Spectral C*-categories and Fell bundles with path-lifting

Following Crane's suggestion that categorification should be of fundamental importance in quantising gravity, we show that finite dimensional even $S^o$-real spectral triples over \bbc are already nothing more than full C*-categories together with a self-adjoint section of their domain and range maps, while the latter are equivalent to unital saturated Fell bundles over pair groupoids equipped with a path-lifting operator given by a normaliser. Interpretations can be made in the direction of quantum Higgs gravity. These geometries are automatically quantum geometries and we reconstruct the classical limit, that is, general relativity on a Riemannian spin manifold.Comment: 20 pages, 1 figur

Scaling Laws for Non-Intercommuting Cosmic String Networks

We study the evolution of non-interacting and entangled cosmic string networks in the context of the velocity-dependent one-scale model. Such networks may be formed in several contexts, including brane inflation. We show that the frozen network solution $L\propto a$, although generic, is only a transient one, and that the asymptotic solution is still $L\propto t$ as in the case of ordinary (intercommuting) strings, although in the present context the universe will usually be string-dominated. Thus the behaviour of two strings when they cross does not seem to affect their scaling laws, but only their densities relative to the background.Comment: Phys. Rev. D (in press); v2: final published version (references added, typos corrected

Structural studies of mesoporous ZrO2_{2}-CeO2_{2} and ZrO2_{2}-CeO2_{2}/SiO2_{2} mixed oxides for catalytical applications

In this work the synthesis of ZrO$_{2}$-CeO$_{2}$ and ZrO$_{2}$-CeO$_{2}$/SiO$_{2}$ were developed, based on the process to form ordered mesoporous materials such as SBA-15 silica. The triblock copolymer Pluronic P-123 was used as template, aiming to obtain crystalline single phase walls and larger specific surface area, for future applications in catalysis. SAXS and XRD results showed a relationship between ordered pores and the material crystallization. 90% of CeO$_{2}$ leaded to single phase homogeneous ceria-zirconia solid solution of cubic fluorite structure (Fm$\bar{3}$m). The SiO$_{2}$ addition improved structural and textural properties as well as the reduction behavior at lower temperatures, investigated by XANES measurements under H$_{2}$ atmosphere