Minimal surfaces with positive genus and finite total curvature in H2×R\mathbb{H}^2 \times \mathbb{R}

We construct the first examples of complete, properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other nondegenerate summands. We also establish that every horizontal catenoid is nondegenerate. Finally, using the same techniques, we are able to produce properly embedded minimal surfaces with infinitely many ends. Each annular end has finite total curvature and is asymptotic to a vertical totally geodesic plane.Comment: 32 pages, 4 figures. This revised version will appear in Geometry and Topolog

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

Preroughening, Diffusion, and Growth of An FCC(111) Surface

Preroughening of close-packed fcc(111) surfaces, found in rare gas solids, is an interesting, but poorly characterized phase transition. We introduce a restricted solid-on-solid model, named FCSOS, which describes it. Using mostly Monte Carlo, we study both statics, including critical behavior and scattering properties, and dynamics, including surface diffusion and growth. In antiphase scattering, it is shown that preroughening will generally show up at most as a dip. Surface growth is predicted to be continuous at preroughening, where surface self-diffusion should also drop. The physical mechanism leading to preroughening on rare gas surfaces is analysed, and identified in the step-step elastic repulsion.Comment: Revtex + uuencoded figures, to appear in Physical Review Letter

Charge dynamics of a single donor coupled to a few electrons quantum dot in silicon

We study the charge transfer dynamics between a silicon quantum dot and an individual phosphorous donor using the conduction through the quantum dot as a probe for the donor ionization state. We use a silicon n-MOSFET (metal oxide field effect transistor) biased near threshold in the SET regime with two side gates to control both the device conductance and the donor charge. Temperature and magnetic field independent tunneling time is measured. We measure the statistics of the transfer of electrons observed when the ground state D0 of the donor is aligned with the SET states

Self similar expanding solutions of the planar network flow

We prove the existence of self-similar expanding solutions of the curvature flow on planar networks where the initial configuration is any number of half-lines meeting at the origin. This generalizes recent work by Schn\"urer and Schulze which treats the case of three half-lines. There are multiple solutions, and these are parametrized by combinatorial objects, namely Steiner trees with respect to a complete negatively curved metric on the unit ball which span $k$ specified points on the boundary at infinity. We also provide a sharp formulation of the regularity of these solutions at $t=0$

Effects of submerged vegetation on water clarity across climates

A positive feedback between submerged vegetation and water clarity forms the backbone of the alternative state theory in shallow lakes. The water clearing effect of aquatic vegetation may be caused by different physical, chemical, and biological mechanisms and has been studied mainly in temperate lakes. Recent work suggests differences in biotic interactions between (sub)tropical and cooler lakes might result in a less pronounced clearing effect in the (sub)tropics. To assess whether the effect of submerged vegetation changes with climate, we sampled 83 lakes over a gradient ranging from the tundra to the tropics in South America. Judged from a comparison of water clarity inside and outside vegetation beds, the vegetation appeared to have a similar positive effect on the water clarity across all climatic regions studied. However, the local clearing effect of vegetation decreased steeply with the contribution of humic substances to the underwater light attenuation. Looking at turbidity on a whole-lake scale, results were more difficult to interpret. Although lakes with abundant vegetation (>30%) were generally clear, sparsely vegetated lakes differed widely in clarity. Overall, the effect of vegetation on water clarity in our lakes appears to be smaller than that found in various Northern hemisphere studies. This might be explained by differences in fish communities and their relation to vegetation. For instance, unlike in Northern hemisphere studies, we find no clear relation between vegetation coverage and fish abundance or their diet preference. High densities of omnivorous fish and coinciding low grazing pressures on phytoplankton in the (sub)tropics may, furthermore, weaken the effect of vegetation on water clarity