Critical nematic correlations throughout the superconducting doping range in Bi2-zPbzSr2-yLayCuO6+x.

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-Tc superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi2-zPbzSr2-yLayCuO6+x. The ratio of the phase correlation length ξCDW to the orientation correlation length ξorient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.

Recurrent activity in neuronal avalanches.

A new statistical analysis of large neuronal avalanches observed in mouse and rat brain tissues reveals a substantial degree of recurrent activity and cyclic patterns of activation not seen in smaller avalanches. To explain these observations, we adapted a model of structural weakening in materials. In this model, dynamical weakening of neuron firing thresholds closely replicates experimental avalanche size distributions, firing number distributions, and patterns of cyclic activity. This agreement between model and data suggests that a mechanism like dynamical weakening plays a key role in recurrent activity found in large neuronal avalanches. We expect these results to illuminate the causes and dynamics of large avalanches, like those seen in seizures.

Experimental evidence that shear bands in metallic glasses nucleate like cracks.

Highly time-resolved mechanical measurements, modeling, and simulations show that large shear bands in bulk metallic glasses nucleate in a manner similar to cracks. When small slips reach a nucleation size, the dynamics changes and the shear band rapidly grows to span the entire sample. Smaller nucleation sizes imply lower ductility. Ductility can be increased by increasing the nucleation size relative to the maximum ("cutoff") shear band size at the upper edge of the power law scaling range of their size distribution. This can be achieved in three ways: (1) by increasing the nucleation size beyond this cutoff size of the shear bands, (2) by keeping all shear bands smaller than the nucleation size, or (3) by choosing a sample size smaller than the nucleation size. The discussed methods can also be used to rapidly order metallic glasses according to ductility.

Topology of the energy landscape of sheared amorphous solids and the irreversibility transition.

Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior-for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition-the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.

The duration-energy-size enigma for acoustic emission.

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ Amaxx and Amax ~ Dχ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and 'half-moon' shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Sliding Avalanches Between Nacreous Tablets.

Nacre, also known as mother of pearl, possesses extraordinary mechanical properties resulting from its intriguing hierarchical brick-and-mortar microstructures. Despite prior studies, interactions between nanoasperities during sliding still need to be elucidated. In this study, we measure slip events between nanograins of microlayers at high temporal resolution during torsion-induced sliding. We model the slips as avalanches caused by interactions of atoms on nanograin surfaces, from which power laws and scaling functions describing statistics and dynamics of slip events are studied. The largest avalanche occurs when nanograins leave each other after the maximum contact. The agreement between measurements and predictions shows that avalanches act essentially in the inhomogeneous sliding of nacreous tablets. Further insights into nanofriction provided in this work may lead to the development of nanoscale tribological systems.

Applied-force oscillations in avalanche dynamics.

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or "slip avalanches." In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force control. The studies show very good agreement between simulations and experiments. We find that an oscillatory external driving force changes the average avalanche shapes only for avalanches with durations close to the period of oscillation of the external force. This effect on the avalanche shapes can be addressed in experiments by choosing suitable specimen dimensions so that the mechanical resonance does not interact with the avalanche dynamics. These results are important for the interpretation of avalanche experiments with built-in oscillators, and for the prediction and analysis of avalanche dynamics in systems with resonant vibrations.

Networks and Hierarchies: How Amorphous Materials Learn to Remember.

We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and subcycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provide new insight into the mechanisms that lead to reversible and irreversible behavior in amorphous solids.

Yield Precursor Dislocation Avalanches in Small Crystals: The Irreversibility Transition.

The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other nonequilibrium systems under external loading such as colloidal suspensions. These other systems exhibit transitions with clear analogies to work hardening and yield stress, with many typically undergoing purely elastic behavior only after "training" through repeated cyclic loading; studies in these other systems show a power-law scaling of the hysteresis loop extent and of the training time as the peak load approaches a so-called reversible-to-irreversible transition (RIT). We discover here that deformation of small crystals shares these key characteristics: yielding and hysteresis in uniaxial compression experiments of single-crystalline Cu nano- and micropillars decay under repeated cyclic loading. The amplitude and decay time of the yield precursor avalanches diverge as the peak stress approaches failure stress for each pillar, with a power-law scaling virtually equivalent to RITs in other nonequilibrium systems.

Aftershocks in slowly compressed bulk metallic glasses: Experiments and theory.

We observe two distinct interevent time patterns in the slip avalanches of compressed bulk metallic glasses (BMGs). Small slip avalanches cluster together in time, but large slip avalanches recur roughly periodically. We compare the timing patterns of BMG slip avalanches with timing patterns of earthquakes and with the predictions of a mean-field model. The time clustering of small avalanches is similar to the known time clustering of earthquake foreshocks and aftershocks.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials.

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Avalanches and scaling collapse in the large-N Kuramoto model.

We study avalanches in the Kuramoto model, defined as excursions of the order parameter due to ephemeral episodes of synchronization. We present scaling collapses of the avalanche sizes, durations, heights, and temporal profiles, extracting scaling exponents, exponent relations, and scaling functions that are shown to be consistent with the scaling behavior of the power spectrum, a quantity independent of our particular definition of an avalanche. A comprehensive scaling picture of the noise in the subcritical finite-N Kuramoto model is developed, linking this undriven system to a larger class of driven avalanching systems.

Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations.

Atomistic simulations of binary amorphous systems with over 4 million atoms are performed. Systems of two interatomic potentials of the Lennard-Jones type, LJ12-6 and LJ9-6, are simulated. The athermal quasistatic shearing protocol is adopted, where the shear strain is applied in a stepwise fashion with each step followed by energy minimization. For each avalanche event, the shear stress drop (Δσ), the hydrostatic pressure drop (Δσ_{h}), and the potential energy drop (ΔE) are computed. It is found that, with the avalanche size increasing, the three become proportional to each other asymptotically. The probability distributions of avalanche sizes are obtained and values of scaling exponents fitted. In particular, the distributions follow a power law, P(ΔU)∼ΔU^{-τ}, where ΔU is a measure of avalanche sizes defined based on shear stress drops. The exponent τ is 1.25±0.1 for the LJ12-6 systems, and 1.15±0.1 for the LJ9-6 systems. The value of τ for the LJ12-6 systems is consistent with that from an earlier atomistic simulation study by Robbins et al. [Phys. Rev. Lett. 109, 105703 (2012)]PRLTAO0031-900710.1103/PhysRevLett.109.105703, but the fitted values of other scaling exponents differ, which may be because the shearing protocol used here differs from that in their study.

Universal slip dynamics in metallic glasses and granular matter - linking frictional weakening with inertial effects.

Slowly strained solids deform via intermittent slips that exhibit a material-independent critical size distribution. Here, by comparing two disparate systems - granular materials and bulk metallic glasses - we show evidence that not only the statistics of slips but also their dynamics are remarkably similar, i.e. independent of the microscopic details of the material. By resolving and comparing the full time evolution of avalanches in bulk metallic glasses and granular materials, we uncover a regime of universal deformation dynamics. We experimentally verify the predicted universal scaling functions for the dynamics of individual avalanches in both systems, and show that both the slip statistics and dynamics are independent of the scale and details of the material structure and interactions, thus settling a long-standing debate as to whether or not the claim of universality includes only the slip statistics or also the slip dynamics. The results imply that the frictional weakening in granular materials and the interplay of damping, weakening and inertial effects in bulk metallic glasses have strikingly similar effects on the slip dynamics. These results are important for transferring experimental results across scales and material structures in a single theory of deformation dynamics.

Avalanche statistics from data with low time resolution.

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distribution of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.

Probabilistic model of waiting times between large failures in sheared media.

Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρ_{T}(t)=λ(F(t))P(F(t))exp[-∫_{0}^{t}dτλ(F(τ))P(F(τ))], where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.

Avalanche Statistics Identify Intrinsic Stellar Processes near Criticality in KIC 8462852.

The star KIC8462852 (Tabby's star) has shown anomalous drops in light flux. We perform a statistical analysis of the more numerous smaller dimming events by using methods found useful for avalanches in ferromagnetism and plastic flow. Scaling exponents for avalanche statistics and temporal profiles of the flux during the dimming events are close to mean field predictions. Scaling collapses suggest that this star may be near a nonequilibrium critical point. The large events are interpreted as avalanches marked by modified dynamics, limited by the system size, and not within the scaling regime.

Experiments and Model for Serration Statistics in Low-Entropy, Medium-Entropy, and High-Entropy Alloys.

High-entropy alloys (HEAs) are new alloys that contain five or more elements in roughly-equal proportion. We present new experiments and theory on the deformation behavior of HEAs under slow stretching (straining), and observe differences, compared to conventional alloys with fewer elements. For a specific range of temperatures and strain-rates, HEAs deform in a jerky way, with sudden slips that make it difficult to precisely control the deformation. An analytic model explains these slips as avalanches of slipping weak spots and predicts the observed slip statistics, stress-strain curves, and their dependence on temperature, strain-rate, and material composition. The ratio of the weak spots' healing rate to the strain-rate is the main tuning parameter, reminiscent of the Portevin-LeChatellier effect and time-temperature superposition in polymers. Our model predictions agree with the experimental results. The proposed widely-applicable deformation mechanism is useful for deformation control and alloy design.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Reversibility and criticality in amorphous solids.

The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.