Pulsating active matter

We propose and study some diffusive models where the internal states of particles are subject to a periodic drive. Inspired by some biological tissues, we consider dense assemblies of repulsive particles whose sizes are periodically increasing and decreasing. We show that the competition between steric repulsion and size synchronization triggers an instability which promotes a wealth of dynamical patterns, such as spiral waves and a defect turbulence. In a lattice version of this dynamics, we show that the discrete symmetry of states enforces an effective energy landscape which can counteract the drive to arrest the dynamics, and leads again to the emergence of spiral waves. In both models, using analytical coarse-graining, we rationalize the emergence of dynamical patterns from the breakdown of rotational invariance at the hydrodynamic level.