On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$

Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems: The Black Hole Regime

The Cauchy+characteristic matching (CCM) problem for the scalar wave equation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for the coupled Einstein-Klein-Gordon system of equations, assuming a regular center of symmetry. Here, the time evolution after the formation of a black hole is pursued, using a CCM formulation of the governing equations perturbed around the Schwarzschild background. An extension of the matching scheme allows for arbitrary matching boundary motion across the coordinate grid. As a proof of concept, the late time behavior of the dynamics of the scalar field is explored. The power-law tails in both the time-like and null infinity limits are verified.Comment: To appear in Phys. Rev. D, 9 pages, revtex, 5 figures available at http://www.astro.psu.edu/users/nr/preprints.htm

Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The matching interface between the space-like and characteristic foliations is constructed by imposing continuity conditions on metric, extrinsic curvature and scalar field variables, ensuring smoothness across the matching surface. The accuracy of the method is established for all ranges of $M/R$, most notably, with a detailed comparison of invariant observables against reference solutions obtained with a calibrated, global, null algorithm.Comment: Submitted to Phys. Rev. D, 16 pages, revtex, 7 figures available at http://nr.astro.psu.edu:8080/preprints.htm

Mission design for LISA Pathfinder

Here we describe the mission design for SMART-2/LISA Pathfinder. The best trade-off between the requirements of a low-disturbance environment and communications distance is found to be a free-insertion Lissajous orbit around the first co-linear Lagrange point of the Sun-Earth system L1, 1.5x 10^6 km from Earth. In order to transfer SMART-2/LISA Pathfinder from a low Earth orbit, where it will be placed by a small launcher, the spacecraft carries out a number of apogee-raise manoeuvres, which ultimatively place it to a parabolic escape trajectory towards L1. The challenges of the design of a small mission are met, fulfilling the very demanding technology demonstration requirements without creating excessive requirements on the launch system or the ground segment.Comment: 7 pages, 6 figures, 5th International LISA Symposium, see http://www.landisoft.de/Markus-Landgra

Kinematic groups across the MW disc: insights from models and from the RAVE catalogue

With the advent of the Gaia data, the unprecedented kinematic census of great part of the Milky Way disc will allow us to characterise the local kinematic groups and new groups in different disc neighbourhoods. First, we show here that the models predict a stellar kinematic response to the spiral arms and bar strongly dependent on disc position. For example, we find that the kinematic groups induced by the spiral arm models change significantly if one moves only ~ 0.6 kpc in galactocentric radius, but ~ 2 kpc in azimuth. There are more and stronger groups as one approaches the spiral arms. Depending on the spiral pattern speed, the kinematic imprints are more intense in nearby vicinities or far from the Sun. Secondly, we present a preliminary study of the kinematic groups observed by RAVE. This sample will allow us, for the first time, to study the dependence on Galactic position of the (thin and thick) disc moving groups. In the solar neighbourhood, we find the same kinematics groups as detected in previous surveys, but now with better statistics and over a larger spatial volume around the Sun. This indicates that these structures are indeed large scale kinematic features.Comment: 4 pages, 3 figures, to appear in the proceedings of "Assembling the Puzzle of the Milky Way", Le Grand Bornand (April 17-22, 2011), C. Reyle, A. Robin, M. Schultheis (eds.

The missing atom as a source of carbon magnetism

Atomic vacancies have a strong impact in the mechanical, electronic and magnetic properties of graphene-like materials. By artificially generating isolated vacancies on a graphite surface and measuring their local density of states on the atomic scale, we have shown how single vacancies modify the electronic properties of this graphene-like system. Our scanning tunneling microscopy experiments, complemented by tight binding calculations, reveal the presence of a sharp electronic resonance at the Fermi energy around each single graphite vacancy, which can be associated with the formation of local magnetic moments and implies a dramatic reduction of the charge carriers' mobility. While vacancies in single layer graphene naturally lead to magnetic couplings of arbitrary sign, our results show the possibility of inducing a macroscopic ferrimagnetic state in multilayered graphene samples just by randomly removing single C atoms.Comment: Accepted for publication in Physical Review Letter

Combined Effects of the North Atlantic Oscillation and the Arctic Oscillation on Sea Surface Temperature in the Alborán Sea

We explored the possible effects of the North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) on interannual sea surface temperature (SST) variations in the Albora´n Sea, both separately and combined. The probability of observing mean annual SST values higher than average was related to NAO and AO values of the previous year. The effect of NAO on SST was negative, while that of AO was positive. The pure effects of NAO and AO on SST are obscuring each other, due to the positive correlation between them. When decomposing SST, NAO and AO in seasonal values, we found that variation in mean annual SST and mean winter SST was significantly related to the mean autumn NAO of the previous year, while mean summer SST was related to mean autumn AO of the previous year. The one year delay in the effect of the NAO and AO on the SST could be partially related to the amount of accumulated snow, as we found a significant correlation between the total snow in the North Albora´n watershed for a year with the annual average SST of the subsequent year. A positive AO implies a colder atmosphere in the Polar Regions, which could favour occasional cold waves over the Iberian Peninsula which, when coupled with precipitations favoured by a negative NAO, may result in snow precipitation. This snow may be accumulated in the high peaks and melt down in spring-summer of the following year, which consequently increases the runoff of freshwater to the sea, which in turn causes a diminution of sea surface salinity and density, and blocks the local upwelling of colder water, resulting in a higher SST.CGL2009-11316 (Ministerio de Ciencia e Innovación, Spain, and FEDER

An Expanding HI Photodissociated Region Associated with the Compact HII Region G213.880-11.837 in the GGD 14 Complex

We present high angular and spectral resolution HI 21~cm line observations toward the cometary-shaped compact HII region G213.880-11.837 in the GGD~14 complex.The kinematics and morphology of the photodissociated region, traced by the HI line emission, reveal that the neutral gas is part of an expanding flow. The kinematics of the HI gas along the major axis of G213.880-11.837 shows that the emission is very extended toward the SE direction, reaching LSR radial velocities in the tail of about 14 km/s. The ambient LSR radial velocity of the molecular gas is 11.5 km/s, which suggests a champagne flow of the HI gas. This is the second (after G111.61+0.37) cometary HII/HI region known.Comment: Accepted for publication in the Astronomical Journal (10 pages, 4 figures, 1 table

Exceptional orthogonal polynomials and the Darboux transformation

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction