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Dionisios Margetis : A tale of three scales in modeling crystal surface relaxation

Crystals play a critical role in the design of novel devices. The surface of a crystal can evolve with time and give rise to a variety of interesting structures used in applications. In this evolution, several length and time scales, from the atomistic to the continuum, are implicated. The description of their linkages poses challenging questions. How can surface evolution at large scales, possibly described by PDEs, emerge from the motion of mesoscale crystal defects? And how does the description of such defects arise from atomistic motion? In this talk, I will address recent progress and open challenges in answering these questions. In particular, I will discuss how facets, macroscopically flat surface regions, lead to PDE free boundary problems with nontrivial microstructures.

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