(A note on) self-similarity in granular media

TL;DR

This paper demonstrates that self-similarity naturally occurs in granular media with specific intergrain potentials, clarifying an overlooked aspect in existing literature.

Contribution

It explicitly establishes the presence of self-similarity in granular media with power-law intergrain potentials, filling a gap in prior research.

Findings

Self-similarity appears in granular media with potential V ∝ δ^{p+1}

This phenomenon was previously known but not explicitly stated in literature

Clarifies the conditions under which self-similarity occurs in granular systems

Abstract

It is shown that the phenomenon of self-similarity appears in granular media, with an intergrain potential $V \propto \delta^{p+1}$, $p > 1$, where $\delta$ is the overlap between the grains. Although this fact can be traced back in the literature, this has not been put explicitly.