Equilibrium distribution of symmetric self-assembled structures

Many self-assembled structures are symmetric and are composed of identical subunits. The assembled structure depends not only on subunit position, but also on orientation, (ie. virus capsids, Janus particles, and liquid crystals). We find the equilibrium distribution of various symmetric self-assembly systems by enumerating all possible clusters. The degeneracy of the minima depends on the symmetry of the cluster. Theoretical results are compared with numerical simulations of the Langevin equation and macroscopic experiments. The validity of this comparison is proven by deriving the Smoluchowski equation for interacting elements that depend on orientation.