Synchronization of flexible sheets

TL;DR

This paper demonstrates that flexible sheets with symmetric forcing can spontaneously break symmetry and synchronize in-phase due to elastic deformation interactions in a fluid, highlighting elasticity's role in biological synchronization.

Contribution

It introduces a physical mechanism showing how symmetric internal forcing in flexible sheets leads to symmetry-breaking and synchronization through elastic deformation in fluid interactions.

Findings

Flexible sheets deform to break symmetry in fluid interactions.

Synchronization to in-phase conformation minimizes energy dissipation.

Elasticity plays a crucial role in symmetry-breaking and synchronization.

Abstract

When swimming in close proximity, some microorganisms such as spermatozoa synchronize their flagella. Previous work on swimming sheets showed that such synchronization requires a geometrical asymmetry in the flagellar waveforms. Here we inquire about a physical mechanism responsible for such symmetry-breaking in nature. Using a two-dimensional model, we demonstrate that flexible sheets with symmetric internal forcing, deform when interacting with each other via a thin fluid layer in such a way as to systematically break the overall waveform symmetry, thereby always evolving to an in-phase conformation where energy dissipation is minimized. This dynamics is shown to be mathematically equivalent to that obtained for prescribed waveforms in viscoelastic fluids, emphasizing the crucial role of elasticity in symmetry-breaking and synchronization.