Aggregation of Finite-Size Particles with Variable Mobility

New model equations are derived for dynamics of aggregation of finite-size particles. The differences from standard Debye-Hückel and Keller-Segel models are that 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. Extensions to two and three dimenstions are also discussed.