Temporal analysis of acoustic emission from a plunged granular bed

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., the 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 granular AE events. For the natural-time analysis, the existence of self-organized critical states is revealed by calculating the variance of natural time χ(k), where kth 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.