Brun expansions of stepped surfaces

Brun expansions of stepped surfaces

Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on particular discrete planes and surfaces – namely stepped planes and stepped surfaces. We show that dual maps can be seen as discretizations of toral automorphisms. We then provide a connection between stepped planes and ...

PREFACE Stepped surfaces

Single-phase-field model of stepped surfaces.

We formulate a phase-field description of step dynamics on vicinal surfaces that makes use of a single dynamical field, at variance with previous analogous works in which two coupled fields are employed, namely, a phase-field proper plus the physical adatom concentration. Within an asymptotic sharp interface limit, our formulation is shown to retrieve the standard Burton-Cabrera-Frank model in ...

Functional stepped surfaces, flips, and generalized substitutions

A substitution is a non-erasing morphism of the free monoid. The notion of multidimensional substitution of non-constant length acting on multidimensional words introduced in [AI01,ABS04,Fer05a,Fer05b,Fer05c] is proved to be well-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated with any us...

Diffraction from stepped surfaces in thermal equilibrium

We have performed Monte Carlo simulations of the diffraction from simple two-dimensional models of vicinal surfaces in order to aid interpretation of measured diffraction profiles. At low temperature, we find the sharp diffraction features predicted from the analogy of stepped surfaces with two-dimensional incommensurate phases. These sharp features vanish only near the roughening temperature o...