Research on: Hydrodynamic Limits of Particle Systems in Epitaxial Growth

Sep 11 - 13, 2015

University of Maryland, College Park
Center for Scientific Computation and Mathematical Modeling

CSIC Bldg. #406 Room 4148
University of Maryland
College Park, Maryland 20742
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ABSTRACT

In recent years, serious research efforts in mathematics are directed toward analyzing the limits of atomistic models for crystal surfaces. These models include stochastic lattice-gas models and other stochastic schemes that may bear analogies with schemes for shocks in hyperbolic conservation laws. Such promising descriptions form a starting point in understanding multiple-scale aspects of epitaxial growth, which is instrumental for the design and fabrication of modern opto-electronics. In the formal limit where the lattice spacing approaches zero, an alternate description of epitaxial growth may emerge, e.g., a mesoscale continuum theory with effective parameters or variables that depend on atomistic features. The intricacies of this limit need to be further explored.

GOALS

This research program is a continuation of the KI-Net activity ``Research on: Hydrodynamics Limits of Particle Systems for Crystal Surfaces''  held at CSCAMM in September 2013, building on new results obtained by some of the participants since then. The major goal of this 2015 meeting is to improve mathematical understanding of hydrodynamic limits coming from particle schemes for crystals. This KIT (Kinetic Interaction Team) will bring together senior and junior experts in this area, both in modeling and analysis, in order to advance mathematical knowledge in stochastic lattice-gas and other atomistic models and their limits. The topics to be studied include analytical and computational/numerical approaches, such as kinetic Monte Carlo methods and master-equation approaches.

CONFIRMED PARTICIPANTS

INFORMATION FOR PARTICIPANTS

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Email: dio@math.umd.edu