Higher genus partition functions of meromorphic conformal field theories

It is shown that the higher genus vacuum amplitudes of a meromorphic conformal field theory determine the affine symmetry of the theory uniquely, and we give arguments that suggest that also the representation content with respect to this affine symmetry is specified, up to automorphisms of the finite Lie algebra. We illustrate our findings with the self-dual theories at c=16 and c=24; in particular, we give an elementary argument that shows that the vacuum amplitudes of the E_8\times E_8 theory and the Spin(32)/Z_2 theory differ at genus g=5. The fact that the discrepancy only arises at rather high genus is a consequence of the modular properties of higher genus amplitudes at small central charges. In fact, we show that for c\leq 24 the genus one partition function specifies already the partition functions up to g\leq 4 uniquely. Finally we explain how our results generalise to non-meromorphic conformal field theories.Comment: 43 pages, 7 figure

On the use of the proximity force approximation for deriving limits to short-range gravitational-like interactions from sphere-plane Casimir force experiments

We discuss the role of the proximity force approximation in deriving limits to the existence of Yukawian forces - predicted in the submillimeter range by many unification models - from Casimir force experiments using the sphere-plane geometry. Two forms of this approximation are discussed, the first used in most analyses of the residuals from the Casimir force experiments performed so far, and the second recently discussed in this context in R. Decca et al. [Phys. Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force approximation overestimates the expected Yukawa force and that the relative deviation from the exact Yukawa force is of the same order of magnitude, in the realistic experimental settings, as the relative deviation expected between the exact Casimir force and the Casimir force evaluated in the proximity force approximation. This implies both a systematic shift making the actual limits to the Yukawa force weaker than claimed so far, and a degree of uncertainty in the alpha-lambda plane related to the handling of the various approximations used in the theory for both the Casimir and the Yukawa forces. We further argue that the recently discussed form for the proximity force approximation is equivalent, for a geometry made of a generic object interacting with an infinite planar slab, to the usual exact integration of any additive two-body interaction, without any need to invoke approximation schemes. If the planar slab is of finite size, an additional source of systematic error arises due to the breaking of the planar translational invariance of the system, and we finally discuss to what extent this may affect limits obtained on power-law and Yukawa forces.Comment: 11 page, 5 figure

The Sagittarius Dwarf spheroidal Galaxy Survey (SDGS) II: The stellar content and constraints on the star formation history

A detailed study of the Star Formation History of the Sgr dSph galaxy is performed through the analysis of the data from the Sagittarius Dwarf Galaxy Survey (SDGS; Bellazzini, Ferraro & Buonanno 1999). Accurate statistical decontamination of the SDGS Color - Magnitude diagrams allow us to obtain many useful constraints on the age and metal content of the Sgr stellar populations in three different region of the galaxy. A coarse metallicity distribution of Sgr stars is derived, ranging from [Fe/H]~ -2.0 to [Fe/H]~ -0.7, the upper limit being somewhat higher in the central region of the galaxy. A qualitative global fit to all the observed CMD features is attempted, and a general scheme for the Star Formation History of the Sgr is derived. According to this scheme, star formation began at very early time from a low metal content Inter Stellar Medium and lasted for several Gyr, coupled with progressive chemical enrichment. The Star Formation Rate (SFR) had a peak from 8 to 10 gyr ago when the mean metallicity was in the range -1.3<= [Fe/H] <= -0.7. After that maximum, the SFR rapidly decreased and very low rate star formation took place until ~1-0.5 Gyr ago.Comment: 21 pages, 12 figures, figg. 1,2,3,5,6,10 and 11 provided in lower resolution format. For full resolution versions see http://www.bo.astro.it/bap/BAPhome.html Accepted by MNRA

Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excluding some very specific ones) the Bernoulli Dirac system is localized, independently of the mass.Comment: 9 pages, no figures - J. Physics A: Math. Ge

The decay of massive closed superstrings with maximum angular momentum

We study the decay of a very massive closed superstring (i.e. \alpha' M^2>> 1) in the unique state of maximum angular momentum. This is done in flat ten-dimensional spacetime and in the regime of weak string coupling, where the dominant decay channel is into two states of masses M_1, M_2. We find that the lifetime surprisingly grows with the first power of the mass M: T =c \alpha' M. We also compute the decay rate for each values of M_1, M_2. We find that, for large M, the dynamics selects only special channels of decay: modulo processes which are exponentially suppressed, for every decay into a state of given mass M_1, the mass M_2 of the other state is uniquely determined.Comment: 22 pages, 4 figure

Environmental Impact Assessment, on the Operation of Conventional and More Electric Large Commercial Aircraft

Global aviation is growing exponentially and there is a great emphasis on trajectory optimization to reduce the overall environmental impact caused by aircraft. Many optimization techniques exist and are being studied for this purpose. The CLEAN SKY Joint Technology Initiative for aeronautics and Air transport, a European research activity run under the Seventh Framework program, is a collaborative initiative involving industry, research organizations and academia to introduce novel technologies to improve the environmental impact of aviation. As part of the overall research activities, "green" aircraft trajectories are addressed in the Systems for Green Operations (SGO) Integrated Technology Demonstrator. This paper studies the impact of large commercial aircraft trajectories optimized for different objectives applied to the on board systems. It establishes integrated systems models for both conventional and more electric secondary power systems and studies the impact of fuel, noise, time and emissions optimized trajectories on each configuration. It shows the significant change in the fuel burn due to systems operation and builds up the case as to why a detailed aircraft systems model is required within the optimization loop. Typically, the objective in trajectory optimization is to improve the mission performance of an aircraft or reduce the environmental impact. Hence parameters such as time, fuel burn, emissions and noise are key optimization objectives. In most instances, trajectory optimization is achieved by using models that represent such parameters. For example aircraft dynamics models to describe the flight performance, engine models to calculate the fuel burn, emissions and noise impact, etc. Such techniques have proved to achieve the necessary level of accuracy in trajectory optimization. This research enhances previous techniques by adding in the effect of systems power in the optimization process. A comparison is also made between conventional power systems and more electric architectures. In the conventional architecture, the environmental control system and the ice protection system are powered by engine bleed air while actuators and electrics are powered by engine shaft power off-takes. In the more electric architecture, bleed off take is eliminated and the environmental control system and ice protection system are also powered electrically through engine shaft power off takes

Low frequency gray-body factors and infrared divergences: rigorous results

Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a 1D Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.Comment: 41 pages, 5 figure