Scaling behavior in a nonlocal and nonlinear diffusion equation

We present the results of analytical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing nonequilibrium processes ranging from aggregation phenomena to the cooperation of individuals. On tuning the initial conditions, a dynamical transition with a universal scaling behavior is observed between two different asymptotic (in time) solutions. The scaling behavior at the transition is also obtained in a self-organized manner, independent of the initial conditions, on temporally evolving the diffusion equation subjected to a mirror symmetry transformation.