Simulating Nonholonomic Dynamics

This paper develops different discretization schemes for nonholonomic mechanical systems through a discrete geometric approach. The proposed methods are designed to account for the special geometric structure of the nonholonomic motion. Two different families of nonholonomic integrators are developed and examined numerically: the geometric nonholonomic integrator (GNI) and the reduced d'Alembert-Pontryagin integrator (RDP). As a result, the paper provides a general tool for engineering applications, i.e. for automatic derivation of numerically accurate and stable dynamics integration schemes applicable to a variety of robotic vehicle models

Universality Classes of Diagonal Quantum Spin Ladders

We find the classification of diagonal spin ladders depending on a characteristic integer $N_p$ in terms of ferrimagnetic, gapped and critical phases. We use the finite algorithm DMRG, non-linear sigma model and bosonization techniques to prove our results. We find stoichiometric contents in cuprate $CuO_2$ planes that allow for the existence of weakly interacting diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl

A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole

Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative $(l\geq 2)$ second-order perturbations of a Schwarzschild black hole. In particular, we construct the second order Zerilli and Regge-Wheeler equations under the presence of any two first-order modes, reconstruct the perturbed metric in terms of the master scalars, and compute the radiated energy at null infinity. The results of this paper enable systematic studies of generic second order perturbations of the Schwarzschild spacetime. In particular, studies of mode-mode coupling and non-linear effects in gravitational radiation, the second-order stability of the Schwarzschild spacetime, or the geometry of the black hole horizon.Comment: 14 page

Hokupa'a-Gemini Discovery of Two Ultracool Companions to the Young Star HD 130948

We report the discovery of two faint ultracool companions to the nearby (d~17.9 pc) young G2V star HD 130948 (HR 5534, HIP 72567) using the Hokupa'a adaptive optics instrument mounted on the Gemini North 8-meter telescope. Both objects have the same common proper motion as the primary star as seen over a 7 month baseline and have near-IR photometric colors that are consistent with an early-L classification. Near-IR spectra taken with the NIRSPEC AO instrument on the Keck II telescope reveal K I lines, FeH, and water bandheads. Based on these spectra, we determine that both objects have spectral type dL2 with an uncertainty of 2 spectral subclasses. The position of the new companions on the H-R diagram in comparison with theoretical models is consistent with the young age of the primary star (<0.8 Gyr) estimated on the basis of X-ray activity, lithium abundance and fast rotation. HD 130948 B and C likely constitute a pair of young contracting brown dwarfs with an orbital period of about 10 years, and will yield dynamical masses for L dwarfs in the near future.Comment: 10 pages, 3 figures, (13 total pages

Yukawa terms in noncommutative SO(10) and E6 GUTs

We propose a method for constructing Yukawa terms for noncommutative SO(10) and E6 GUTs, when these GUTs are formulated within the enveloping-algebra formalism. The most general noncommutative Yukawa term that we propose contains, at first order in thetamunu, the most general BRS invariant Yukawa contribution whose only dimensionful parameter is the noncommutativity parameter. This noncommutative Yukawa interaction is thus renormalisable at first order in thetamunu.Comment: 14 pages, no figure

Abundant Z-cyanomethanimine in the interstellar medium: paving the way to the synthesis of adenine

We report the first detection in the interstellar medium of the Z-isomer of cyanomethanimine (HNCHCN), an HCN dimer proposed as precursor of adenine. We identified six transitions of Z-cyanomethanimine, along with five transitions of E-cyanomethanimine, using IRAM 30m observations towards the Galactic Center quiescent molecular cloud G+0.693. The Z-isomer has a column density of (2.0$\pm$0.6)$\times$10$^{14}$ cm$^{-2}$ and an abundance of 1.5$\times$10$^{-9}$. The relative abundance ratio between the isomers is [Z/E]$\sim$6. This value cannot be explained by the two chemical formation routes previously proposed (gas-phase and grain surface), which predicts abundances ratios between 0.9 and 1.5. The observed [Z/E] ratio is in good agreement with thermodynamic equilibrium at the gas kinetic temperature (130$-$210 K). Since isomerization is not possible in the ISM, the two species may be formed at high temperature. New chemical models, including surface chemistry on dust grains and gas-phase reactions, should be explored to explain our findings. Whatever the formation mechanism, the high abundance of Z-HNCHCN shows that precursors of adenine are efficiently formed in the ISM.Comment: Accepted in Monthly Notices of the Royal Astronomical Society Letter

Complex organic molecules in the Galactic Centre: the N-bearing family

We present an unbiased spectral line survey toward the Galactic Centre (GC) quiescent giant molecular cloud (QGMC), G+0.693 using the GBT and IRAM 30$\,$ telescopes. Our study highlights an extremely rich organic inventory of abundant amounts of nitrogen (N)-bearing species in a source without signatures of star formation. We report the detection of 17 N-bearing species in this source, of which 8 are complex organic molecules (COMs). A comparison of the derived abundances relative to H$_2$ is made across various galactic and extragalactic environments. We conclude that the unique chemistry in this source is likely to be dominated by low-velocity shocks with X-rays/cosmic rays also playing an important role in the chemistry. Like previous findings obtained for O-bearing molecules, our results for N-bearing species suggest a more efficient hydrogenation of these species on dust grains in G+0.693 than in hot cores in the Galactic disk, as a consequence of the low dust temperatures coupled with energetic processing by X-ray/cosmic ray radiation in the GC.Comment: 24 pages, 23 figures, 7 tables, accepted for publication in MNRA

Mechanical systems subjected to generalized nonholonomic constraints

We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit formula to obtain the ``post-impact'' momentum in terms of the ``pre-impact'' momentum.Comment: 24 pages, no figure