Thermodynamics of stressed solids: Slow deformation and roughening of material interfaces

At every turn in nature we are confronted with complex patterns. Patterns often formed in multiphase systems by an intricate dynamics of mass transport, e.g. diffusion and/or advection, and mass exchange between individual phases. Here we consider instabilities of phase boundaries in idealized stressed multiphase systems. Specifically, we study the growth of small perturbations of surfaces by considering mass transport from regions, where the stress and chemical potential is high, to surrounding regions where the stress and chemical potential is low. We present a linear stability analysis for various stress configurations and their corresponding stability diagrams.