Temporal analysis of acoustic emission from a plunged granular bed

Abstract

The statistical property of acoustic emission (AE) events from a plunged granular bed is analyzed by means of actual time and natural time analyses. These temporal analysis methods allow us to investigate the details of AE events that follow a power-law distribution. In the actual time analysis, the calm time distribution and the decay of the event-occurrence density after the largest event (i.e., Omori-Utsu law) are measured. Although the former always shows a power-law form, the latter does not always obey a power law. Markovianity of the event-occurrence process is also verified using a scaling law by assuming that both of them exhibit power laws. We find that the effective shear strain rate is a key parameter to classify the emergence rate of power-law nature and Markovianity in the granular AE events. For the natural time analysis, the existence of self organized critical (SOC) states is revealed by calculating the variance of natural time $χ_k$, where $k$th natural time of N events is defined as $χ_k=k/N$. In addition, the energy difference distribution can be fitted by a $q$-Gaussian form, which is also consistent with the criticality of the system.