Many physical systems involve a spherical support, such as droplets, vesicles, fullerenes and protein assemblies. Quadrupoles on different lattices are shown to orient in interesting ways that result various degrees of symmetry breaking.

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond $\ell_{\rm r}$, scale associated to induced velocity reversals, which typically extremely large and often cannot even be measured. Below nematic long-range. We construct study a hydrodynamic theory for this de facto phase its structu...