Re-entrant Layer-by-Layer Etching of GaAs(001)

We report the first observation of re-entrant layer-by-layer etching based on {\it in situ\/} reflection high-energy electron-diffraction measurements. With AsBr$_3$ used to etch GaAs(001), sustained specular-beam intensity oscillations are seen at high substrate temperatures, a decaying intensity with no oscillations at intermediate temperatures, but oscillations reappearing at still lower temperatures. Simulations of an atomistic model for the etching kinetics reproduce the temperature ranges of these three regimes and support an interpretation of the origin of this phenomenon as the site-selectivity of the etching process combined with activation barriers to interlayer adatom migration.Comment: 11 pages, REVTeX 3.0. Physical Review Letters, in press

Decay rates for a class of diffusive-dominated interaction equations

We analyse qualitative properties of the solutions to a mean-field equation for particles interacting through a pairwise potential while diffusing by Brownian motion. Interaction and diffusion compete with each other depending on the character of the potential. We provide sufficient conditions on the relation between the interaction potential and the initial data for diffusion to be the dominant term. We give decay rates of Sobolev norms showing that asymptotically for large times the behavior is then given by the heat equation. Moreover, we show an optimal rate of convergence in the $L^1$-norm towards the fundamental solution of the heat equation.Comment: 22 page

Regulatory interactions between two actin nucleators, Spire and Cappuccino

Spire and Cappuccino are actin nucleation factors that are required to establish the polarity of Drosophila melanogaster oocytes. Their mutant phenotypes are nearly identical, and the proteins interact biochemically. We find that the interaction between Spire and Cappuccino family proteins is conserved across metazoan phyla and is mediated by binding of the formin homology 2 (FH2) domain from Cappuccino (or its mammalian homologue formin-2) to the kinase noncatalytic C-lobe domain (KIND) from Spire. In vitro, the KIND domain is a monomeric folded domain. Two KIND monomers bind each FH2 dimer with nanomolar affinity and strongly inhibit actin nucleation by the FH2 domain. In contrast, formation of the Spire–Cappuccino complex enhances actin nucleation by Spire. In Drosophila oocytes, Spire localizes to the cortex early in oogenesis and disappears around stage 10b, coincident with the onset of cytoplasmic streaming

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Ab initio study of step formation and self-diffusion on Ag(100)

Using the plane wave pseudopotential method we performed density functional theory calculations on the stability of steps and self-diffusion processes on Ag(100). Our calculated step formation energies show that the {111}-faceted step is more stable than the {110}-faceted step. In accordance with experimental observations we find that the equilibrium island shape should be octagonal very close to a square with predominately {111}-faceted steps. For the (100) surface of fcc metals atomic migration proceeds by a hopping or an exchange process. For Ag(100) we find that adatoms diffuse across flat surfaces preferentially by hopping. Adatoms approaching the close-packed {111}-faceted step edges descend from the upper terrace to the lower level by an atomic exchange with an energy barrier almost identical to the diffusion barrier on flat surface regions. Thus, within our numerical accuracy (approx +- 0.05 eV) there is no additional step-edge barrier to descent. This provides a natural explanation for the experimental observations of the smooth two-dimensional growth in homoepitaxy of Ag(100). Inspection of experimental results of other fcc crystal surfaces indicates that our result holds quite generally.Comment: 10 pages, 9 figures. Submitted to Phys. Rev B (October 31, 1996

Atomic Scale Modelling of Two-Dimensional Molecular Self-Assembly on a Passivated Si Surface

International audienceThe self-assembly of two-dimensional (2D) molecular structures on a solid surface relies on the subtle balance between non covalent intermolecular and molecule-surface forces. The energetics of 2D molecular lattices forming different patterns on a passivated semiconductor surface are here investigated by a combination of atomistic simulation methods. Density-functional theory provides structure and charges of the molecules, while metadynamics with empirical forces provides a best guess for the lowest-energy adsorption sites of single molecules and dimers. Subsequently, molecular dynamics simulations of extended molecular assemblies with empirical forces yield the most favorable lattice structures at finite temperature and pressure.The theoretical results are in good agreement with scanning tunneling microscopy observations of self-assembled molecular monolayers on a B-doped Si(111) surface, thus allowing to rationalize the competition of long-range dispersion forces between the molecules and the surface. Such a result demonstrates the interest of this predictive approach for further progress in supramolecular chemistry on semiconductor surface