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On the mathematical modeling of crystal facets: A PDE approach with a touch of discreteness

Banff International Research Station for Mathematical Innovation and Discovery

Advances in materials science have enabled the observation and control of microstructures such as nanoscale defects with remarkable precision. In this talk, I will discuss recent progress and open challenges in understanding how small-scale details in the kinetics of crystal surfaces can macroscopically influence the surface morphological evolution. In particular, the evolution of crystal surface plateaus, facets, is characterized by an effective behavior at the macroscale that is not necessarily only the outcome of averaging, but instead may be dominated by certain discrete (microscopic) events. This "idiosyncrasy" of facet evolution raises challenging but interesting mathematical questions. My talk will explore via selected examples and methods how the kinetics of microscale defects near facets can plausibly leave their imprints to continuum-scale problems, at larger scales. The main tool is a fourth-order nonlinear PDE for the surface height profile. I will address and provide an answer to the question: Can this continuum description be reconciled with the motion of line defects (steps) at the nanoscale, and how

Mathematics; Partial differential equations; Numerical analysis

video/mp4

Author affiliation: University of Maryland, College Park

2019-03-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68740

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/