Abstract: Swarmalators are active particles that have internal phases and also swarm through space. Phase synchronization is affected by spatial arrangement, and spatial motion is affected by phase synchronization. Swarmalators have recently been realized in robotics labs, and may also play a role in describing collective behavior of biological organisms. In this work I will describe the effects of time delay in interactions on collective dynamics of a population of swarmalators. Delay resulted in the appearance of new collective states. One such state is a pseudo-crystaline structure - in which swarmalators form a quasi-static cluster, and another is a boiling state in which swarmalators near the boundary of the cluster perform convective motions. In both cases, the route to these states takes place through an oscillatory transient in which the whole cluster “breathes”. Remarkably, just a pair of nonlinear equations (in a system of N swarmalators) describes the behavior of the cluster during this transient. This system also exhibits an intriguing aging phenomenon. I will describe the specific mechanism by which the system ages - which involves gradual increase in the hexatic order parameter, accompanied by a series of annihilations of coordination number defect pairs.

Contact: Evgeniy Khain (Oakland University)