Nonequilibrium Interface Dynamics:
Hierarchical Modeling and Multiscale Simulation of Materials Interfaces

CSIC Building (#406), Seminar Room 4122.
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Theory and Simulation of 3D Crystal Growth: Shape Control

Dr. John Lowengrub

Mathematics at UC Irvine

Abstract:   In this talk, we consider the quasi-steady evolution of growing crystals in 3-D. A reexamination of this problem reveals that the Mullins-Sekerka instability may be suppressed by appropriately varying the undercooling (far-field temperature) in time. For example, in 3-D, by imposing the far-field temperature flux (rather than a temperature condition), we demonstrate that there exist critical conditions of flux at which self- similar or nearly self-similar nonlinear evolution occurs and the shape is dominated by a given mode leading to non-spherical, nearly shape invariant growing crystals. This result was predicted by our previous linear analysis and suggests that our theory is applicable to real physical systems. We provide a simulation of a physical experiment that could be carried out in a laboratory in which a desired shape of a crystal is achieved and maintained during growth by appropriately prescribing the far-field heat flux. This work has important implications for shape control in processing applications. To simulate the problem numerically, we use a boundary element method with a fully adaptive surface triangulation. This enables us to simulate 3-D crystals stably and accurately well into the nonlinear regime. This work is joint with Dr. Vittorio Cristini (Dept. Math, Dept Biomed Eng. UCI)