An analytic solution for weak-field Schwarzschild geodesics

It is well known that the classical gravitational two body problem can be transformed into a spherical harmonic oscillator by regularization. We find that a modification of the regularization transformation has a similar result to leading order in general relativity. In the resulting harmonic oscillator, the leading-order relativistic perturbation is formally a negative centrifugal force. The net centrifugal force changes sign at three Schwarzschild radii, which interestingly mimics the innermost stable circular orbit (ISCO) of the full Schwarzschild problem. Transforming the harmonic-oscillator solution back to spatial coordinates yields, for both timelike and null weak-field Schwarzschild geodesics, a solution for $t,r,\phi$ in terms of elementary functions of a variable that can be interpreted as a generalized eccentric anomaly. The textbook expressions for relativistic precession and light deflection are easily recovered. We suggest how this solution could be combined with additional perturbations into numerical methods suitable for applications such as relativistic accretion or dynamics of the Galactic-centre stars.Comment: 8 pages; Published in the MNRAS; The definitive version is available at www.blackwell-synergy.co

Simulations of the Population of Centaurs I: The Bulk Statistics

Large-scale simulations of the Centaur population are carried out. The evolution of 23328 particles based on the orbits of 32 well-known Centaurs is followed for up to 3 Myr in the forward and backward direction under the influence of the 4 massive planets. The objects exhibit a rich variety of dynamical behaviour with half-lives ranging from 540 kyr (1996 AR20) to 32 Myr (2000 FZ53). The mean half-life of the entire sample of Centaurs is 2.7 Myr. The data are analyzed using a classification scheme based on the controlling planets at perihelion and aphelion, previously given in Horner et al (2003). Transfer probabilities are computed and show the main dynamical pathways of the Centaur population. The total number of Centaurs with diameters larger than 1 km is estimated as roughly 44300, assuming an inward flux of one new short-period comet every 200 yrs. The flux into the Centaur region from the Edgeworth-Kuiper belt is estimated to be 1 new object every 125 yrs. Finally, the flux from the Centaur region to Earth-crossing orbits is 1 new Earth-crosser every 880 yrsComment: 15 pages, 2 figures, MNRAS in pres

Large Anomalous Hall effect in a silicon-based magnetic semiconductor

Magnetic semiconductors are attracting high interest because of their potential use for spintronics, a new technology which merges electronics and manipulation of conduction electron spins. (GaMn)As and (GaMn)N have recently emerged as the most popular materials for this new technology. While Curie temperatures are rising towards room temperature, these materials can only be fabricated in thin film form, are heavily defective, and are not obviously compatible with Si. We show here that it is productive to consider transition metal monosilicides as potential alternatives. In particular, we report the discovery that the bulk metallic magnets derived from doping the narrow gap insulator FeSi with Co share the very high anomalous Hall conductance of (GaMn)As, while displaying Curie temperatures as high as 53 K. Our work opens up a new arena for spintronics, involving a bulk material based only on transition metals and Si, and which we have proven to display a variety of large magnetic field effects on easily measured electrical properties.Comment: 19 pages with 5 figure

Thermodynamic properties of 1,2-cyclohexanediols

© 2015 Pleiades Publishing, Ltd. The enthalpy values for the combustion and formation of crystalline cis and trans-1,2-cyclohexanediols are determined via bomb calorimetry. The vapor pressures of the compounds and their enthalpies of sublimation are measured. Using quantum-chemical methods, the reliability of the experimental data is estimated, the molecular structures of the compounds are studied, and the structures of the most stable conformers are established. The energy values of the intramolecular hydrogen bonds in the diol molecules are found