Parameter Dependence of Multiscale Systems and Nanostructures on Crystals

Abstract

In the first part of this article (Sections 1 and 2) we study atomic steps on surfaces of crystals. The crystals under consideration are called “unorthodox” since their atomic steps form increasingly fine nanostructures when the temperature decreases. Using a physical model for the shape of atomic steps on the surface of these crystals (the HMM-model) we perform numerical simulations for terrace- and islandlike shapes of atomic steps. In the second part of this article (Section 3) we present a method for obtaining information on the parameter dependence of multiscale systems by means of Γ-convergence. We apply this concept to derive partial information on the temperature dependence of some of the physical constants in the HMM-model and reveal a more complicated interplay of the various parameters than originally expected. Our method may prove useful also in other physical problems with multiple scales.