Deterministic and stochastic chaos characterize laboratory earthquakes

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical changes associated with the transition from stable to unstable motion. We find that the seismic cycle exhibits characteristics of a low-dimensional system with average dimension similar to that of natural slow earthquakes (<5). We also investigate local properties of the attractor and find maximum instantaneous dimension ≳10, indicating that some regions of the phase space require a high number of degrees of freedom (dofs). Our analysis does not preclude deterministic chaos, but the lab seismic cycle is best explained by a random attractor based on rate- and state-dependent friction whose dynamics is stochastically perturbed. We find that minimal variations of 0.05% of the shear and normal stresses applied to the experimental fault influence the large-scale dynamics and the recurrence time of labquakes. While complicated motion including period doubling is observed near the stability transition, even in the fully unstable regime we do not observe truly periodic behavior. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics. As applied to tectonic faults, our results imply that even small stress field fluctuations (≲150 kPa) can induce coefficient of variations in earthquake repeat time of a few percent. Moreover, these perturbations can drive an otherwise fast-slipping fault, close to the critical stability condition, into a mixed behavior involving slow and fast ruptures

Timescale of Emplacement and Rheomorphism of the Green Tuff Ignimbrite (Pantelleria, Italy)

We present a multidisciplinary study based on Differential Scanning Calorimetry (DSC), paleomagnetic analysis, and numerical modeling to gain information on the timescales of syn- and post-depositional ductile deformation of the strongly welded and rheomorphic Green Tuff ignimbrite (GT; Pantelleria, Italy). DSC measurements allow the determination of glass fictive temperatures (Tf; i.e., the parameter accounting for the cooling dependence of glass structure and properties). Using a Tf-based geospeedometry procedure, we infer the cooling rate (qc) experienced by the glassy phases in different lithofacies within the GT formation. Glass shards from the basal pumice fall deposit record a fast qc of ∼10°C/s. In contrast, the ignimbrite body returns slow qc values depending on the stratigraphic position and lithofacies (basal/upper vitrophyres, fiamme-rich and rheomorphic layers), ranging from ∼10−2 to ∼10−6 °C/s. Moreover, paleomagnetic analyses of the natural remanent magnetization of ignimbrite matrix and embedded lithic clasts indicate an emplacement temperature higher than 550–600°C. By integrating calorimetric and paleomagnetic datasets, we constrain a conductive cooling model, describing the ignimbrite's temperature-time-viscosity (T–t–η) evolution from the eruptive temperature to below Tf. Outcomes suggest that the upper and basal vitrophyres deformed and quenched over hours, indicating that the entire GT underwent intense syn-depositional ductile deformation. Furthermore, the central body remained above Tf for a much longer timespan (>1 month), enabling post-emplacement rheomorphic flow. Lastly, we discuss the critical role of mechanisms such as shear heating and retrograde solubility of volatiles, in locally controlling the rheological behavior of the GT

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Extreme value statistics for dynamical systems with noise

We study the distribution of maxima ( extreme value statistics ) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former case, we show that, by perturbing rational or irrational rotations with additive noise, an extreme value law appears, regardless of the intensity of the noise, while unperturbed rotations do not admit such limiting distributions. In the case of deterministic chaotic dynamics, we will consider observables specially designed to study the recurrence properties in the neighbourhood of periodic points. Hence, the exponential limiting law for the distribution of maxima is modified by the presence of the extremal index , a positive parameter not larger than one, whose inverse gives the average size of the clusters of extreme events. The theory predicts that such a parameter is unitary when the system is perturbed randomly. We perform sophisticated numerical tests to assess how strong the impact of noise level is when finite time series are considered. We find agreement with the asymptotic theoretical results but also non-trivial behaviour in the finite range. In particular, our results suggest that, in many applications where finite datasets can be produced or analysed, one must be careful in assuming that the smoothing nature of noise prevails over the underlying deterministic dynamics

Signatures of the 1976-1977 Regime Shift in the North Pacific Revealed by Statistical Analysis

Regime shifts are abrupt changes in an ecosystem that may propagate through multiple trophic levels and have pronounced effects on the biotic and abiotic environment, potentially resulting in ecosystem reorganization. There are multiple mechanisms that could cause such abrupt events including natural and anthropogenic factors. In the North Pacific, a major shift in the physics of the system, including a sudden increase in sea surface temperature, was reported in 1977 with a prominent biological response in the lower trophic levels and subsequent effects on the fisheries and economy of the region. Here we investigate the statistics of physical processes that could have triggered and maintained the late 1970s shift. The hypothesis of an extreme sea level pressure event abruptly changing the oceanic conditions in winter 1976–1977, which was maintained by long‐term changes in air‐sea interaction processes, is tested. Using dynamical proxies, we show the occurrence of an extreme atmospheric event, specifically a persistent Aleutian Low during winter 1976–1977, which constitutes a substantial part of the triggering mechanism of the regime shift. Subsequent sudden changes in the net heat flux occurred in the western North Pacific, particularly in the Kuroshio Extension region, which contributed to the maintenance of the new regime

Covid-19 vaccine hesitancy in systemic sclerosis

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