Birational automorphisms of quartic Hessian surfaces

We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice of rank 26 and signature . The generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of Kondo. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface.

     

Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion

The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed flow factors in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Laguerre geometry of surfaces with plane lines of curvature

We study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate allL- minimal surfaces with plane curvature lines. Partially supported by MURST 40.     

Molecular beam epitaxy

Molecular beam epitaxy (MBE) is a process for growing thin, epitaxial films of a wide variety of materials, ranging from oxides to semiconductors to metals. It was first applied to the growth of compound semiconductors. That is still the most common usage, in large part because of the high technological value of such materials to the electronics industry. In this process beams of atoms or molecules in an ultra-high vacuum environment are incident upon a heated crystal that has previously been processed to produce a nearly atomically clean surface. The arriving constituent atoms form a crystalline layer in registry with the substrate, i.e., an epitaxial film. These films are remarkable because the composition can be rapidly changed, producing crystalline interfaces that are almost atomically abrupt. Thus, it has been possible to produce a large range of unique structures, including quantum well devices, superlattices, lasers, etc., all of which benefit from the precise control of composition during growth. Because of the cleanliness of the growth environment and because of the precise control over composition, MBE structures closely approximate the idealized models used in solid state theory.

This discussion is intended as an introduction to the concept and the experimental procedures used in MBE growth. The refinement of experimental procedures has been the key to the successful fabrication of electronically significant devices, which in turn has generated the widespread interest in the MBE as a research tool. MBE experiments have provided a wealth of new information bearing on the general mechanisms involved in epitaxial growth, since many of the phenomena initially observed during MBE have since been repeated using other crystal growth processes. We also summarize the general types of layered structures that have contributed to the rapid expansion of interest in MBE and its various offshoots. Finally we consider some of the problems that remain in the growth of heteroepitaxial structures, specifically, the problem of mismatch in lattice constant between layers and between layer and substrate. The discussion is phenomenological, not theoretical; MBE has been primarily an experimental approach based on simple concepts.     

An atomistic view of electrochemistry

One of the most important tasks of modern, physical electrochemistry is the development of an atomistic picture of the solid/liquid interface in order to provide the basis for a mechanistic understanding of electrochemical processes. Electrochemists seek answers to the same questions as their surface science colleagues (e.g., electronic and structure properties of surfaces and adlayers), but are faced with the fact that in electrochemistry the contact of the solid with a condensed phase, the electrolyte, makes life much more difficult. Nevertheless, electrochemists succeeded in the last 20 years to develop an electrochemical surface science by adopting experimental techniques and theoretical concepts from surface physicists.

This article describes the various routes electrochemists have used to obtain a detailed characterization of electrode surfaces in particular, and of the electrochemical interface in general. Success in physical electrochemistry is based on the development of non-traditional in situ methods to complement the classical, current- and voltage-based techniques. The former range from optical spectroscopies, linear and non-linear, to in situ X-ray diffraction and scanning tunneling microscopy. The current status of electrochemical surface science and its most important future goals are briefly addressed.     

The possible role of intermediate NH species in oscillations of the NO+H2 reaction on noble metal surfaces

A comparative study of the thermodynamic properties of adsorbed NH_n species (n = 0, 1, 2, 3) on transition metal surfaces is performed by using the semi-empirical method of interacting bonds. The principal difference between single crystal surfaces exhibiting oscillatory behavior in the NO+H₂ reaction, and those surfaces which do not show such a behavior is that the combination reaction of NH species can easily proceed in the former case, whereas it is substantially endothermic on the latter surfaces.A trigger-like route for the oscillatory behavior is considered where the combination reaction of NH species operates as a temporary reaction pathway. This pathway practically does not contribute to the N₂ formation until the nitrogen coverage reaches some critical value, which ensures a sufficiently close distance between adjacent NH particles. The trigger pathway starts upon reaching that stage initiating the surface wave propagation, and stops immediately when the wave propagation is completed. The surface becomes then nearly clean and ready for the next oscillatory cycle. In this way, the feedback mechanism and the critical point of the regular wave initiation can be understood without any further assumptions. An alternative key reaction is also considered.     

Hydrogen adsorption on Mo1−xRex(110) (x=0–0.25) surfaces

The effects of adsorbed H on the Mo_1−xRe_x(110), x=0, 0.05, 0.15, and 0.25, surfaces have been investigated using low-energy electron diffraction (LEED) and high-resolution electron energy loss spectroscopy (HREELS). For the x=0.15 alloy only, a c(2×2) LEED pattern is observed at a coverage Θ0.25 ML. A (2×2) pattern is observed for H coverages around Θ0.5 ML from surfaces with x=0, 0.05, and 0.15. Both c(2×2) and (2×2) patterns are attributed to reconstruction of the substrate. At higher coverages, a (1×1) pattern is observed. For the alloy surface with x=0.25, only a (1×1) pattern is obtained for all H coverages. Two H vibrations are observed in HREELS spectra for all Re concentrations, which shift to higher energies at intermediate coverages. Both peaks exhibit an isotopic shift, confirming their assignment to hydrogen. For Re concentrations of x=0.15 and higher, a third HREELS peak appears at 50 meV as H (D) coverage approaches saturation. This peak does not shift in energy with isotopic substitution, yet cannot be explained by contamination. The intrinsic width of the loss peaks depends on the Re concentration in the surface region and becomes broader with increasing x. This broadening can be attributed to surface inhomogeneity, but may also reflect increased delocalization of the adsorbed hydrogen atom.     

Selectivity of complex heterogeneous catalytic reactions over energetically nonuniform surfaces

The selectivity in parallel and consecutive heterogeneous catalytic reactions over nonuniform surfaces has been analyzed within the framework of the surface electron gas model. Equations for the selectivity are derived in the case of slow adsorption (no rate-limiting steps). Conditions when the nonuniform character of real catalytic surfaces should be taken into account in modeling of the selectivity behavior are discussed.