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.

This work presents Sketch2Scene, a framework that automatically turns a freehand sketch drawing inferring multiple scene objects to semantically valid, well arranged scenes of 3D models. Unlike the existing works on sketch-based search and composition of 3D models, which typically process individual sketched objects one by one, our technique performs co-retrieval and co-placement of 3D relevant models by jointly processing the sketched objects. This is enabled by summarizing functional and spatial relationships among models in a large collection of 3D scenes as structural groups. Our technique greatly reduces the amount of user intervention needed for sketch-based modeling of 3D scenes and fits well into the traditional production pipeline involving concept design followed by 3D modeling. A pilot study indicates that the 3D scenes automatically synthesized by our technique in seconds are comparable to those manually created by an artist in hours in terms of visual aesthetics.

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We give an elementary proof of the existence of an asymptotic expansion in powers of$k$of the Bergman kernel associated to$L$^{$k$}, where$L$is a positive line bundle over a compact complex manifold. We also give an algorithm for computing the coefficients in the expansion.