Droplet formation in binary and ternary stochastic systems

Thomas Wanner
George Mason University

Stochastic partial differential equation systems serve as basic models for several phase separation phenomena in multi-component metal alloys. In a process called nucleation, the additive noise in the system forces the formation of localized droplets formed by one or more components of the system. In this talk, I will discuss dynamical aspects of this behavior in the context of stochastic versions of the celebrated Cahn-Hilliard and Cahn-Morral models. In addition to a brief description of the theoretical background, numerical studies will be presented in the context of alloys consisting of three metallic components which give a statistical classification for the distribution of droplet types as the component structure of the alloy is varied. We relate these statistics to the equilibrium structure of the deterministic Cahn-Morral system and show that even highly unstable equilibria can be observed during the nucleation process, and in fact serve as organizing centers for the dynamics. In addition, we try to shed some light on the size of the generated droplets by considering binary systems perturbed by degenerate noise of certain wavelengths.