A Novel Continuum
Model of the Evolution of
Crystalline Material
Dr. Daniel Kandel
Dept. of Physics of Complex Systems
Weizmann Institute of Science, Israel
Abstract: Continuum models are particularly
suitable for studies of the evolution of crystals on macroscopic scales. However,
crystals frequently have microscopic defects such as facet edges and dislocations.
Standard continuum models break down in the vicinity of these defects, which show up as
singularities. I will discuss a new definition of the continuum limit, which we
developed in order to solve this general problem. The new approach is called
Configurational Continuum, and is valid even at singularities. Far from singularities
the model is equivalent to standard continuum, while in the vicinity of a singularity
it is equivalent to an "atomistic" description of the system. The exact treatment of
microscopic defects in the continuum is achieved by following the evolution of an
ensemble of microscopic configurations rather than a single one. The applicability
of the model will be demonstrated on a 1D model of interacting particles and on a
model of the kinetics of atomic steps on a crystalline surface.
Location: CSCAMM is located on the 4th floor of the CSIC Building #406, between
the A.V. Williams Building #115 and parking lot XX. Directions can be found at home.cscamm.umd.edu/directions.
