Karin A. Dahmen

Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present results of numerical simulations in three dimensions.

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.

Self-driven mode switching of earthquake activity on a fault system

Theoretical results based on two different modeling approaches indicate that the seismic response of a fault system to steady tectonic loading can exhibit persisting fluctuations in the form of self-driven switching of the response back and forth between two distinct modes of activity. The first mode is associated with clusters of intense seismic activity including the largest possible earthquakes in the system and frequency‐size event statistics compatible with the characteristic earthquake distribution. The second mode is characterized by relatively low moment release consisting only of small and intermediate size earthquakes and frequency‐size event statistics following a truncated power law. The average duration of each activity mode scales with the time interval of a large earthquake cycle in the system. The results are compatible with various long geologic, paleoseismic, and historical records. The mode switching phenomenon may also exist in responses of other systems with many degrees of freedom and nonlinear dynamics.

AVALANCHES, BARKHAUSEN NOISE, AND PLAIN OLD CRITICALITY

We explain Barkhausen noise in magnetic systems in terms of avalanches of domains 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 nontrivial predictions of the shape of the distribution up to 50{percent} above the critical point, where two decades of scaling are still observed. We simulate systems with up to 1000{sup 3} domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2D and 6{minus}{epsilon} predictions, and compare to a variety of experiments. {copyright} {ital 1995 The American Physical Society.}

Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach

Hysteresis loops are often seen in experiments at first-order phase transformations, when the system goes out of equilibrium. They may have a macroscopic jump (roughly as in the supercooling of liquids) or they may be smoothly varying (as seen in most magnets). We have studied the nonequilibrium zero-temperature random-field Ising-model as a model for hysteretic behavior at first-order phase transformations. As disorder is added, one finds a transition where the jump in the magnetization (corresponding to an infinite avalanche) decreases to zero. At this transition we find a diverging length scale, power-law distributions of noise (avalanches), and universal behavior. We expand the critical exponents about mean-field theory in 6{minus}{epsilon} dimensions. Using a mapping to the pure Ising model, we Borel sum the 6{minus}{epsilon} expansion to {ital O}({epsilon}{sup 5}) for the correlation length exponent. We have developed a method for directly calculating avalanche distribution exponents, which we perform to {ital O}({epsilon}). Our analytical predictions agree with numerical exponents in two, three, four, and five dimensions [Perkovi{acute c} {ital et} {ital al}., Phys. Rev. Lett. {bold 75}, 4528 (1995)]. {copyright} {ital 1996 The American Physical Society.}

Bulk metallic glasses deform via slip avalanches.

For the first time in metallic glasses, we extract both the exponents and scaling functions that describe the nature, statistics, and dynamics of slip events during slow deformation, according to a simple mean field model. We model the slips as avalanches of rearrangements of atoms in coupled shear transformation zones (STZs). Using high temporal resolution measurements, we find the predicted, different statistics and dynamics for small and large slips thereby excluding self-organized criticality. The agreement between model and data across numerous independent measures provides evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.

Tuned Critical Avalanche Scaling in Bulk Metallic Glasses

Ingots of the bulk metallic glass (BMG), Zr64.13Cu15.75Ni10.12Al10 in atomic percent (at. %), are compressed at slow strain rates. The deformation behavior is characterized by discrete, jerky stress-drop bursts (serrations). Here we present a quantitative theory for the serration behavior of BMGs, which is a critical issue for the understanding of the deformation characteristics of BMGs. The mean-field interaction model predicts the scaling behavior of the distribution, D(S), of avalanche sizes, S, in the experiments. D(S) follows a power law multiplied by an exponentially-decaying scaling function. The size of the largest observed avalanche depends on experimental tuning-parameters, such as either imposed strain rate or stress. Similar to crystalline materials, the plasticity of BMGs reflects tuned criticality showing remarkable quantitative agreement with the slip statistics of slowly-compressed nanocrystals. The results imply that material-evaluation methods based on slip statistics apply to both crystalline and BMG materials.

Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

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 three, four, and five dimensions, with systems with up to a billion spins (1000{sup 3}). thinsp {copyright} {ital 1999} {ital The American Physical Society}

Universal pulse shape scaling function and exponents: Critical test for avalanche models applied to Barkhausen noise

In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the nonequilibrium zero-temperature Random Field Ising Model, 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.

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.