Band width estimates via the Dirac operator

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the distance between the boundary components of $V$ is at most $C_n/\sqrt{\sigma}$, where $C_n = \sqrt{(n-1)/{n}} \cdot C$ with $C < 8(1+\sqrt{2})$ being a universal constant. This verifies a conjecture of Gromov for such manifolds. In particular, our result applies to all high-dimensional closed simply connected manifolds $M$ which do not admit a metric of positive scalar curvature. We also establish a quadratic decay estimate for the scalar curvature of complete metrics on manifolds, such as $M \times \mathbb{R}^2$, which contain $M$ as a codimension two submanifold in a suitable way. Furthermore, we introduce the "$\mathcal{KO}$-width" of a closed manifold and deduce that infinite $\mathcal{KO}$-width is an obstruction to positive scalar curvature.Comment: 24 pages, 2 figures; v2: minor additions and improvements; v3: minor corrections and slightly improved estimates. To appear in J. Differential Geo

Optical constants of refractory oxides at high temperatures

Many cosmic dust species, among them refractory oxides, form at temperatures higher than 300 K. Nevertheless, most astrophysical studies are based on the room-temperature optical constants of solids, such as corundum and spinel. A more realistic approach is needed for these materials, especially in the context of modeling late-type stars. We aimed at deriving sets of optical constants of selected, astrophysically relevant oxide dust species with high melting points. A high-temperature-high-pressure-cell and a Fourier-transform spectrometer were used to measure reflectance spectra of polished samples. For corundum (alpha-Al$_2$O$_3$), spinel (MgAl$_2$O$_4$), and alpha-quartz (SiO$_2$), temperature-dependent optical constants were measured from 300 K up to more than 900 K. Small particle spectra were also calculated from these data. All three examined oxides show a significant temperature dependence of their mid-IR bands. For the case of corundum, we find that the 13$\mu$m emission feature - seen in the IR spectra of many AGB stars - can very well be assigned to this mineral species. The best fit of the feature is achieved with oblate corundum grains at mean temperatures around 550 K. Spinel remains a viable carrier of the 13$\mu$m feature as well, but only for T < 300 K and nearly spherical grain shapes. Under such circumstances, spinel grains may also account for the 31.8$\mu$m band that is frequently seen in sources of the 13$\mu$m feature and which has not yet been identified with certainty.Comment: Astronomy & Astrophysics, accepted, 26 February 2013. Article with 18 pages and 15 figure

Slant products on the Higson-Roe exact sequence

We construct a slant product $/ \colon \mathrm{S}_p(X \times Y) \times \mathrm{K}_{1-q}(\mathfrak{c}^{\mathrm{red}}Y) \to \mathrm{S}_{p-q}(X)$ on the analytic structure group of Higson and Roe and the K-theory of the stable Higson corona of Emerson and Meyer. The latter is the domain of the co-assembly map $\mu^\ast \colon \mathrm{K}_{1-\ast}(\mathfrak{c}^{\mathrm{red}}Y) \to \mathrm{K}^\ast(Y)$. We obtain such products on the entire Higson--Roe sequence. They imply injectivity results for external product maps. Our results apply to products with aspherical manifolds whose fundamental groups admit coarse embeddings into Hilbert space. To conceptualize the class of manifolds where this method applies, we say that a complete $\mathrm{spin}^{\mathrm{c}}$-manifold is Higson-essential if its fundamental class is detected by the co-assembly map. We prove that coarsely hypereuclidean manifolds are Higson-essential. We draw conclusions for positive scalar curvature metrics on product spaces, particularly on non-compact manifolds. We also obtain equivariant versions of our constructions and discuss related problems of exactness and amenability of the stable Higson corona.Comment: 82 pages; v2: Minor improvements. To appear in Ann. Inst. Fourie

Feasibility Study: Vertical Farm EDEN

Hundreds of millions of people around the world do not have access to sufficient food. With the global population continuing to increase, the global food output will need to drastically increase to meet demands. At the same time, the amount of land suitable for agriculture is finite, so it is not possibly to meet the growing demand by simply increasing the use of land. Thus, to be able to feed the entire global population, and continue to do so in the future, it will be necessary to drastically increase the food output per land area. One idea which has been recently discussed in the scientific community is called Vertical Farming (VF), which cultivates food crops on vertically stacked levels in (high-rise) buildings. The Vertical Farm, so it is said, would allow for more food production in a smaller area. Additionally, a Vertical Farm could be situated in any place (e.g. Taiga- or desert regions, cities), which would make it possible to reduce the amount of transportation needed to deliver the crops to the supermarkets. The technologies required for the Vertical Farm are well-known and already being used in conventional terrestrial greenhouses, as well as in the designs of bioregenerative Life Support Systems for space missions. However, the economic feasibility of the Vertical Farm, which will determine whether this concept will be developed or not, has not yet been adequately assessed. Through a Concurrent Engineering (CE) process, the DLR Institute for Space Systems (RY) in Bremen, aims to apply its know-how of Controlled Environment Agriculture (CEA) Technologies in space systems to provide valuable spin-off projects on Earth and to provide the first engineering study of a Vertical Farm to assess its economic feasibility

The Core Composition of a White Dwarf in a Close Double Degenerate System

We report the identification of the double degenerate system NLTT 16249 that comprises a normal, hydrogen-rich (DA) white dwarf and a peculiar, carbon-polluted white dwarf (DQ) showing photospheric traces of nitrogen. We disentangled the observed spectra and constrained the properties of both stellar components. In the evolutionary scenario commonly applied to the sequence of DQ white dwarfs, both carbon and nitrogen would be dredged up from the core. The C/N abundance ratio (~ 50) in the atmosphere of this unique DQ white dwarf suggests the presence of unprocessed material (14N) in the core or in the envelope. Helium burning in the DQ progenitor may have terminated early on the red-giant branch after a mass-ejection event leaving unprocessed material in the core although current mass estimates do not favor the presence of a low-mass helium core. Alternatively, some nitrogen in the envelope may have survived an abridged helium-core burning phase prior to climbing the asymptotic giant-branch. Based on available data, we estimate a relatively short orbital period (P <~ 13 hrs) and on-going spectroscopic observations will help determine precise orbital parameters.Comment: Accepted for publication in ApJ Letter