Nonequilibrium Interface Dynamics:
Fundamental Physical Issues in Nonequilibrium Interface Dynamics

CSIC Building (#406), Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions

Three Topics from Epitaxial Growth and Interface Motion

Dr. Robert Kohn

Courant Institute at New York University

Abstract:   The link between atomic-scale and continuum growth models remains poorly understood. Opportunities for progress include (1) new classes of continuum growth models; (2) new interpretations of standard growth laws; and (3) new approaches to systematic coarse-graining. I'll discuss one topic from each category, namely: Topic 1: A new type of epitaxial growth law, which represents the surface height and adatom density separately (joint with T.S. Lo). In this setting one accounts explicitly for nucleation, and for the uphill current associated with asymmetric attachment. Topic 2: A new kinetic interpretation for motion by curvature (joint with S. Serfaty). Motion by curvature is "thermodynamic," i.e. it represents steepest-descent for perimeter. Surprisingly, it also has a "kinetic" interpretation -- directly analogous to the interpretation of motion-by-constant-velocity via Huyghen's principle. Topic 3: A new approach to the coarse-graining of step-flow models (joint with N.K. Yip and T.S. Lo). Following Politi and Villain, one can derive a PDE by treating the atomic height as a small parameter. However the PDE is not valid across peaks and valleys: they must be treated as free boundaries, with boundary conditions that express the essential physics of nucleation and healing.