Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics

We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real analytically on the metric $g$ in suitable Sobolev topologies. As an application we obtain local well-posedness of the geodesic equation for fractional Sobolev metrics on the space of all Riemannian metrics.Comment: 31 page

Probing the gluon density of the proton in the exclusive photoproduction of vector mesons at the LHC: A phenomenological analysis

The current uncertainty on the gluon density extracted from the global parton analysis is large in the kinematical range of small values of the Bjorken - $x$ variable and low values of the hard scale $Q^2$. An alternative to reduces this uncertainty is the analysis of the exclusive vector meson photoproduction in photon - hadron and hadron - hadron collisions. This process offers a unique opportunity to constrain the gluon density of the proton, since its cross section is proportional to the gluon density squared. In this paper we consider current parametrizations for the gluon distribution and estimate the exclusive vector meson photoproduction cross section at HERA and LHC using the leading logarithmic formalism. We perform a fit of the normalization of the $\gamma h$ cross section and the value of the hard scale for the process and demonstrate that the current LHCb experimental data are better described by models that assume a slow increasing of the gluon distribution at small - $x$ and low $Q^2$.Comment: 8 pages, 6 figures, 1 table. Version published in European Physical Journal

Curved Graphene Nanoribbons: Structure and Dynamics of Carbon Nanobelts

Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect ratio. In this work we investigated the energetics and dynamical aspects of CNBs formed from rolling up CNRs. We have carried out molecular dynamics simulations using reactive empirical bond-order potentials. Our results show that similarly to CNSs, CNBs formation is dominated by two major energy contribution, the increase in the elastic energy due to the bending of the initial planar configuration (decreasing structural stability) and the energetic gain due to van der Waals interactions of the overlapping surface of the rolled layers (increasing structural stability). Beyond a critical diameter value these scrolled structures can be even more stable (in terms of energy) than their equivalent planar configurations. In contrast to CNSs that require energy assisted processes (sonication, chemical reactions, etc.) to be formed, CNBs can be spontaneously formed from low temperature driven processes. Long CNBs (length of $\sim$ 30.0 nm) tend to exhibit self-folded racket-like conformations with formation dynamics very similar to the one observed for long carbon nanotubes. Shorter CNBs will be more likely to form perfect scrolled structures. Possible synthetic routes to fabricate CNBs from graphene membranes are also addressed

Radial dependence of line profile variability in seven O9--B0.5 stars

Massive stars show a variety of spectral variability: presence of discrete absorption components in UV P-Cygni profiles, optical line profile variability, X-ray variability, radial velocity modulations. Our goal is to study the spectral variability of single OB stars to better understand the relation between photospheric and wind variability. For that, we rely on high spectral resolution, high signal-to-noise ratio optical spectra collected with the spectrograph NARVAL on the Telescope Bernard Lyot at Pic du Midi. We investigate the variability of twelve spectral lines by means of the Temporal Variance Spectrum (TVS). The selected lines probe the radial structure of the atmosphere, from the photosphere to the outer wind. We also perform a spectroscopic analysis with atmosphere models to derive the stellar and wind properties, and to constrain the formation region of the selected lines. We show that variability is observed in the wind lines of all bright giants and supergiants, on a daily timescale. Lines formed in the photosphere are sometimes variable, sometimes not. The dwarf stars do not show any sign of variability. If variability is observed on a daily timescale, it can also (but not always) be observed on hourly timescales, albeit with lower amplitude. There is a very clear correlation between amplitude of the variability and fraction of the line formed in the wind. Strong anti-correlations between the different part of the temporal variance spectrum are observed. Our results indicate that variability is stronger in lines formed in the wind. A link between photospheric and wind variability is not obvious from our study, since wind variability is observed whatever the level of photospheric variability. Different photospheric lines also show different degrees of variability.Comment: 13 pages, 9 figures + appendix. A&A accepted. Figures degraded for arxiv submissio