Glasner DMS-0807423 The investigator considers fluid and solid interfaces that have multiscale behavior, spatiotemporal interaction and large scale organization. One component of this project focuses on the evolution of gravitational and surface tension induced free surface instabilities in viscous fluids, which give rise to coherent structures like fluid droplets, ridges and jets. Perturbative techniques and computational studies lead toward a description of large-scale condensation and geophysical processes. A second component of the project involves dynamical models of material microstructures. Patterning in systems with nonlocal interactions, such as block copolymer mixtures, is studied from the point of view of dynamical development, utilizing formal and numerical approximations, and homogenization techniques that yield statistical descriptions. The motion of grain boundaries in crystalline surface evolution and pattern formation equations also is investigated, seeking to characterize the singular structures that emerge both from energetic and geometric perspectives. The investigator studies how fluid and solid interfaces move and interact in complicated, large systems. Models and simulations are developed that are used to explain laboratory observations and that have capabilities to predict and control dynamics for design and manufacturing. Fluid flows that are studied have applications ranging from industrial coatings to geophysical morphology, such as cave formations. The solid systems of interest include block copolymers, "designer" materials that hold considerable promise for nano-engineering. The project also includes educational aims that expose undergraduates to modeling and computation and train graduate students for scientific careers.