Asymptotic analysis and numerical simulations of atomic steps on crystalline surfaces


Marc Oliver Rieger
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA

and

Scuola Normale Superiore
Pisa, Italy
rieger@sns.it


Heinrich-Gregor Zirnstein
MPI for Mathematics in the Sciences
Leipzig, Germany
zirnstei@mis.mpg.de

Abstract: We study atomic steps on surfaces of crystals. the crystals under consideration are called ``unorthodox'' since their atomic steps show increasing oscillations for decreasing temperatures. Using a physical model for the shape of atomic steps on the surface of these crystals we perform numerical simulations for terrace- and island-like shapes of atomic steps. Moreover we use the $\Gamma$-limit approximation of the model to compare its solutions with experimental data and derive information on the temperature depenence of the relevant physical constants. this method may prove useful also in other physical problems th multiple scales.

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