The six-dimensional self-dual tensor

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant form. In particular, it is shown that the field-sttrength tensor satisfies a non-linear generalised self-duality constraint. The self-duality equation is rewritten in five-dimensional notation and shown to be identical to the corresponding equation in the non-covariant formalism.     

Morphological anisotropy during migration enhanced epitaxy of GaAs(0 0 1)

The GaAs(0 0 1) surface morphology and structure during growth by migration enhanced epitaxy (MEE) has been studied by reflection high energy electron diffraction and scanning tunneling microscopy. Changes induced by varying the incident As/Ga flux ratio, growth temperature and the total amount of material deposited in each cycle have been studied and the results compared with GaAs(0 0 1) growth by conventional molecular beam epitaxy (MBE). Comparison of the surface morphology at the end of the Ga and As cycles indicates no clear evidence for any enhancement in the Ga adatom diffusion length during the Ga cycle. However, the morphological anisotropy of the growth front does change significantly and it is proposed that this changing anisotropy during MEE enables Ga adatom diffusion along both azimuths. The surface anisotropy during MEE growth is found to increase with the Ga/As ratio. Although there is a clear correlation between composition and morphology, we have also found that highly ordered and flat surfaces are not necessarily an indication of stoichiometric material. We also attempt to clarify a recent controversy on the structure of the c(4 × 4) reconstruction by studying the surface structure at the end of the As cycle as a function of the As/Ga ratio.     

Rayleigh Conductivity and Self-Sustained Oscillations

The theory of self-sustaining oscillations of low Mach number, high Reynolds number shear layers, and jets impinging on edges and corners is discussed. Such oscillations generate narrow band sound, and are usually attributed to the formation of discrete vortices whose interactions with the edge or corner produce impulsive pressures that trigger the cyclic formation of new vorticity. A linearized analysis of these interactions is described in which free shear layers are treated as vortex sheets. Details are given for shear flow over wall apertures and shallow cavities, and for jet–edge interactions. The operating stages of the oscillations correspond to complex eigenvalues of the linear theory: for wall apertures and edge tones they are poles in the upper half of the complex frequency plane of the Rayleigh conductivity of the “window” spanned by the shear flow; for shallow wall cavities they are poles of a frequency-dependent drag coefficient. It is argued that the frequencies defined by the real parts of the complex frequencies at these poles determine the operating stage Strouhal numbers observed experimentally. Strouhal number predictions for a shallow wall cavity are in good agreement with data extrapolated to zero Mach number from measurements in air; edge tone predictions are in excellent accord with data from various sources in the literature. Received 3 January 1997 and accepted 13 February 1997     

Diffusion,evaporation, and surface enrichment of a plasticizing additive in an annealed polymer thin film

We present the first measurements of the simultaneous diffusion, surface enhancement, and evaporation of a plasticizer from a polymer, thin-film matrix using neutron reflection techniques. The reflectivity profiles as a function of the annealing time at an elevated temperature yield the time-dependent, plasticizer volume fraction profiles in a polyester–polyurethane (Estane) film. Thin, plasticizer-enriched layers form at both the polymer/substrate and polymer/air interfaces for annealed and unannealed samples. The diffusion equations for a material diffusing through a film and then evaporating into a vacuum at the free surface describe the loss of the plasticizer from the film for annealed samples. The loss of the plasticizer from the film is not limited by the movement of the plasticizer through the polymer matrix but is dominated by the plasticizer's rate of evaporation from the surface. The rate of evaporation and the volume fraction profiles for the plasticizer at the substrate interface are both consistent with surface attractions dominating over bulk attractions between the miscible plasticizer and the polymer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3258–3266, 2004     

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