The mesoscale morphology of homoepitaxial GaAs surfaces is explained with an anisotropic and nonlinear Kardar-Parisi-Zhang (KPZ) model in which adatoms are incorporated into the film from a metastable surface layer. Evaporation-condensation between the film and the metastable layer is proposed as the microscopic physical origin of the KPZ description, as well as of the excess noise observed in the power spectral density. The parabolic mounds observed experimentally in films grown on rough substrates are in good agreement with the surface shape expected from the solution of the KPZ equation in the large amplitude limit.

Using atomic force microscopy and in situ elastic light scattering we show that the surface of molecular beam epitaxy ͑MBE͒ grown GaAs tends towards an equilibrium roughness independent of the initial condition, as predicted by kinetic roughening theory. Two separate continuum growth equations are consistent with the observed equilibrium roughness, namely, the Kardar-Parisi-Zhang ͑KPZ͒ equation ‫ץ‬h/‫ץ‬tϭٌ 2 hϩ(/2) ϫ(ٌh) 2 ϩ, where h is the surface height and represents nonconservative noise, and the MBE equation ‫ץ‬h/‫ץ‬tϭϪٌ 4 hϪ(⌳/2)ٌ 2 (ٌh) 2 ϩ c , where c represents conservative noise. These equations represent different physical smoothing mechanisms, so to distinguish between them we have numerically solved both equations. A novel geometric implementation of the nonlinear terms avoids instabilities associated with stiffness of the equations. We find that the time and length scale dependence of the smoothing of initially rough substrates is consistent with the KPZ equation but not the MBE equation. As the growth temperature is increased the coefficient increases relative to , but the KPZ description remains valid over the entire measured temperature range of 550-600°C. Reducing the As overpressure increases the anisotropy of the surface morphology. We provide a physical interpretation of the KPZ equation in which the incorporation rate of mobile adatoms on the surface is governed by evaporation/condensation type dynamics. These results provide important insight into the MBE growth mechanism of GaAs.

Managing the appearance of images across different display environments is a difficult problem, exacerbated by the proliferation of high dynamic range imaging technologies. Tone reproduction is often limited to luminance adjustment and is rarely calibrated against psychophysical data, while color appearance modeling addresses color reproduction in a calibrated manner, albeit over a limited luminance range. Only a few image appearance models bridge the gap, borrowing ideas from both areas. Our take on scene reproduction reduces computational complexity with respect to the state-of-the-art, and adds a spatially varying model of lightness perception. The predictive capabilities of the model are validated against all psychophysical data known to us, and visual comparisons show accurate and robust reproduction for challenging high dynamic range scenes.

[1] The ablation hollows or ''suncups'' that form on the surface of snowfields in summer are a wonderful example of pattern formation in nature. Suncups reduce the albedo of the snow and set a characteristic length for interaction of wind with the snowpack. They also contain information about the properties of the snow and its ablation rate, which could be extracted if we had a more quantitative understanding of how suncups form. A mathematical model is proposed that explains the shape, size, and dynamical behavior of suncups in terms of the interaction of solar radiation with the snowpack. Using a perturbation method, we derive a nonlinear partial differential equation for the time-dependent shape of the snow surface from an approximate physical model for the interaction of solar radiation with snow. The resulting equation, which is similar to the Kuramoto-Sivashinsky equation in fluid mechanics, has solutions with characteristic length and amplitude. We find expressions for the characteristic size of suncups in terms of the spectrally averaged diffusion length of solar radiation in snow. The model correctly describes the shape of suncups, with their spatially ordered patterns of parabolic valleys and V-shaped ridges. It is also in remarkably good agreement with the observed length scales and growth rates. Depending on the relative values of the coefficients of the nonlinear terms in the differential equation, the suncup patterns can be either stationary in time or chaotic.

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