No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek–Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery’s equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics–Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek–Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.

The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical BusemannPetty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corresponding analogue of the Busemann-Petty centroid inequality is established for convex bodies.