Enlargeability and index theory

Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal $C^*$-algebra of the fundamental group of M. Our proof is independent from the injectivity of the Baum-Connes assembly map for the fundamental group of M and relies on the construction of a certain infinite dimensional flat vector bundle out of a sequence of finite dimensional vector bundles on M whose curvatures tend to zero. Besides the well known fact that M does not carry a metric with positive scalar curvature, our results imply that the classifying map $M \to B \pi_1(M)$ sends the fundamental class of M to a nontrivial homology class in H_n(B \pi_1(M) ; \Q). This answers a question of Burghelea (1983).Comment: 32 pages, final version accepted for publication, added relation to Gromov's 1-systole, typos corrected; to appear in Journal of Differential Geometr

The space of metrics of positive scalar curvature

We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics. Along the way we construct smooth fiber bundles over spheres whose total spaces have non-vanishing A-hat-genera, thus establishing the non-multiplicativity of the A-hat-genus in fibre bundles with simply connected base.Comment: 24 pages, v2: minor additions and corrections, based in particular on comments of referees, v3: minor corrections, final version, to appear in Publ.Math. IHE

Comparison of different sources for laboratory X-ray microscopy

This paper describes the setup of two different solutions for laboratory X-ray microscopy working with geometric magnification. One setup uses thin-film transmission targets with an optimized tungsten-layer thickness and the electron gun and optics of an electron probe micro analyzer to generate a very small X-ray source. The other setup is based on a scanning electron microscope and uses microstructured reflection targets. We also describe the structuring process for these targets. In both cases we show that resolutions of 100 nm can be achieved. Also the possibilities of computed tomography for 3D imaging are explored and we show first imaging examples of high-absorption as well as low-absorption specimens to demonstrate the capabilities of the setups.Comment: 6 pages, 4 figures, proceedings of the 14th International Workshop on Radiation Imaging Detector

The strong Novikov conjecture for low degree cohomology

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational K-homology and homology via the Chern character). Our result implies homotopy invariance of higher signatures associated to these cohomology classes. This consequence was first established by Connes-Gromov-Moscovici and Mathai. Our approach is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our previous work. In contrast to the argument of Mathai, our approach is independent of (and indeed gives a new proof of) the result of Hilsum-Skandalis on the homotopy invariance of the index of the signature operator twisted with bundles of small curvature.Comment: 11 page

Neutrino signature of supernova hydrodynamical instabilities in three dimensions

The first full-scale three-dimensional (3D) core-collapse supernova (SN) simulations with sophisticated neutrino transport show pronounced effects of the standing accretion shock instability (SASI) for two high-mass progenitors (20 and 27 M_sun). In a low-mass progenitor (11.2 M_sun), large-scale convection is the dominant nonradial hydrodynamic instability in the postshock accretion layer. The SASI-associated modulation of the neutrino signal (80 Hz in our two examples) will be clearly detectable in IceCube or the future Hyper-Kamiokande detector, depending on progenitor properties, distance, and observer location relative to the main SASI sloshing direction. The neutrino signal from the next galactic SN can therefore diagnose the nature of the hydrodynamic instability.Comment: 6 pages, including 4 figures. Results unchanged. Matches published version in PRL. Animated visualization available at: http://www.mpa-garching.mpg.de/ccsnarchive/data/Hanke2013_movie/index.htm

Core-Collapse Supernovae: Reflections and Directions

Core-collapse supernovae are among the most fascinating phenomena in astrophysics and provide a formidable challenge for theoretical investigation. They mark the spectacular end of the lives of massive stars and, in an explosive eruption, release as much energy as the sun produces during its whole life. A better understanding of the astrophysical role of supernovae as birth sites of neutron stars, black holes, and heavy chemical elements, and more reliable predictions of the observable signals from stellar death events are tightly linked to the solution of the long-standing puzzle how collapsing stars achieve to explode. In this article our current knowledge of the processes that contribute to the success of the explosion mechanism are concisely reviewed. After a short overview of the sequence of stages of stellar core-collapse events, the general properties of the progenitor-dependent neutrino emission will be briefly described. Applying sophisticated neutrino transport in axisymmetric (2D) simulations with general relativity as well as in simulations with an approximate treatment of relativistic effects, we could find successful neutrino-driven explosions for a growing set of progenitor stars. First results of three-dimensional (3D) models have been obtained, and magnetohydrodynamic simulations demonstrate that strong initial magnetic fields in the pre-collapse core can foster the onset of neutrino-powered supernova explosions even in nonrotating stars. These results are discussed in the context of the present controversy about the value of 2D simulations for exploring the supernova mechanism in realistic 3D environments, and they are interpreted against the background of the current disagreement on the question whether the standing accretion shock instability (SASI) or neutrino-driven convection is the crucial agency that supports the onset of the explosion.Comment: 36 pages, 20 figures (43 eps files); submitted to Progress of Theoretical and Experimental Physics (PTEP

Self-sustained asymmetry of lepton-number emission: A new phenomenon during the supernova shock-accretion phase in three dimensions

During the stalled-shock phase of our 3D hydrodynamical core-collapse simulations with energy-dependent, 3-flavor neutrino transport, the lepton-number flux (nue minus antinue) emerges predominantly in one hemisphere. This novel, spherical-symmetry breaking neutrino-hydrodynamical instability is termed LESA for "Lepton-number Emission Self-sustained Asymmetry." While the individual nue and antinue fluxes show a pronounced dipole pattern, the heavy-flavor neutrino fluxes and the overall luminosity are almost spherically symmetric. Initially, LESA seems to develop stochastically from convective fluctuations, it exists for hundreds of milliseconds or more, and it persists during violent shock sloshing associated with the standing accretion shock instability. The nue minus antinue flux asymmetry originates mainly below the neutrinosphere in a region of pronounced proto-neutron star (PNS) convection, which is stronger in the hemisphere of enhanced lepton-number flux. On this side of the PNS, the mass-accretion rate of lepton-rich matter is larger, amplifying the lepton-emission asymmetry, because the spherical stellar infall deflects on a dipolar deformation of the stalled shock. The increased shock radius in the hemisphere of less mass accretion and minimal lepton-number flux (antinue flux maximum) is sustained by stronger convection on this side, which is boosted by stronger neutrino heating because the average antinue energy is higher than the average nue energy. Asymmetric heating thus supports the global deformation despite extremely nonstationary convective overturn behind the shock. While these different elements of LESA form a consistent picture, a full understanding remains elusive at present. There may be important implications for neutrino-flavor oscillations, the neutron-to-proton ratio in the neutrino-heated supernova ejecta, and neutron-star kicks, which remain to be explored.Comment: 21 pages, 15 figures; new results and new figure added; accepted by Ap

Induction motors improvement for a variable speed drive

New improvement way of induction motors for a variable speed drive when changing mass dimension indices has been proposed. It allows for improvement of energy indices and reduction of running costs. The analysis of simulation results has been carried out and calculation results of economic efficiency of the achieved methods of approach to energy effective induction motors design have been suggested