Mesoscopic simulation for self-organization in surface processes

The self-organization of particles in a system through a diffusive mechanism is known as Ostwald ripening. This phenomenon is an example of a multiscale problem in that the microscopic level interaction of the particles can greatly impact the macroscale or observable morphology of the system. The mesoscopic model of this physical situation is a stochastic partial differential equation which can be derived from the appropriate particle system. This model is studied through the use of recently developed and benchmarked spectral schemes for the simulation of solutions to stochastic partial differential equations. The results included here demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system at the macroscopic level.