The evolution of geophysical shape descriptors under distance-driven flows

TL;DR

This paper studies how geophysical shape descriptors like axis ratios and roundness evolve over time under distance-driven flows, providing exact conditions and comparing with curvature-driven models of abrasion.

Contribution

It offers new theoretical results on the monotonic and quasiconcave evolution of shape descriptors under distance-driven flows, extending Aristotle's particle shape models.

Findings

Exact conditions for Aristotle's claims are established.

Shape descriptors exhibit monotonic or quasiconcave evolution.

Comparison with curvature-driven flows highlights similarities and differences.

Abstract

We investigate the evolution of axis ratios, roundness (isoperimetric ratio) and the number of static balance points under distance-driven flows. The latter have already been proposed by Aristotle as models of particle shape evolution and recent studies indicate that they may serve as models for frictional abrasion. We show exact conditions under which Aristotle's original claims are true. For several geophysical shape descriptors we prove monotonic or quasiconcave time evolution and compare these results with results from the literature on curvature-driven flows as models of collisional abrasion.