Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure

A vanishing theorem for a class of logarithmic D-modules

Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = Cn. Let D X be a locally weakly quasi-homogeneous free divisor defined by a polynomial f. In this paper we prove that, locally, the annihilating ideal of 1/fk over DX is generated by linear differential operators of order 1 (for k big enough). For this purpose we prove a vanishing theorem for the extension groups of a certain logarithmic DX–module with OX. The logarithmic DX–module is naturally associated with D (see Notation 1.1). This result is related to the so called Logarithmic Comparison Theorem