Growth Inside a Corner: The Limiting Interface Shape
Mon, Jan. 16th 2012, 14:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We investigate the growth of a crystal, built by depositing elementary bricks inside a corner. This system can be modeled by an Ising ferromagnet endowed with zero-temperature spin-flip dynamics. In the long-time limit, the interface of this crystal approaches a deterministic growing limiting shape. par In two dimensions, the limiting shape is known and its area increases linearly with time. We explain how fluctuations of this shape can be calculated by Bethe Ansatz. par In three dimensions, the average shape is not known. Building on results for the corresponding two-dimensional system and accounting for basic three-dimensional symmetries, we conjecture a governing equation for the evolution of the interface profile. The analytical solution of this equation is in excellent agreement with simulations of the growth process. Generalizations to arbitrary spatial dimension will also be given.