Fingerprints of Random Flows?

TL;DR

This paper investigates the patterns formed by small rods in a 2D random flow, revealing the emergence and evolution of singularities in their direction field similar to fingerprint ridges.

Contribution

It provides a theoretical explanation for the formation and disappearance of singularities in the orientation field of rods advected by random flows.

Findings

Scar lines form where rods abruptly change direction by π.

Scar lines become narrow and heal over, leaving point singularities.

Point singularities resemble those seen in fingerprint patterns.

Abstract

We consider the patterns formed by small rod-like objects advected by a random flow in two dimensions. An exact solution indicates that their direction field is non-singular. However, we find from simulations that the direction field of the rods does appear to exhibit singularities. First, ` scar lines' emerge where the rods abruptly change direction by $\pi$. Later, these scar lines become so narrow that they ` heal over' and disappear, but their ends remain as point singularities, which are of the same type as those seen in fingerprints. We give a theoretical explanation for these observations.