DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Dionisios Margetis, University of Maryland, College Park

**Title: ***
Kinetic Aspects of Crystal Surface Evolution: Modeling and Analysis
*

**Abstract:**
I will present recent progress on applying concepts of kinetic theory
and PDEs to the evolution of crystalline epitaxial systems.
The major goal is to bridge analytically two length scales:
(i) the nanoscale, where line defects (``steps'') are evident; and
(ii) the macroscale, where nonlinear PDEs for the height profile are applied.
The starting point are coupled differential equations for the positions of steps. I will focus on three main results:
(a) For one-dimensional morphologies, the motion of steps is described in terms of BBGKY hierarchies for correlation functions. I will show how these hierarchies connect to the continuum limit, i.e., a single PDE for the surface height profile.
(b) The homogenization of reconstructed crystal surfaces,
where different phases coexist at the microscale, gives
rise to an interesting generalization of Fick's diffusion law.
(c) For geometries with rotational symmetry, a nonlinear parabolic PDE for the surface height approximately reduces to a hyperbolic PDE in Lagrangian coordinates. This PDE predicts shock-wave type solutions associated with moving boundaries of flat surface regions (facets).

**Time:** Friday, April 10, 2009, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491