Viscoelastic effects in avalanche dynamics: a key to earthquake statistics

Nonequilibrium phase diagram for the serration statistics during slow deformation of refractory high-entropy alloys

Diverse slip behaviors are observed in HfNbTaTiZr refractory high-entropy alloy during tensile tests. Slow-avalanche and fast-runaway phases are identified by analyzing scaling relationships among slip statistics. Slow avalanches display a scaling collapse in temporal shapes, aligning with mean-field slip theory, while system-spanning fast-runaway avalanches show a Gaussian shape, indicating rapid nucleation due to dynamic weakening. Through time scale analysis, we construct a nonequilibrium phase diagram elucidating the influence of temperature and strain rate variations on solute-dislocation interaction.

AI-NERD: Elucidation of relaxation dynamics beyond equilibrium through AI-informed X-ray photon correlation spectroscopy

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales. However, spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work, we have developed an unsupervised deep learning (DL) framework for automated classification of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system. We demonstrate how this method can be used to accelerate exploration of large datasets to identify samples of interest, and we apply this approach to directly correlate microscopic dynamics with macroscopic properties of a model system. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

Pinning of crack fronts by hard and soft inclusions: A phase field study

Through tridimensonal numerical simulations of cracks propagating in material with an elastic moduli heterogeneity, it is shown that the presence of a simple inclusion can dramatically affect the propagation of the crack. Both the presence of soft and hard inclusions can lead to the arrest of a crack front. Here the mechanism leading to the arrest of the crack are described and shown to depend on the nature of the inclusion. This is also the case in regimes where the presence of the inclusion leads to a slowdown of the crack.

Viscoelastic Slider Blocks as a Model for a Seismogenic Fault

In this work, a model is proposed to examine the role of viscoelasticity in the generation of simulated earthquake-like events. This model serves to investigate how nonlinear processes in the Earth's crust affect the triggering and decay patterns of earthquake sequences. These synthetic earthquake events are numerically simulated using a slider-block model containing viscoelastic standard linear solid (SLS) elements to reproduce the dynamics of an earthquake fault. The simulated system exhibits elements of self-organized criticality, and results in the generation of avalanches that behave similarly to naturally occurring seismic events. The model behavior is analyzed using the Epidemic-Type Aftershock Sequence (ETAS) model, which suitably represents the observed triggering and decay patterns; however, parameter estimates deviate from those resulting from natural aftershock sequences. Simulated aftershock sequences from this model are characterized by slightly larger p-values, indicating a faster-than-normal decay of aftershock rates within the system. The ETAS fit, along with realistic simulated frequency-size distributions, supports the inclusion of viscoelastic rheology to model the seismogenic fault dynamics.

Quasistatic deformation of yield stress materials: Homogeneous or localized?

We analyze a mesoscopic model of a shear stress material with a three-dimensional slab geometry, under an external quasistatic deformation of a simple shear type. Relaxation is introduced in the model as a mechanism by which an unperturbed system achieves progressively mechanically more stable configurations. Although in all cases deformation occurs via localized plastic events (avalanches), we find qualitatively different behavior depending on the degree of relaxation in the model. For no or low relaxation, yielding is homogeneous in the sample, and even the largest avalanches become negligible in size compared with the system size (measured as the thickness of the slab L_{z}) when this is increased. On the contrary, for high relaxation, the deformation localizes in an almost two-dimensional region where all avalanches occur. Scaling analysis of the numerical results indicates that in this case, the linear size of the largest avalanches is comparable with L_{z}, even when this becomes very large. We correlate the two scenarios with a qualitative difference in the flow curve of the system in the two cases, which is monotonous in the first case and velocity weakening in the second case.

Scaling theory for the statistics of slip at frictional interfaces

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress σ^{*}, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a power law corresponding to "avalanches" and a "narrow" distribution of system-spanning "fracture" events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

The debate on the earthquake magnitude correlations: a meta-analysis

Among the most important questions that await an answer in seismology, perhaps one is whether there is a correlation between the magnitudes of two successive seismic events. The answer to this question is considered of fundamental importance given the potential effect in forecasting models, such as Epidemic Type Aftershock Sequence models. After a meta-analysis of 29 papers, we speculate that given the lack of studies carried out with realistic physical models and given the possible bias due to the lack of events recorded in the experimental seismic catalogs, important improvements are necessary on both fronts to be sure to provide a statistically relevant answer.

Sheared granular matter and the empirical relations of seismicity

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Generic mechanism for remote triggering of earthquakes

"Remote triggering" refers to the inducement of earthquakes by weak perturbations that emanate from faraway sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. Linearly stable stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a need for resonance), which trigger an instability with exponential oscillatory growth. Once nonlinear effects kick in, the blow up in mean-square displacements can reach 15-20 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

Nonequilibrium athermal random-field Ising model on hexagonal lattices

We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.

Signature of Transition between Granular Solid and Fluid: Rate-Dependent Stick Slips in Steady Shearing

Despite extensive studies on either smooth granular-fluid flow or the solidlike deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of interparticle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers J decades below reported values, we answer how a granular system can transition to the regime sustained by solid-to-solid friction that goes beyond existing paradigms based on suspension rheology.

Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions

Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this Letter we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

Thermally rounded depinning of an elastic interface on a washboard potential

The thermal rounding of the depinning transition of an elastic interface sliding on a washboard potential is studied through analytic arguments and very accurate numerical simulations. We confirm the standard view that well below the depinning threshold the average velocity can be calculated considering thermally activated nucleation of defects. However, we find that the straightforward extension of this analysis to near or above the depinning threshold does not fully describe the physics of the thermally assisted motion. In particular, we find that exactly at the depinning point the average velocity does not follow a pure power law of the temperature as naively expected by the analogy with standard phase transitions but presents subtle logarithmic corrections. We explain the physical mechanisms behind these corrections and argue that they are nonpeculiar collective effects which may also apply to the case of interfaces sliding on uncorrelated disordered landscapes.

Non-trivial avalanches triggered by shear banding in compression of metallic glass foams

Ductile metallic glass foams (DMGFs) are a new type of structural material with a perfect combination of high strength and toughness. Owing to their disordered atomic-scale microstructures and randomly distributed macroscopic voids, the compressive deformation of DMGFs proceeds through multiple nanoscale shear bands accompanied by local fracture of cellular structures, which induces avalanche-like intermittences in stress–strain curves. In this paper, we present a statistical analysis, including distributions of avalanche size, energy dissipation, waiting times and aftershock sequence, on such a complex dynamic process, which is dominated by shear banding. After eliminating the influence of structural disorder, we demonstrate that, in contrast to the mean-field results of their brittle counterparts, scaling laws in DMGFs are characterized by different exponents. It is shown that the occurrence of non-trivial scaling behaviours is attributed to the localized plastic yielding, which effectively prevents the system from building up a long-range correlation. This accounts for the high structural stability and energy absorption performance of DMGFs. Furthermore, our results suggest that such shear banding dynamics introduce an additional characteristic time scale, which leads to a universal gamma distribution of waiting times.

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

Unified phase diagram of reversible-irreversible, jamming, and yielding transitions in cyclically sheared soft-sphere packings

Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram.

Correlations between avalanches in the depinning dynamics of elastic interfaces

We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean-field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain a simple field theory which describes the first deviations from this uncorrelated behavior in a ε=d_{c}-d expansion below the upper critical dimension d_{c} of the model. We apply it to calculate the correlations between (i) avalanche sizes (ii) avalanche dynamics in two successive avalanches, or more generally, in two avalanches separated by a uniform displacement W of the interface. For (i) we obtain the correlations of the total sizes, of the local sizes, and of the total sizes with given seeds (starting points). For (ii) we obtain the correlations of the velocities, of the durations, and of the avalanche shapes. In general we find that the avalanches are anticorrelated, the occurrence of a larger avalanche making more likely the occurrence of a smaller one, and vice versa. Examining the universality of our results leads us to conjecture several exact scaling relations for the critical exponents that characterize the different distributions of correlations. The avalanche size predictions are confronted to numerical simulations for a d=1 interface with short range elasticity. They are also compared to our recent related work on static avalanches (shocks). Finally we show that the naive extrapolation of our result into the thermally activated creep regime at finite temperature predicts strong positive correlations between the forward motion events, as recently observed in numerical simulations.

Universal Scaling of the Velocity Field in Crack Front Propagation

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are, however, difficult to characterize in experiments at a finite drive. Here, we show that the correlation functions of the velocity field along the front allow us to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient, and can be extended to all systems displaying avalanche dynamics.

Multiscale relaxation in aging colloidal gels: From localized plastic events to system-spanning quakes

Relaxation of internal stresses through a cascade of microscopic restructuring events is the hallmark of many materials, ranging from amorphous solids like glasses and gels to geological structures subjected to a persistent external load. By means of photon correlation imaging, a recently developed technique that blends the powers of scattering and imaging, we provide a spatially and temporally resolved survey of the restructuring and aging processes that spontaneously occur in physical gels originating from an arrested phase separation. We show that the temporal dynamics is characterized by an intermittent sequence of spatially localized "microquakes" that eventually lead to global rearrangements occurring at a rate that scales with the gel age. Notably, these dramatic upheavals of the gel structure are heralded by a progressive acceleration of the microscopic gel dynamics that originates from recognizable active spots and then spreads at a large but finite speed through the gel. Within the "slack" phase between two of these "macroquakes," the fluctuations of the degree of temporal correlation obey a non-Gaussian statistics described by a generalized logistic distribution. The evidence we obtained bear consistent analogies with the stress relaxation processes taking place in earthquake sequences and with the intermittent restructuring of plastic crystals at the microscale.

Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

Random critical point separates brittle and ductile yielding transitions in amorphous materials

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.

Universal avalanche statistics and triggering close to failure in a mean-field model of rheological fracture

The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system. Here, we investigate the effects of transient hardening on (i) the activity rate and (ii) the statistical properties of avalanches. We find the explicit representation of transient hardening in the presence of generalized viscoelasticity and solve the corresponding mean-field model of fracture. In the quasistatic limit, the accelerated energy release is invariant with respect to rheology and the avalanche propagation can be reinterpreted in terms of a stochastic counting process. A single universality class can be defined from such analogy, and all statistical properties depend only on the distance to criticality. We also prove that interevent correlations emerge due to the hardening-even in the quasistatic limit-that can be interpreted as "aftershocks" and "foreshocks."

Threshold-induced correlations in the Random Field Ising Model

We present a numerical study of the correlations in the occurrence times of consecutive crackling noise events in the nonequilibrium zero-temperature Random Field Ising model in three dimensions. The critical behavior of the system is portrayed by the intermittent bursts of activity known as avalanches with scale-invariant properties which are power-law distributed. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations show that the observed correlations emerge upon applying a finite threshold to the pertaining signals when defining events of interest. Such events are called subavalanches and are obtained by separation of original avalanches in the thresholding process. The correlations are evidenced by power law distributed waiting times and are present in the system even when the original avalanche triggerings are described by a random uncorrelated process.

Creep and thermal rounding close to the elastic depinning threshold

We study the slow stochastic dynamics near the depinning threshold of an elastic interface in a random medium by solving a particularly suited model of hopping interacting particles that belongs to the quenched-Edwards-Wilkinson depinning universality class. The model allows us to compare the cases of uniformly activated and Arrhenius activated hops. In the former case, the velocity accurately follows a standard scaling law of the force and noise intensity with the analog of the thermal rounding exponent satisfying a modified "hyperscaling" relation. For the Arrhenius activation, we find, both numerically and analytically, that the standard scaling form fails for any value of the thermal rounding exponent. We propose an alternative scaling incorporating logarithmic corrections that appropriately fits the numerical results. We argue that this anomalous scaling is related to the strong correlation between activated hops that, alternated with deterministic depinning-like avalanches, occur below the depinning threshold. We rationalize the spatiotemporal patterns by making an analogy of the present model in the near-threshold creep regime with some well-known models with extremal dynamics, particularly the Bak-Sneppen model.

Avalanches dynamics in reaction fronts in disordered flows

We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics

In the presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps called avalanches, while, at much smaller fields, these interfaces creep by thermal activation. In this Letter, we develop a novel numerical technique that captures the ultraslow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatiotemporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assemble in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee these correlated dynamics being experimentally accessible by magnetooptical imaging of ferromagnetic films.

Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady-state plastic flow, focusing on systems with low internal dissipation. We analyze the distributions of avalanche sizes and durations and the density of shear transformations when varying the damping strength. In contrast to avalanches in the overdamped case, dominated by the yielding point universal exponents, inertial avalanches are controlled by a nonuniversal damping-dependent feedback mechanism, eventually turning negligible the role of correlations. Still, some general properties of avalanches persist and new scaling relations can be proposed.

Linking scales in sea ice mechanics

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell-elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws.This article is part of the themed issue 'Microdynamics of ice'.

Interevent Correlations from Avalanches Hiding Below the Detection Threshold

Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or clustered, evidenced by power-law-distributed waiting times separating two consecutive activity bursts. We show how such interevent correlations arise simply because of a finite detection threshold, created by the limited sensitivity of the measurement apparatus, or used to subtract background activity or noise from the activity signal. Data from crack-propagation experiments and numerical simulations of a nonequilibrium crack-line model demonstrate how thresholding leads to correlated bursts of activity by separating the avalanche events into subavalanches. The resulting temporal subavalanche correlations are well described by our general scaling description of thresholding-induced correlations in crackling noise.

Power-law rheology controls aftershock triggering and decay

The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.

Universal correlations between shocks in the ground state of elastic interfaces in disordered media

The ground state of an elastic interface in a disordered medium undergoes collective jumps upon variation of external parameters. These mesoscopic jumps are called shocks, or static avalanches. Submitting the interface to a parabolic potential centered at w, we study the avalanches which occur as w is varied. We are interested in the correlations between the avalanche sizes S_{1} and S_{2} occurring at positions w_{1} and w_{2}. Using the functional renormalization group (FRG), we show that correlations exist for realistic interface models below their upper critical dimension. Notably, the connected moment 〈S_{1}S_{2}〉^{c} is up to a prefactor exactly the renormalized disorder correlator, itself a function of |w_{2}-w_{1}|. The latter is the universal function at the center of the FRG; hence, correlations between shocks are universal as well. All moments and the full joint probability distribution are computed to first nontrivial order in an ε expansion below the upper critical dimension. To quantify the local nature of the coupling between avalanches, we calculate the correlations of their local jumps. We finally test our predictions against simulations of a particle in random-bond and random-force disorder, with surprisingly good agreement.

Scaling laws in earthquake occurrence: Disorder, viscosity, and finite size effects in Olami-Feder-Christensen models

The relation between seismic moment and fractured area is crucial to earthquake hazard analysis. Experimental catalogs show multiple scaling behaviors, with some controversy concerning the exponent value in the large earthquake regime. Here, we show that the original Olami, Feder, and Christensen model does not capture experimental findings. Taking into account heterogeneous friction, the viscoelastic nature of faults, together with finite size effects, we are able to reproduce the different scaling regimes of field observations. We provide an explanation for the origin of the two crossovers between scaling regimes, which are shown to be controlled both by the geometry and the bulk dynamics.

Spontaneous instabilities and stick-slip motion in a generalized Hébraud-Lequeux model

We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.

Avalanche structural rearrangement through cracking-healing in weakly stressed cold dusty plasma liquids

We experimentally investigate the spatiotemporal dynamical behaviors of the avalanche structural rearrangement through micro-cracking-healing in weakly stressed cold dusty plasma liquids, and the kinetic origins for their different spatial and temporal classifications. The crystalline ordered domains can be cracked or temporarily sustain and transfer the weak stress to remote regions for cracking-healing. It is found that cracking sites form a fractal network with cluster size following power law distribution in the xyt space. The histograms of the persistent times for sustaining regional ordered and disordered structure, the temporal cracking burst width, and quiescent time between two bursts all follow power law decays with fast descending tails. Cracking can be classified into a single temporal burst with simple line like spatial patterns and the successive cracking fluctuation with densely packed cracking clusters. For an ordered region, whether the Burgers vectors of the incoming dislocations from the boundary allow direct dislocation reduction is the key for the above two classifications through cracking a large ordered domain into medium scale corotating ordered domains or small patches. The low regional structural order at the end of a cracking burst can be regarded as an alarm for predicting the short quiescent period before the next cracking burst.

Mechanical origin of aftershocks

Aftershocks are the most striking evidence of earthquake interactions and the physical mechanisms at the origin of their occurrence are still intensively debated. Novel insights stem from recent results on the influence of the faulting style on the aftershock organisation in magnitude and time. Our study shows that the size of the aftershock zone depends on the fault geometry. We find that positive correlations among parameters controlling aftershock occurrence in time, energy and space are a stable feature of seismicity independently of magnitude range and geographic areas. We explain the ensemble of experimental findings by means of a description of the Earth Crust as an heterogeneous elastic medium coupled with a Maxwell viscoelastic asthenosphere. Our results show that heterogeneous stress distribution in an elastic layer combined with a coupling to a viscous flow are sufficient ingredients to describe the physics of aftershock triggering.

Avalanche-size distributions in mean-field plastic yielding models

We discuss the size distribution N(S) of avalanches occurring at the yielding transition of mean-field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form N(S)∼S(-τ). However (contrary to what is found in its depinning counterpart), the value of τ depends on details of the dynamic protocol used. For random triggering of avalanches we recover the τ=3/2 exponent typical of mean-field models, which, in particular, is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary.

Frictional dynamics of viscoelastic solids driven on a rough surface

We study the effect of viscoelastic dynamics on the frictional properties of a (mean-field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed: at fast driving, above a critical threshold V(c), the system slides at the drive velocity and displays a friction force with velocity weakening. Below V(c) the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

Aftershocks and Omori's law in a modified Carlson-Langer model with nonlinear viscoelasticity

A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear viscoelasticity. Several aftershocks are generated after the main shock owing to the damping of the additional viscoelastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.

Aftershock production rate of driven viscoelastic interfaces

We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the decay law of aftershocks with time can be understood by considering the typical roughness of the interface and its evolution due to relaxation. In models where there is a single viscoelastic relaxation time there is an exponential decay of the number of aftershocks with time. In models in which viscoelastic relaxation is wave-vector dependent we typically find a power-law dependence of the decay rate that is compatible with the Omori law. The factors that determine the value of the decay exponent are analyzed.