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We report an analysis of the discontinuous plastic flow of a multiprincipal-element alloy, ${\mathrm{Co}}_{17.5}{\mathrm{Cr}}_{12.5}{\mathrm{Fe}}_{55}{\mathrm{Ni}}_{10}{\mathrm{Mo}}_{5}$ (atomic percent, at. %), in the temperature range of 0.5--4.2 K showing serrated deformation curves. Using the analytical techniques, we studied the statistics of the stress drops associated with the unstable plastic flow. The analysis showed that the complexity and heterogeneity of a discontinuous plastic flow were reduced when the temperature was lowered. This behavior was associated with the effects of dynamic recovery and adiabatic heating on the dislocation-density evolution.

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)F4, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field)., 14 pages, 3 figures

Shear banding causes deformation to be heavily restricted in small volumes of a material, leading to catastrophic failure of materials. Yet how shear bands form is generally not known. Here, the authors follow the entire process of shear banding in the nanocrystalline ceramic (NCC) nanopillars of ZrN using $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ microscopy. The evidence obtained shows that the nanopillars deform through intermittent granular activities due to the nucleation and propagation of dislocations. The stress drops associated with these activities, however, are small as dislocation avalanches are restricted by the nanograin size. Shear band forms in NCC through localized and cooperative granular activities involving nanocrack formation.

Ferroelectric-field switching in $\mathrm{BaTi}{\mathrm{O}}_{3}$ generates ``Barkhausen noise'' when domain walls are displaced. We show by acoustic emission spectroscopy that electric-field switching of ${90}^{\ensuremath{\circ}}$ boundaries generates large strain fields, which emit acoustic phonons during ferroelectric hysteresis measurements. We use highly sensitive receivers (microphones) to measure the time sequences of noise in close analogy to noise patterns in ferroelastic and magnetic materials. Domain-wall interactions and jamming generate the ``crackling noise'' that follows scale invariant avalanche dynamics: the avalanche energy and amplitude probability distribution functions follow power laws with exponents $\ensuremath{\varepsilon}=1.65$ (energy) and \ensuremath{\tau}\ensuremath{'} = 2.25 (amplitudes). Aftershocks are very common and follow Omori law with probability $\ensuremath{\sim}{t}^{\ensuremath{-}p}$ where $t$ is the time elapsed after the main shock and $p$ is the Omori exponent $p\ensuremath{\sim}1$. The interevent times follow a double power-law distribution with exponents 0.9 for small times and 2.2 for the larger times. The scaling behavior is consistent with predictions of mean field theory.

We measure and analyze the statistics of nanoindentation pop-ins in a bulk metallic glass that has been annealed after being subjected to high pressure torsion. We argue that these pop-ins are avalanches of slip events. Larger slip avalanches are observed after annealing at higher temperatures. The slip avalanche size distribution shows scaling behavior and suggests the existence of a critical annealing temperature. Results are shown to be consistent with the predictions of a simple mean field theory. This implies that the statistics of slip avalanches in nanoindentation can be used to extract information about the structure, history, density, and free volume of the material. The methods employed here are expected to be applicable to a wide range of materials.

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.

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.

We report moment distribution results from a laboratory experiment, similar in character to an isolated strike-slip earthquake fault, consisting of sheared elastic plates separated by a narrow gap filled with a two-dimensional granular medium. Local measurement of strain displacements of the plates at 203 spatial points located adjacent to the gap allows direct determination of the event moments and their spatial and temporal distributions. We show that events consist of spatially coherent, larger motions and spatially extended (noncoherent), smaller events. The noncoherent events have a probability distribution of event moment consistent with an M(-3/2) power law scaling with Poisson-distributed recurrence times. Coherent events have a log-normal moment distribution and mean temporal recurrence. As the applied normal pressure increases, there are more coherent events and their log-normal distribution broadens and shifts to larger average moment.

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd_2Fe_(14)B becomes a room-temperature realization of the random field Ising model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field, where thermal fluctuations dominate the dynamics.

We explore the scaling behavior and complexity in the shear-branching process during the compressive deformation of a bulk metallic glass Zr(64.13)Cu(15.75)Al(10)Ni(10.12) (at. %) at cryogenic temperatures. The fractal dimension of the stress rate signal ranges from 1.22 to 1.72 with decreasing temperature and a larger shear-branching rate occurs at lower temperature. A stochastic model is introduced for the shear-branching process. In particular, at a temperature of 213K, the shear-branching process evolves as a self-similar random process. In addition, the complexity of the stress rate signal conforms to the larger activation energy of the shear transformation zone at lower temperatures.

Slowly compressed microcrystals deform via intermittent slip events, observed as displacement jumps or stress drops. Experiments often use one of two loading modes: an increasing applied stress (stress driven, soft), or a constant strain rate (strain driven, hard). In this work we experimentally test the influence of the deformation loading conditions on the scaling behavior of slip events. It is found that these common deformation modes strongly affect time series properties, but not the scaling behavior of the slip statistics when analyzed with a mean-field model. With increasing plastic strain, the slip events are found to be smaller and more frequent when strain driven, and the slip-size distributions obtained for both drives collapse onto the same scaling function with the same exponents. The experimental results agree with the predictions of the used mean-field model, linking the slip behavior under different loading modes.

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an epsilon expansion about six dimensions. We present the results of simulations in 3, 4, and 5 dimensions, with systems with up to a billion spins (1000^3)., Comment: Condensed and updated version of cond-mat/9609072,``Disorder-Induced Critical Phenomena in Hysteresis: A Numerical Scaling Analysis''

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed., 21 pages, RevTex, 6 figures (ps, eps)

We explain Barkhausen noise in magnetic systems in terms of avalanches near a plain old critical point in the hysteretic zero-temperature random-field Ising model. The avalanche size distribution has a universal scaling function, making non-trivial predictions of the shape of the distribution up to 50\% above the critical point, where two decades of scaling are still observed. We simulate systems with up to $1000^3$ domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2d and $6-\epsilon$ predictions, and compare to a variety of experimental Barkhausen measurements., Comment: 12 pages, 2 PostScript figures. Pedagogical introduction with mpeg movies available at http://www.lassp.cornell.edu/LASSP_Science.html

We show that slowly sheared metallic nanocrystals deform via discrete strain bursts (slips), whose size distributions follow power laws with stress-dependent cutoffs. We show for the first time that plasticity reflects tuned criticality, by collapsing the stress-dependent slip-size distributions onto a predicted scaling function. Both power-law exponents and scaling function agree with mean-field theory predictions. Our study of 7 materials and 2 crystal structures, at various deformation rates, stresses, and crystal sizes down to 75 nm, attests to the universal characteristics of plasticity.

The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the infinite avalanche'' first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6[minus][epsilon] dimensions, to first order in [epsilon]. Despite [epsilon]=3, the values obtained agree reasonably well with the numerical values in three dimensions.

We present a numerical study of the $\Delta H(M,\Delta M)$ method and its ability to accurately determine intrinsic switching field distributions in interacting granular magnetic materials such as perpendicular recording media. In particular, we study how this methodology fails for large ferromagnetic inter-granular interactions, at which point the associated strongly correlated magnetization reversal cannot be properly represented by the mean-field approximation, upon which the $\Delta H(M,\Delta M)$ method is based. In this study, we use a 2-dimensional array of symmetric hysterons that have an intrinsic switching field distribution of standard deviation $\sigma$ and ferromagnetic nearest-neighbor interactions $J$. We find the $\Delta H(M,\Delta M)$ method to be very accurate for small $J/\sigma$ values, while substantial errors develop once the effective exchange field becomes comparable with $\sigma$, corroborating earlier results from micromagnetic simulations. We furthermore demonstrate that this failure is correlated with deviations from data set redundancy, which is a key property of the mean-field approximation. Thus, the $\Delta H(M,\Delta M)$ method fails in a well defined and quantifiable manner that can be easily assessed from the data sets alone.

Barkhausen noise as found in magnets is studied both with and without the presence of long-range (LR) demagnetizing fields using the non-equilibrium, zero-temperature random-field Ising model. Two distinct subloop behaviors arise and are shown to be in qualitative agreement with experiments on thin film magnets and soft ferromagnets. With LR fields present subloops resemble a self-organized critical system, while their absence results in subloops that reflect the critical point seen in the saturation loop as the system disorder is changed. In the former case, power law distributions of noise are found in subloops, while in the latter case history-induced critical scaling is studied in avalanche size distributions, spin-flip correlation functions, and finite-size scaling of the second moments of the size distributions. Results are presented for simulations of over 10^8 spins., 4 pages, 3 figures

In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the non-equilibrium zero temperature Random Field Ising Model (RFIM), we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents $\tau$ and $1/\sigma\nu z$ in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling functions as well as between different experiments., Comment: 19 pages (in preprint format), 5 figures, 1 table