Avalanche statistics from data with low time resolution

Abstract

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.

Similarity of internal and external friction: Soft matter frictional instabilities obey mean field dissipation through slip avalanches

“…The names of these exponents are complicated for historical reasons. The mean field model predicts σ ρ = 1/2 and σ υz = 1/2 [5,6,20]. The scaling for the largest events again is slightly different from that of the small ones, consistent with the weakening prediction of the model that predicts FIG.…”

Transforming Mesoscale Granular Plasticity Through Particle Shape

“…To avoid this, we pass the first derivative of the stress data ∆q/∆ through a high pass filter to remove baseline drift, similar to the method used in Ref. [18] to correct for low time resolution data. Specifically, we subtract from ∆q/∆ a Gaussian-smoothed version of itself, where the strain scale of the smoothing is the approximate duration of an event.…”

“…On the experimental side, discerning between τ = 1.3 and 1.5 requires several decades of events to be observed and careful analysis [8,17,18]. Most importantly, experimental investigation into the plasticity mechanisms operative at the mesoscale has been scarce due to the difficulty of varying local interactions in systems whose constituent units are atoms, molecules, or even bubbles.…”

“…This measure, volatility, is model-independent and is particularly useful in comparing broadly distributed fluctuations in data with different or changing baselines [35]. Importantly, it sidesteps the issue faced in many plasticity experiments, of accurately locating and measuring the magnitude of stress drops [18,36], giving a robust method to quantify the jerkiness of plasticity data across experiments and even across systems. Plotting volatility versus the angle of internal friction, a measure of a granular material's shear strength [32], then enables us to extract trends in the way particle geometry correlates with strength and fluctuations in the plastic regime.…”

From critical behavior to catastrophic runaways: comparing sheared granular materials with bulk metallic glasses

“…See [5] for a schematic diagram and [1] for other details. The avalanches in the specimen were identified, characterized, and measured using previously established methods [1,26]. Of particular interest are the total stress drop S during an event (which is its "size"), the total duration t of the event (the "duration"), and the maximum magnitude M of the time derivative of the stresstime trace during the avalanche (the "maximum stress drop rate").…”