A K-Theoretic Proof of Boutet de Monvel's Index Theorem for Boundary Value Problems

We study the C*-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with non-empty boundary. We find short exact sequences in K-theory 0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact ideal and T*X' the cotangent bundle of the interior of X. Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show that the Fredholm index of an elliptic element in A is given as the composition of the topological index with mapping K_1(A/K)->K_0(C_0(T*X')) defined above. This relation was first established by Boutet de Monvel by different methods.Comment: Title slightly changed. Accepted for publication in Journal fuer die reine und angewandte Mathemati

Galactic Nonlinear Dynamic Model

We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance with the observational data.Comment: 6 pages, 1 figure. Talk given in the 7th Alexander Friedmann International Seminar, June 29 to July 5, 2008, Joao Pessoa, PB, Brazi

Giant planets around two intermediate-mass evolved stars and confirmation of the planetary nature of HIP67851 c

Precision radial velocities are required to discover and characterize planets orbiting nearby stars. Optical and near infrared spectra that exhibit many hundreds of absorption lines can allow the m/s precision levels required for such work. However, this means that studies have generally focused on solar-type dwarf stars. After the main-sequence, intermediate-mass stars (former A-F stars) expand and rotate slower than their progenitors, thus thousands of narrow absorption lines appear in the optical region, permitting the search for planetary Doppler signals in the data for these types of stars. We present the discovery of two giant planets around the intermediate-mass evolved star HIP65891 and HIP107773. The best Keplerian fit to the HIP65891 and HIP107773 radial velocities leads to the following orbital parameters: P=1084.5 d; m$_b$sin$i$ = 6.0 M$_{jup}$; $e$=0.13 and P=144.3 d; m$_b$sin$i$ = 2.0 M$_{jup}$; $e$=0.09, respectively. In addition, we confirm the planetary nature of the outer object orbiting the giant star HIP67851. The orbital parameters of HIP67851c are: P=2131.8 d, m$_c$sin$i$ = 6.0 M$_{jup}$ and $e$=0.17. With masses of 2.5 M$_\odot$ and 2.4 M$_\odot$ HIP65891 and HIP107773 are two of the most massive stars known to host planets. Additionally, HIP67851 is one of five giant stars that are known to host a planetary system having a close-in planet ($a <$ 0.7 AU). Based on the evolutionary states of those five stars, we conclude that close-in planets do exist in multiple systems around subgiants and slightly evolved giants stars, but probably they are subsequently destroyed by the stellar envelope during the ascent of the red giant branch phase. As a consequence, planetary systems with close-in objects are not found around horizontal branch stars.Comment: Accepted for publication in A&

Evidence from stellar rotation of enhanced disc dispersal: (I) The case of the triple visual system BD-21 1074 in the β\beta Pictoris association

The early stage of stellar evolution is characterized by a star-disc locking mechanism. The disc-locking prevents the star to spin its rotation up, and its timescale depends on the disc lifetime. Some mechanisms can significantly shorten this lifetime, allowing a few stars to start spinning up much earlier than other stars. In the present study, we aim to investigate how the properties of the circumstellar environment can shorten the disc lifetime. We have identified a few multiple stellar systems, composed of stars with similar masses, which belong to associations with a known age. Since all parameters that are responsible for the rotational evolution, with the exception of environment properties and initial stellar rotation, are similar for all components, we expect that significant differences among the rotation periods can only arise from differences in the disc lifetimes. A photometric timeseries allowed us to measure the rotation periods of each component, while high-resolution spectra provided us with the fundamental parameters, $v\sin{i}$ and chromospheric line fluxes. The rotation periods of the components differ significantly, and the component B, which has a closer companion C, rotates faster than the more distant and isolated component A. We can ascribe the rotation period difference to either different initial rotation periods or different disc-locking phases arising from the presence of the close companion C. In the specific case of BD$-$21 1074, the second scenario seems to be more favored. In our hypothesis of different disc-locking phase, any planet orbiting this star is likely formed very rapidly owing to a gravitational instability mechanism, rather than core accretion. Only a large difference of initial rotation periods alone could account for the observed period difference, leaving comparable disc lifetimes.Comment: Accepted by Astronomy & Astrophysics on July 31, 2014; Pages 12, Figs.

Ripples in Tapped or Blown Powder

We observe ripples forming on the surface of a granular powder in a container submitted from below to a series of brief and distinct shocks. After a few taps, the pattern turns out to be stable against any further shock of the same amplitude. We find experimentally that the characteristic wavelength of the pattern is proportional to the amplitude of the shocks. Starting from consideration involving Darcy's law for air flow through the porous granulate and avalanche properties, we build up a semi-quantitative model which fits satisfactorily the set of experimental observations as well as a couple of additional experiments.Comment: 7 pages, four postscript figures, submitted PRL 11/19/9