  In this paper we study a new model for patterns in two dimensions, inspired
by diblock copolymer melts with a dominant phase. The model is simple enough to
be amenable not only to numerics but also to analysis, yet sophisticated enough
to reproduce hexagonally packed structures that resemble the cylinder patterns
observed in block copolymer experiments.
  Starting from a sharp-interface continuum model, a nonlocal energy functional
involving a Wasserstein cost, we derive the new model using Gamma-convergence
in a limit where the volume fraction of one phase tends to zero. The limit
energy is defined on atomic measures; in three dimensions the atoms represent
small spherical blobs of the minority phase, in two dimensions they represent
thin cylinders of the minority phase.
  We then study minimisers of the limit energy. Numerical minimisation is
performed in two dimensions by recasting the problem as a computational
geometry problem involving power diagrams. The numerical results suggest that
the small particles of the minority phase tend to arrange themselves on a
triangular lattice as the number of particles goes to infinity. This is proved
in the companion paper Bourne, Peletier & Theil and agrees with patterns
observed in block copolymer experiments. This is a rare example of a nonlocal
energy-driven pattern formation problem in two dimensions where it can be
proved that the optimal pattern is periodic.
