abbdd278_Es___Numerical_Methods_Seminar__TITLE
[DATE] 03/6/06 [SPEAKER] Dionisios Margetis MIT [TITLE] 
Mathematical modeling of crystal surfaces: From discrete schemes to continuum laws Dionisios Margetis Department of Mathematics, M.I.T. Abstract: In traditional settings such as fluids and classical elasticity the starting point (``truth'') is identified with continuum equations. But in many cases of mathematical modeling this perspective is changed: The truth is atomistic, or takes the form of discrete schemes, by which continuum laws must be determined at the macroscale. The issue of connections between different scales is largely unresolved. In this talk I focus on the evolution of crystal surfaces as a prototypical case of coupling between scales, with implications in the design of novel devices. The governing, discrete equations represent the motion of interacting line defects, atomic ``steps''. In the continuum limit a nonlinear PDE is derived for the surface height, and free-boundary problems are formulated for the surface motion. I show analytically how microscopic details of the crystal enter the requisite boundary conditions, and thus affect evolution at the macroscale.
CCMA PDEs & Numerical Methods Seminar
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