Nontrivial temporal scaling in a Galilean stick-slip dynamics

TL;DR

This paper investigates the complex temporal scaling behaviors in the stick-slip dynamics of a rough cylinder on an inclined plane, revealing fractal dissipation patterns and novel statistical properties relevant to friction and earthquake models.

Contribution

It demonstrates nontrivial temporal scaling laws and fractal dissipation sets in a physical system, advancing understanding beyond classical models.

Findings

Identification of robust nontrivial temporal scaling laws

Dissipation occurs on a fractal set with fixed dimension

Distribution of inactivity periods relates to a random Cantor set

Abstract

We examine the stick-slip fluctuating response of a rough massive non-rotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The experiments presented here, which are reminiscent of the Galileo's works with rolling objects on inclines, have brought in the last years important new insights into the friction between surfaces in relative motion and are of relevance for earthquakes, differing from classical block-spring models by the mechanism of energy input in the system. Robust nontrivial temporal scaling laws appearing in the dynamics of this system are reported, and it is shown that the time-support where dissipation occurs approaches a statistical fractal set with a fixed value of dimension. The distribution of periods of inactivity in the intermittent motion of the cylinder is also studied and found to be closely related to the lacunarity of a random version of the classic triadic Cantor set on the line.