## 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.