Zero Surface Tension Limit of Viscous Surface Waves

We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the “semi-small” initial data, we prove the zero surface tension limit of the problem within a local time interval. The unique local strong solution with surface tension is constructed as the limit of a sequence of approximate solutions to a special parabolic regularization. For the small initial data, we prove the global-in-time zero surface tension limit of the problem.     

Surface magnetism

The main lines of surface magnetism research before and after 1975 are reported. The overall changes of magnetic properties in surfaces and interfaces were investigated by a wide variety of experimental and theoretical techniques. A softened temperature dependence of magnetization, enhanced moments in clean surfaces, the existence of magnetic surface anisotropies and the sensitive dependence of magnetic surface properties on the structural and physicochemical state of the surface are now generally accepted.     

Surface defects

Lack of information on defects may impede progress in understanding many surface properties. A survey is made of the evidence for the effects of defects in various types of experiment. Work function measurements, LEED, decoration and chemical reactivity, atomic steps and high temperature properties are among the topics briefly reviewed. An extensive bibliography is given. There is a need for an agreed experimental protocol to deal with the problem of characterizing the degree of perfection of a specimen surface. The routine measurement of the work function may be provide the best simple means for monitoring defect concentrations.     

Quantum Theory of Surface Polaritons on a Rough Surface

In this paper, we present the quantum field theory of the surface phonon-polaritolis on a rough polar crystal surface. The dispersion relations of the surface phonon-polaritons and the dispersion relations of polariton leaking modes owing to the interaction between bulk TO mode with the surface effect and photons are derived. We also study the k-dependence of the electric field strength in each polariton branch. The numerical calculations for the dispersion relations and the k-dependence of the electric field strength are carried out for a stepped Gap surface. The results show that the surface roughness depressed the frequency of the surface phonon-polariton below its values in the absence of the surface roughness. For the frequencies of the polariton leaking modes, the photon-like one is enhanced by the surface roughness and the phonon-like one b depressed. Our evaluations also illustrate that the surface roughness introduces a strong dependence on the k-dependence of the electric field strength in each polariton branch.     

Area-Preserving Surface Diffeomorphisms

We prove some generic properties for C^r, r = 1,2,. . .,∞, area-preserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [10] on S² to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem. Research supported in part by National Science Foundation.     

Surface raman ellipsometry

A method for achieving the ultrahigh sensitivity required for surface Raman spectroscopy is described. Polarization selective heterodyne detection permits shot-noise limited subnomolayer detection with classically noisy picosecond laser sources. Preliminary experimental results show that the polarization selectivity can be used to reduce the overwhelming thermally induced changes in metal surface reflectivity.     

Surface gap solitons

We put forward the existence of surface gap solitons at the interface between uniform media and an optical lattice with defocusing nonlinearity. Such new type of solitons forms when the incident and reflected waves at the interface of the lattice experience Bragg scattering, and feature a combination of the unique properties of both surface waves and gap solitons. We discover that gap surface solitons exist only when the lattice depth exceeds a threshold value, that they can be made completely stable, and that they can form stable bound states.     

Surface orbital magnetism

We compute the surface correction to the density of states of a particle in a convex box subjected to a magnetic field. Applying these results to orbital magnetism, we find that at high temperatures or weak magnetic fields the surface magnetization is always paramagnetic, but oscillations appear at low temperatures. In two dimensions they can give very large paramagnetic contributions near integer values of the filling factor. Explicit formulas are given for the zero-field susceptibility and for samples with a cylindrical shape in arbitrary magnetic field.