Eur. Phys. J. E (2020) 43: 32
https://doi.org/10.1140/epje/i2020-11954-y

Regular Article

Ghost-patterning and non-patterning in a draining film model

School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

^* e-mail: r.m.l.evans@leeds.ac.uk

Received: 29 October 2018
Accepted: 5 May 2020
Published online: 29 May 2020

Abstract

Patterns can form when the uniform state of any system is unstable so that some non-uniform motif grows in amplitude. Here, we identify an alternative way to form non-trivial structures, which we call “ghost-patterns”. Ghost-patterns emerge from noisy initial conditions when all non-uniform modes decay in amplitude except for one non-trivial motif which fails to decay. Hence, in seeking structured states, it is not necessary to find positive growth rates. We demonstrate ghost-patterns in an idealized non-equilibrium model intended to emulate draining thin-film suspensions.