PHYSICAL MATHEMATICS SEMINAR
TITLE: A VARIATIONAL APPROACH TO THE DYNAMICS
OF STEPPED NANOSTRUCTURE SURFACES
SPEAKER: VIVEK SHENOY
Division of Engineering
Brown University
ABSTRACT:
I will talk about a variational formulation that we have recently
developed to study the singular evolution equations that govern the
dynamics of surface modulations on crystals below the roughening
temperature. The basic idea of the formulation is to expand the surface
shape in terms of a complete set of basis functions, and to use a
variational principle equivalent to the continuum evolution equations to
obtain coupled nonlinear ordinary differential equations for the expansion
coefficients.
Unlike several earlier approaches that rely on ad hoc regularization
procedures to handle the singularities in the evolution equations, the
only inputs required in the present approach are the orientation dependent
surface energies and the diffusion constants. The method will be applied
to study the morphological equilibration of patterned unidirectional and
bidirectional sinusoidal modulations on semiconductor surfaces and the
growth of quantum dots and quantum wires via strain-driven self-assembly.
TUESDAY, OCTOBER 7, 2003, 2:30 pm, Building 2, Room 338
Refreshments will be served at 3:30PM in Room 2-349
Massachusetts Institute of Technology, Department of Mathematics,
Cambridge, MA 02139