Nonlinear Dynamics and Chaos: Advances and Perspectives

Thiel, Marco; Kurths, Jürgen; Romano, M. Carmen; Károlyi, György; Moura, Arnaldo Vieira

doi:10.1007/978-3-642-04629-2

Cited by 19 publications

(2 citation statements)

References 45 publications

(70 reference statements)

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“…The indicated features of the dynamics are typical for super-transient chaotic phenomena [72,73] and have been also observed in cyclically driven amorphous solids [74,75]. In view of these analogies, we can argue that the basin of attraction of the synchronized behavior in our model is narrow and finding this attractor becomes increasingly difficult as the system gains access to a larger configurations space by generating slip.…”

Section: B Long Chaotic Transientssupporting

confidence: 60%

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: B Long Chaotic Transientssupporting

confidence: 60%

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

et al. 2016

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“…Thus, entrainment into a cyclonic eddy will increase the tendency of Sargassum rafts to drift northwest in the North Atlantic. Inertial effects are important for correctly modeling these advective responses because inertia may explicitly alter the likelihood of Sargassum crossing an eddy boundary (Beron-Vera et al, 2015;Cartwright et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Inertia Influences Pelagic Sargassum Advection and Distribution

Brooks

Coles

2019

Geophysical Research Letters

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The effect of inertia (resistance to a change in velocity of buoyant finite‐sized objects) on the advection of pelagic Sargassum, a macroalgae, is a function of the size and density of natural Sargassum rafts. Here we present observations of Sargassum density and an approach for estimating an effective radius of Sargassum rafts from remote‐sensing observations. This allows the existing theoretical framework for Lagrangian modeling of inertial effects on spherical particles to be applied to Sargassum. Accounting for inertia yields up to a 20% increase in Sargassum export from the Sargasso Sea southward and provides a return pathway to the tropics that may be important to maintaining a self‐sustaining population. Resolving inertial effects also leads to increases in retention in the Gulf of Mexico and Caribbean Sea, where Sargassum inundation events are increasingly common. Including inertial effects in models of Sargassum advection could improve predictions of these events.

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Chaos-generalized regression neural network prediction model of mine water inflow

Wang

et al. 2021

SN Appl. Sci.

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Artificial neural network (ANN) provides a new way for mine water inflow prediction. However, the effectiveness of prediction using ANN model would not be guaranteed if the influencing factors of water inflow are difficult to quantify or there are only a few observation data. Chaos theory can recover the rich dynamic information hidden in time series. By reconstructing water inflow time series in phase space, the multi-dimensional matrix could be obtained, with each column representing an influencing factor of water inflow and its value representing the change of the influencing factor with time. Therefore, a new prediction model of mine water inflow can be established by combining ANN with chaos theory when lacking data on the influencing factors of water inflow. In the present study, the No. 12 coal mine of Pingdingshan China was selected as the study site. The Chaos-GRNN model and Chaos- BPNN model of mine, water inflow were established by using the water inflow data from February 1976 to December 2013. The model was verified by using the water inflow values in the 24 months from 2014 to 2015. The number embedded dimension (M) of influencing factors of water inflow determined by phase space reconstruction was 7, meaning that there were 7 influencing factors of water inflow and 7 neurons in GRNN input layer, and the time delay was 13 months. The value of GRNN input layer neurons was determined accordingly. The maximum Lyapunov index was 0.0530, and the prediction time of GRNN was 19 months. The two models were evaluated by using four evaluation indices (R, RMSE, MAPE, NSE) and violin plot. It was found that both models can realize the long-term prediction of water inflow, and the prediction effectiveness of Chaos-GRNN model is better than that of Chaos-BPNN model.

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Nonlinear Dynamics and Chaos: Advances and Perspectives

Cited by 19 publications

References 45 publications

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

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

Inertia Influences Pelagic Sargassum Advection and Distribution

Chaos-generalized regression neural network prediction model of mine water inflow

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