Leptonic and Semileptonic Decays of Pseudoscalar Mesons

We employ the relativistic constituent quark model to give a unified description of the leptonic and semileptonic decays of pseudoscalar mesons (\pi, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and other approaches. We reproduce the results of spin-flavor symmetry in the heavy quark limit.Comment: 12 pages LaTeX (elsart.sty) + 4 figures; added references, to appear in Phys. Lett.

Brood cells like conifer cones: the peculiar nesting biology of the osmiine bee Hoplitis (Alcidamea) curvipes (Morawitz, 1871) (Hymenoptera, Megachilidae)

Two nests of Hoplitis curvipes are described from Apulia (Italy) and Dagestan (Russia). Both nests consisted of two brood cells placed side by side under a stone. The cells were neither attached to each other nor to the substrate. They were constructed from leaf fragments, which were imbricately arranged, forming a cone-like structure; each leaf fragment consisted of a basal part that was masticated to leaf pulp and an apical part that protruded freely from the cell wall. The cell wall was formed by the fusion of the masticated basal parts of the leaf fragments and thus entirely consisted of leaf pulp. The cell was sealed with a closing plug made of pure leaf pulp; a few leaf fragments were glued to its outer surface. The cocoon consisted of two layers: the outer layer was restricted to the anterior portion of the cell and had several longitudinal air-exchange slits on its lateral surface, while the inner layer had an air-exchange orifice in its most anterior dome-shaped top. Results of measurements of brood cell dimensions and contents are provided. The nesting biology of species of the H. curvipes group is discussed

On equilibrium tides in fully convective planets and stars

We consider the tidal interaction of a fully convective primary star and a point mass. Using a normal mode decomposition we calculate the evolution of the primary angular velocity and orbit for arbitrary eccentricity e. The dissipation acting on the tidal perturbation is associated with convective turbulence. A novel feature of the Paper is that, to take into account of the fact that there is a relaxation time t_{c}, being the turn-over time of convective eddies, associated with the process, this is allowed to act non locally in time, producing a dependence of the dissipation on tidal forcing frequency. Results are expressed in terms of the Fourier coefficients of the tidal potential. We find analytical approximations for these valid for $e>0.2$. When the tidal response is frequency independent, our results are equivalent to those obtained in the standard constant time lag approximation. When there is the frequency dependence of the dissipative response, the evolution can differ drastically. In that case the system can evolve through a sequence of spin-orbit corotation resonances with Omega_{r}/Omega_{orb}=n/2, where Omega_{r} and Omega_{orb} are the rotation and orbital frequencies and n is an integer. We study this case analytically and numerically.Comment: The size of the shown abstract is reduced. Submitted to MNRA

Mathematical retroreflectors

Retroreflectors are optical devices that reverse the direction of incident beams of light. Here we present a collection of billiard type retroreflectors consisting of four objects; three of them are asymptotically perfect retroreflectors, and the fourth one is a retroreflector which is very close to perfect. Three objects of the collection have recently been discovered and published or submitted for publication. The fourth object - notched angle - is a new one; a proof of its retroreflectivity is given.Comment: 32 pages, 19 figure

Influence of a stellar cusp on the dynamics of young stellar discs and the origin of the S-stars in the Galactic Centre

Observations of the Galactic Centre show evidence of one or two disc-like structures of very young stars orbiting the central super-massive black hole within a distance of a few 0.1 pc. A number of analyses have been carried out to investigate the dynamical behaviour and consequences of these discs, including disc thickness and eccentricity growth as well as mutual interaction and warping. However, most of these studies have neglected the influence of the stellar cusp surrounding the black hole, which is believed to be 1-2 orders of magnitude more massive than the disc(s). By means of N-body integrations using our bhint code, we study the impact of stellar cusps of different compositions. We find that although the presence of a cusp does have an important effect on the evolution of an otherwise isolated flat disc, its influence on the evolution of disc thickness and warping is rather mild in a two-disc configuration. However, we show that the creation of highly eccentric orbits strongly depends on the graininess of the cusp (i.e. the mean and maximum stellar masses): While Chang (2009) recently found that full cycles of Kozai resonance are prevented by the presence of an analytic cusp, we show that relaxation processes play an important role in such highly dense regions and support short-term resonances. We thus find that young disc stars on initially circular orbits can achieve high eccentricities by resonant effects also in the presence of a cusp of stellar remnants, yielding a mechanism to create S-stars and hyper-velocity stars. Furthermore, we discuss the underlying initial mass function (IMF) of the young stellar discs and find no definite evidence for a non-canonical IMF.Comment: 10 pages, 7 figures, 1 table, accepted for publication in MNRA

Heavy- to light-meson transition form factors

Semileptonic heavy -> heavy and heavy -> light meson transitions are studied as a phenomenological application of a heavy-quark limit of Dyson-Schwinger equations. Employing two parameters: E, the difference between the mass of the heavy meson and the effective-mass of the heavy quark; and Lambda, the width of the heavy-meson Bethe-Salpeter amplitude, we calculate f_+(t) for all decays on their entire kinematically accessible t-domain. Our study favours f_B in the range 0.135-0.17 GeV and with E=0.44 GeV and 1/Lambda = 0.14 fm we obtain f_+^{B pi}(0) = 0.46. As a result of neglecting 1/m_c-corrections, we estimate that our calculated values of \rho^2 = 0.87 and f_+^{DK}(0)=0.62 are too low by approximately 15%. However, the bulk of these corrections should cancel in our calculated values of Br(D -> \pi l nu)/Br(D -> K l nu)=0.13 and f_+^{D pi}(0)/f_+^{DK}(0) = 1.16.Comment: 26 pages, 3 figures, REVTE

Aerothermodynamic Analysis of a Reentry Brazilian Satellite

This work deals with a computational investigation on the small ballistic reentry Brazilian vehicle SARA (acronyms for SAt\'elite de Reentrada Atmosf\'erica). Hypersonic flows over the vehicle SARA at zero-degree angle of attack in a chemical equilibrium and thermal non-equilibrium are modeled by the Direct Simulation Monte Carlo (DSMC) method, which has become the main technique for studying complex multidimensional rarefied flows, and that properly accounts for the non-equilibrium aspects of the flows. The emphasis of this paper is to examine the behavior of the primary properties during the high altitude portion of SARA reentry. In this way, velocity, density, pressure and temperature field are investigated for altitudes of 100, 95, 90, 85 and 80 km. In addition, comparisons based on geometry are made between axisymmetric and planar two-dimensional configurations. Some significant differences between these configurations were noted on the flowfield structure in the reentry trajectory. The analysis showed that the flow disturbances have different influence on velocity, density, pressure and temperature along the stagnation streamline ahead of the capsule nose. It was found that the stagnation region is a thermally stressed zone. It was also found that the stagnation region is a zone of strong compression, high wall pressure. Wall pressure distributions are compared with those of available experimental data and good agreement is found along the spherical nose for the altitude range investigated.Comment: The paper will be published in Vol. 42 of the Brazilian Journal of Physic

Simulations of Direct Collisions of Gas Clouds with the Central Black Hole

We perform numerical simulations of clouds in the Galactic Centre (GC) engulfing the nuclear super-massive black hole and show that this mechanism leads to the formation of gaseous accretion discs with properties that are similar to the expected gaseous progenitor discs that fragmented into the observed stellar disc in the GC. As soon as the cloud hits the black hole, gas with opposite angular momentum relative to the black hole collides downstream. This process leads to redistribution of angular momentum and dissipation of kinetic energy, resulting in a compact gaseous accretion disc. A parameter study using thirteen high resolution simulations of homogeneous clouds falling onto the black hole and engulfing it in parts demonstrates that this mechanism is able to produce gaseous accretion discs that could potentially be the progenitor of the observed stellar disc in the GC. A comparison of simulations with different equations of state (adiabatic, isothermal and full cooling) demonstrates the importance of including a detailed thermodynamical description. However the simple isothermal approach already yields good results on the radial mass transfer and accretion rates, as well as disc eccentricities and sizes. We find that the cloud impact parameter strongly influences the accretion rate whereas the impact velocity has a small affect on the accretion rate.Comment: 21 pages, 18 figures, Accepted for publication in MNRA

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes the gravitational potential is dominated by the more massive black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power law cusp.We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted. This effect is analogous to the so-called Kozai effect (Kozai, 1962, Lidov, 1961,1962) well known in celestial mechanics. We develop an analytical theory of secular evolution of the stellar orbits and calculate the rate of tidal disruption. We confront our analytical theory with a simple numerical model and find very good agreement. Our results show that for primary black-hole mass \sim 10^{6}-10^{7}M_{\odot}, the black- hole mass ratio q > 10^{-2}, cusp size \sim 1pc, the tidal disruption rate can be as large as \sim 10^{-2}-1M_{\odot}/yr. This is at least 10^{2}-10^{4} times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical friction time scale, and it is rather short: \sim 10^{5}yr. The dependence of the tidal disruption rate on the mass ratio, as well as on the size of the cusp, is also discussed.Comment: This version has been published in MNRA