This theoretical research will concentrate on three areas: (i) the dynamics of interfaces separating phases of matter; (ii) the kinetics of phase transitions; and, (iii) polymer statistical mechanics. The work on interface dynamics and pattern formation will involve examples from solidification as well as from fluid mechanics, and will contain aspects of both conceptual, e.g., defect dynamics in Hele-Shaw flow, and practical, e.g., materials fabrication, levels. The kinetics of phase transitions work will involve, for example, studies of the phase separation process under a variety of conditions, e.g., external driving fields or shear flows. Aspects of this work may have eventual application to the fabrication of polymer blends. The polymer statistical mechanics research will involve fluctuations in inhomogeneous media and will bear on stabilizing interfaces between different media. %%% The study of interfacial regions between different phases of matter, water and ice, for instance, is one of the most fundamental topics in condensed matter physics and one of the most practical in materials science. Analytical and numerical techniques will be used to study the evolution of interfaces and the kinetics of associated phase changes under a variety of conditions. The research will have important consequences for materials growth and fabrication, as well as basic physics.
