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Traveling and resting crystals in crowds of self-propelled particles

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Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains

When the density within a crowd of self-propelled particles is high enough and when the interactions between these particles are strong enough, then it is plausible to expect that crystallization will occur. We are interested in the formation and in the behavior of such active crystals that are composed of self-propelled particles. To study this kind of materials using a field approach, we combine the classical phase field crystal model by Elder and Grant with the Toner-Tu theory for active media. In this way we obtain an active phase field crystal model. Our approach can further be justified from dynamic density functional theory. The active crystals that we identify can be classified into two groups: either the crystal is resting, meaning that no net density flux is observed, or it is traveling, meaning that the lattice peaks collectively migrate into one direction. As a central result we find that a transition from a resting to a traveling crystal can occur at a threshold value of the active drive. Consequently a variety of different crystalline phases can be identified: resting hexagonal, traveling hexagonal, swinging hexagonal, traveling rhombic, traveling quadratic, resting lamellar, traveling lamellar, resting honeycomb, and traveling honeycomb. Upon quenching from the fluid phase, the traveling crystals emerge through a coarse-graining process from domains of different directions of collective motion. Qualitatively we also studied the impact of additional hydrodynamic interactions between the lattice peaks. Since the properties and response of active crystals can be very different from their equilibrium counterparts, the knowledge of, classification of, and control of the different crystalline states can provide a starting point for the design of new active materials.

Co-author: Hartmut Lowen (Heinrich Heine University Dusseldorf, Germany)

This talk is part of the Isaac Newton Institute Seminar Series series.

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