have seen a revival of interest in the context of experimental [7,8] and numerical [9][10][11][12] studies of binary mixtures of Bose gases.The late time dynamics are well understood. In the absence of driving forces, a dynamic scaling regime with statistically self-similar domain morphology sets in. This regime is well-described by an extension of the Lifshitz-Slyozov-Wagner (LSW) theory [13,14], in which the typical domain radius grows as [15] (whereas for scalar non-conserved order parameter dynamics the growing length is also given by a power law but the exponent is z d = 2). Numerical results in favour of this law were published in [15][16][17] for spin-exchange models although the growth-law can be more complex in particle or polymer phase separating systems, see e.g.[18] and references therein. The pre-asymptotic dynamics leading to this regime have not been discussed in detail in the literature. It was noticed in [19] that the low-temperature evolution of a bidimensional 50:50 binary mixture after a quench from infinite temperature shares many points in common with the one generated by Glauber single spin-flip stochastic dynamics satisfying detailed balance [20,21]. On the one hand, an early approach to critical percolation was noticed, although the time needed to reach this state was not studied in detail. On the other hand, a separation of length-scales in the statistics and morphology of finite size cluster areas and domain wall lengths was observed. Linear or planar objects that are smaller than the typical ones,, satisfy dynamic scaling with respect to d (t), while larger objects were found to be very close to the ones of critical percolation.In this Letter we characterise the early stages of the dynamical process. More precisely, we analyse the way in which the system approaches a state with a stable pattern of critical percolating domains. We monitor a number of observables (to be defined in the main part of the text) and we explain how their behaviour constitu...

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“…The situation is different when the system is not in equilibrium. When the system approaches the critical state, clusters of the new phase are formed by enhanced fluctuation and their size increases as does the correlation length (16)(17)(18). But this happens not instantly because long-range correlations develop gradually leading to the dynamic phase transition of the second order (17).…”

mentioning

confidence: 99%

Natural time analysis of critical phenomena

Varotsos

Sarlis

Skordas

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

136

107

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A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ 1 ð≡hχ 2 i − hχ i 2 Þ of natural time χ , where hfðχ Þi ¼ ∑ p k f ðχ k Þ and p k is the normalized energy released during the kth event of which the natural time is defined as χ k ¼ k∕N and N stands for the total number of events. Then we show that κ 1 becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak-Tang-Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ 1 ¼ 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.short-term earthquake prediction | dynamic exponent | fractional Gaussian noise | fractional Brownian motion | Burridge-Knopoff "train" model I t has been shown that some unique dynamic features hidden behind can be derived from the time series of complex systems, if we analyze them in terms of natural time χ (1-3). For a time series comprising N events, we define an index for the occurrence of the kth event by χ k ¼ k∕N, which we term natural time. In doing so, we ignore the time intervals between consecutive events, but preserve their order and energy Q k . We, then, study the evolution of the pair (χ k , Q k ) by using the normalized power spectrumdefined by ΦðωÞ ¼ ∑ N k¼1 p k expðiωχ k Þ, where ω stands for the angular natural frequency andis the normalized energy for the kth event. In the time-series analysis using natural time, the behavior of ΠðωÞ at ω close to zero is studied for capturing the dynamic evolution, because all the moments of the distribution of the p k can be estimated from ΦðωÞ at ω → 0 (see ref. 4, p. 499). For this purpose, a quantity κ 1 is defined from the Taylor expansionWe found that this quantity, the variance of natural time χ k , is a key parameter for the distribution of energy within the natural time interval (0,1]. Note that χ k is "rescaled" as natural time changes to χ k ¼ k∕ðN þ 1Þ together with rescaling p k ¼ Q k ∕ ∑ Nþ1 n¼1 Q n upon the occurrence of any additional event. It has been demonstrated that this analysis enables recognition of the complex dynamic system under study entering the critical stage (1-3). This occurs when the variance κ 1 converges to 0.070. Originally the condition κ 1 ¼ 0.070 for the approach to criticality was theoretically derived for the seismic electric signals (SES) (1, 2), which are transient low frequency (≤1 Hz) electric signals that have been repeatedly observed before earthquakes (3,5,6). The experimental data showed that κ 1 obtained from SES activities in Greece and Japan attain the value 0.070 (1-3, 7-10). The emission of SES was attributed to a phase transition of second order. It was also shown empirically that the same condition κ 1 ¼ 0.070 holds for other time series, including turbule...

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Domain growth morphology in curvature-driven two-dimensional coarsening

Cited by 76 publications

References 47 publications

Identifying the occurrence time of an impending major earthquake: a review

Identifying the occurrence time of an impending major earthquake: a review

Phase separation and critical percolation in bidimensional spin-exchange models

Natural time analysis of critical phenomena

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