Energetics of metal slabs and clusters: the rectangle-box model

An expansion of energy characteristics of wide thin slab of thickness L in power of 1/L is constructed using the free-electron approximation and the model of a potential well of finite depth. Accuracy of results in each order of the expansion is analyzed. Size dependences of the work function and electronic elastic force for Au and Na slabs are calculated. It is concluded that the work function of low-dimensional metal structure is always smaller that of semi-infinite metal sample. A mechanism for the Coulomb instability of charged metal clusters, different from Rayleigh's one, is discussed. The two-component model of a metallic cluster yields the different critical sizes depending on a kind of charging particles (electrons or ions). For the cuboid clusters, the electronic spectrum quantization is taken into account. The calculated critical sizes of Ag_{N}^{2-} and Au_{N}^{3-} clusters are in a good agreement with experimental data. A qualitative explanation is suggested for the Coulomb explosion of positively charged Na_{\N}^{n+} clusters at 3<n<5.Comment: 11 pages, 6 figures, 1 tabl

High-pressure transport properties of CeRu_2Ge_2

The pressure-induced changes in the temperature-dependent thermopower S(T) and electrical resistivity \rho(T) of CeRu_2Ge_2 are described within the single-site Anderson model. The Ce-ions are treated as impurities and the coherent scattering on different Ce-sites is neglected. Changing the hybridisation \Gamma between the 4f-states and the conduction band accounts for the pressure effect. The transport coefficients are calculated in the non-crossing approximation above the phase boundary line. The theoretical S(T) and \rho(T) curves show many features of the experimental data. The seemingly complicated temperature dependence of S(T) and \rho(T), and their evolution as a function of pressure, is related to the crossovers between various fixed points of the model.Comment: 9 pages, 10 figure

Mid-Infrared interferometry of dust around massive evolved stars

We report long-baseline interferometric measurements of circumstellar dust around massive evolved stars with the MIDI instrument on the Very Large Telescope Interferometer and provide spectrally dispersed visibilities in the 8-13 micron wavelength band. We also present diffraction-limited observations at 10.7 micron on the Keck Telescope with baselines up to 8.7 m which explore larger scale structure. We have resolved the dust shells around the late type WC stars WR 106 and WR 95, and the enigmatic NaSt1 (formerly WR 122), suspected to have recently evolved from a Luminous Blue Variable (LBV) stage. For AG Car, the protoypical LBV in our sample, we marginally resolve structure close to the star, distinct from the well-studied detached nebula. The dust shells around the two WC stars show fairly constant size in the 8-13 micron MIDI band, with gaussian half-widths of ~ 25 to 40 mas. The compact dust we detect around NaSt1 and AG Car favors recent or ongoing dust formation. Using the measured visibilities, we build spherically symmetric radiative transfer models of the WC dust shells which enable detailed comparison with existing SED-based models. Our results indicate that the inner radii of the shells are within a few tens of AU from the stars. In addition, our models favor grain size distributions with large (~ 1 micron) dust grains. This proximity of the inner dust to the hot central star emphasizes the difficulty faced by current theories in forming dust in the hostile environment around WR stars. Although we detect no direct evidence for binarity for these objects, dust production in a colliding-wind interface in a binary system is a feasible mechanism in WR systems under these conditions.Comment: 21 pages, 4 tables, 13 figures. Accepted for publication in the Astrophysical Journa

Dust Formation and He II 4686 emission in the Dense Shell of the Peculiar Type Ib Supernova 2006jc

We present evidence for the formation of dust grains in an unusual Type Ib SN based on late-time spectra of SN 2006jc. The progenitor suffered an LBV-like outburst just 2 yr earlier, and we propose that the dust formation is a consequence of the SN blast wave overtaking that LBV-like shell. The key evidence for dust formation is (a) the appearance of a red/near-IR continuum source fit by 1600 K graphite grains, and (b) fading of the redshifted sides of He I emission lines, yielding progressively more asymmetric blueshifted lines as dust obscures receding material. This provides the strongest case yet for dust formation in any SN Ib/c. Both developments occurred between 51 and 75 d after peak, while other SNe observed to form dust did so after a few hundred days. Geometric considerations indicate that dust formed in the dense swept-up shell between the forward and reverse shocks, and not in the freely expanding SN ejecta. Rapid cooling leading to dust formation may have been aided by extremely high shell densities, as indicated by He I line ratios. The brief epoch of dust formation is accompanied by He II 4686 emission and enhanced X-ray emission. These clues suggest that the unusual dust formation in this object was not due to properties of the SN itself, but instead -- like most peculiarities of SN 2006jc -- was a consequence of the dense environment created by an LBV-like eruption 2 yr before the SN.Comment: ApJ, accepted. added some discussion and 2 figures, better title, conclusions same as previous version. 12 pages, 4 color fig

Quantization of Wilson loops in Wess-Zumino-Witten models

We describe a non-perturbative quantization of classical Wilson loops in the WZW model. The quantized Wilson loop is an operator acting on the Hilbert space of closed strings and commuting either with the full Kac-Moody chiral algebra or with one of its subalgebras. We prove that under open/closed string duality, it is dual to a boundary perturbation of the open string theory. As an application, we show that such operators are useful tools for identifying fixed points of the boundary renormalization group flow.Comment: 24 pages. Version published in JHE

Optical Interferometry of early-type stars with PAVO@CHARA. I. Fundamental stellar properties

We present interferometric observations of 7 main-sequence and 3 giant stars with spectral types from B2 to F6 using the PAVO beam combiner at the CHARA array. We have directly determined the angular diameters for these objects with an average precision of 2.3%. We have also computed bolometric fluxes using available photometry in the visible and infrared wavelengths, as well as space-based ultraviolet spectroscopy. Combined with precise \textit{Hipparcos} parallaxes, we have derived a set of fundamental stellar properties including linear radius, luminosity and effective temperature. Fitting the latter to computed isochrone models, we have inferred masses and ages of the stars. The effective temperatures obtained are in good agreement (at a 3% level) with nearly-independent temperature estimations from spectroscopy. They validate recent sixth-order polynomial (B-V)-$T_\mathrm{eff}$ empirical relations \citep{Boyajian2012a}, but suggest that a more conservative third-order solution \citep{vanBelle2009} could adequately describe the (V-K)-$T_\mathrm{eff}$ relation for main-sequence stars of spectral type A0 and later. Finally, we have compared mass values obtained combining surface gravity with inferred stellar radius (\textit{gravity mass}) and as a result of the comparison of computed luminosity and temperature values with stellar evolutionary models (\textit{isochrone mass}). The strong discrepancy between isochrone and gravity mass obtained for one of the observed stars, $\gamma$\,Lyr, suggests that determination of the stellar atmosphere parameters should be revised.Comment: 13 pages, 9 figures, accepted for publication in MNRA

The anomaly line bundle of the self-dual field theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication in CM

On the Interferometric Sizes of Young Stellar Objects

Long-baseline optical interferometers can now detect and resolve hot dust emission thought to arise at the inner edge of circumstellar disks around young stellar objects (YSOs). We argue that the near-infrared sizes being measured are closely related to the radius at which dust is sublimated by the stellar radiation field. We consider how realistic dust optical properties and gas opacity dramatically affect the predicted location of this dust destruction radius, an exercise routinely done in other contexts but so far neglected in the analysis of near-infrared sizes of YSOs. We also present the accumulated literature of near-infrared YSO sizes in the form of a ``size-luminosity diagram'' and compare with theoretical expectations. We find evidence that large (>~ 1 micron) dust grains predominate in the inner disks of T Tauri and Herbig Ae/Be stars, under the assumption that the inner-most gaseous disks are optically-thin at visible wavelengths.Comment: Accepted by Astrophysical Journa

Boosting Biomass Quantity and Quality by Improved Mixotrophic Culture of the Diatom Phaeodactylum tricornutum

Diatoms are photoautotrophic unicellular algae and are among the most abundant, adaptable, and diverse marine phytoplankton. They are extremely interesting not only for their ecological role but also as potential feedstocks for sustainable biofuels and high-value commodities such as omega fatty acids, because of their capacity to accumulate lipids. However, the cultivation of microalgae on an industrial scale requires higher cell densities and lipid accumulation than those found in nature to make the process economically viable. One of the known ways to induce lipid accumulation in Phaeodactylum tricornutum is nitrogen deprivation, which comes at the expense of growth inhibition and lower cell density. Thus, alternative ways need to be explored to enhance the lipid production as well as biomass density to make them sustainable at industrial scale. In this study, we have used experimental and metabolic modeling approaches to optimize the media composition, in terms of elemental composition, organic and inorganic carbon sources, and light intensity, that boost both biomass quality and quantity of P. tricornutum. Eventually, the optimized conditions were scaled-up to 2 L photobioreactors, where a better system control (temperature, pH, light, aeration/mixing) allowed a further improvement of the biomass capacity of P. tricornutum to 12 g/L

Physical processes leading to surface inhomogeneities: the case of rotation

In this lecture I discuss the bulk surface heterogeneity of rotating stars, namely gravity darkening. I especially detail the derivation of the omega-model of Espinosa Lara & Rieutord (2011), which gives the gravity darkening in early-type stars. I also discuss the problem of deriving gravity darkening in stars owning a convective envelope and in those that are members of a binary system.Comment: 23 pages, 11 figure, Lecture given to the school on the cartography of the Sun and the stars (May 2014 in Besan\c{c}on), to appear in LNP, Neiner and Rozelot edts V2: typos correcte