  New model equations are derived for dynamics of self-aggregation of
finite-size particles. Differences from standard Debye-Huckel and Keller-Segel
models are: the mobility of particles depends on the configuration of their
neighbors and linear diffusion acts on locally-averaged particle density. The
evolution of collapsed states in these models reduces exactly to
finite-dimensional dynamics of interacting particle clumps. Simulations show
these collapsed (clumped) states emerge from smooth initial conditions, even in
one spatial dimension.
