  We construct a continuum model for biological aggregations in which
individuals experience long-range social attraction and short range dispersal.
For the case of one spatial dimension, we study the steady states analytically
and numerically. There exist strongly nonlinear states with compact support and
steep edges that correspond to localized biological aggregations, or clumps.
These steady state clumps are approached through a dynamic coarsening process.
In the limit of large population size, the clumps approach a constant density
swarm with abrupt edges. We use energy arguments to understand the nonlinear
selection of clump solutions, and to predict the internal density in the large
population limit. The energy result holds in higher dimensions as well, and is
demonstrated via numerical simulations in two dimensions.
