Simulations of the Population of Centaurs II: Individual Objects

Detailed orbit integrations of clones of five Centaurs -- namely, 1996 AR20, 2060 Chiron, 1995 SN55, 2000 FZ53 and 2002 FY36 -- for durations of 3 Myr are presented. One of our Centaur sample starts with perihelion initially under the control of Jupiter (1996 AR20), two start under the control of Saturn (Chiron and 1995 SN55) and one each starts under the control of Uranus (2000 FZ53) and Neptune (2002 FY36) respectively. A variety of interesting pathways are illustrated with detailed examples including: capture into the Jovian Trojans, repeated bursts of short-period comet behaviour, capture into mean-motion resonances with the giant planets and into Kozai resonances, as well as traversals of the entire Solar system. For each of the Centaurs, we provide statistics on the numbers (i) ejected, (ii) showing short-period comet behaviour and (iii) becoming Earth and Mars crossing. For example, Chiron has over 60 % of its clones becoming short-period objects, whilst 1995 SN55 has over 35 %. Clones of these two Centaurs typically make numerous close approaches to Jupiter. At the other extreme, 2000 FZ53 has roughly 2 % of its clones becoming short-period objects. In our simulations, typically 20 % of the clones which become short-period comets subsequently evolve into Earth-crossers.Comment: 10 pages, in press at MNRA

The Populations of Comet-Like Bodies in the Solar system

A new classification scheme is introduced for comet-like bodies in the Solar system. It covers the traditional comets as well as the Centaurs and Edgeworth-Kuiper belt objects. At low inclinations, close encounters with planets often result in near-constant perihelion or aphelion distances, or in perihelion-aphelion interchanges, so the minor bodies can be labelled according to the planets predominantly controlling them at perihelion and aphelion. For example, a JN object has a perihelion under the control of Jupiter and aphelion under the control of Neptune, and so on. This provides 20 dynamically distinct categories of outer Solar system objects in the Jovian and trans-Jovian regions. The Tisserand parameter with respect to the planet controlling perihelion is also often roughly constant under orbital evolution. So, each category can be further sub-divided according to the Tisserand parameter. The dynamical evolution of comets, however, is dominated not by the planets nearest at perihelion or aphelion, but by the more massive Jupiter. The comets are separated into four categories -- Encke-type, short-period, intermediate and long-period -- according to aphelion distance. The Tisserand parameter categories now roughly correspond to the well-known Jupiter-family comets, transition-types and Halley-types. In this way, the nomenclature for the Centaurs and Edgeworth-Kuiper belt objects is based on, and consistent with, that for comets.Comment: MNRAS, in press, 11 pages, 6 figures (1 available as postscript, 5 as gif). Higher resolution figures available at http://www-thphys.physics.ox.ac.uk/users/WynEvans/preprints.pd

Low Temperature Photo-oxidation of Chloroperoxidase Compound II

Oxidation of the heme-thiolate enzyme chloroperoxidase (CPO) from Caldariomyces fumago with peroxynitrite (PN) gave the Compound II intermediate, which was photo-oxidized with 365 nm light to give a reactive oxidizing species. Cryo-solvents at pH ≈ 6 were employed, and reactions were conducted at temperatures as low as − 50 °C. The activity of CPO as evaluated by the chlorodimedone assay was unaltered by treatment with PN or by production of the oxidizing transient and subsequent reaction with styrene. EPR spectra at 77 K gave the amount of ferric protein at each stage in the reaction sequence. The PN oxidation step gave a 6:1 mixture of Compound II and ferric CPO, the photolysis step gave an approximate 1:1 mixture of active oxidant and ferric CPO, and the final mixture after reaction with excess styrene contained ferric CPO in 80% yield. In single turnover reactions at − 50 °C, styrene was oxidized to styrene oxide in high yield. Kinetic studies of styrene oxidation at − 50 °C displayed saturation kinetics with an equilibrium constant for formation of the complex of Kbind = 3.8 × 104 M− 1 and an oxidation rate constant of kox = 0.30 s− 1. UV–Visible spectra of mixtures formed in the photo-oxidation sequence at ca. − 50 °C did not contain the signature Q-band absorbance at 690 nm ascribed to CPO Compound I prepared by chemical oxidation of the enzyme, indicating that different species were formed in the chemical oxidation and the photo-oxidation sequence

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

Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

Simulations of the population of Centaurs - II. Individual objects

Detailed orbit integrations of clones of five Centaurs - namely, 1996 AR20, 2060 Chiron, 1995 SN55, 2000 FZ53 and 2002 FY36 - for durations of ∼3 Myr are presented. One of our Centaur sample starts with perihelion initially under the control of Jupiter (1996 AR20), two start under the control of Saturn (Chiron and 1995 SN55) and one each starts under the control of Uranus (2000 FZ53) and Neptune (2002 FY36), respectively. A variety of interesting pathways are illustrated with detailed examples including: capture into the Jovian Trojans, repeated bursts of short-period comet behaviour, capture into mean-motion resonances with the giant planets and into Kozai resonances, as well as traversals of the entire Solar system. For each of the Centaurs, we provide statistics on the numbers (i) ejected, (ii) showing short-period comet behaviour and (iii) becoming Earth- and Mars-crossing. For example, Chiron has over 60 per cent of its clones becoming short-period objects, while 1995 SN55 has over 35 per cent. Clones of these two Centaurs typically make numerous close approaches to Jupiter. At the other extreme, 2000 FZ53 has ∼2 per cent of its clones becoming short-period objects. In our simulations, typically 20 per cent of the clones which become short-period comets subsequently evolve into Earth-crosser

Structural dynamics analysis

Dynamic analysis of large space antenna systems must treat the deployment as well as vibration and control of the deployed antenna. Candidate computer programs for deployment dynamics, and issues and needs for future program developments are reviewed. Some results for mast and hoop deployment are also presented. Modeling of complex antenna geometry with conventional finite element methods and with repetitive exact elements is considered. Analytical comparisons with experimental results for a 15 meter hoop/column antenna revealed the importance of accurate structural properties including nonlinear joints. Slackening of cables in this antenna is also a consideration. The technology of designing actively damped structures through analytical optimization is discussed and results are presented

A New Kinematic Distance Estimator to the LMC

The distance to the Large Magellanic Cloud (LMC) can be directly determined by measuring three of its properties, its radial-velocity field, its mean proper motion, and the position angle \phi_ph of its photometric line of nodes. Statistical errors of 2% are feasible based on proper motions obtained with any of several proposed astrometry satellites, the first possibility being the Full-Sky Astrometric Mapping Explorer (FAME). The largest source of systematic error is likely to be in the determination of \phi_ph. I suggest two independent methods to measure \phi_ph, one based on counts of clump giants and the other on photometry of clump giants. I briefly discuss a variety of methods to test for other sources of systematic errors.Comment: submitted to ApJ, 13 page

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 four massive planets. The objects exhibit a rich variety of dynamical behaviour with half-lives ranging from 540 kyr (1996AR20) to 32 Myr (2000FZ53). The mean half-life of the entire sample of Centaurs is 2.7 Myr. The data are analysed using a classification scheme based on the controlling planets at perihelion and aphelion, previously given in Horner et al. 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 ∼44300, assuming an inward flux of one new short-period comet every 200 yr. The flux into the Centaur region from the Edgeworth-Kuiper Belt is estimated to be one new object every 125 yr. Finally, the flux from the Centaur region to Earth-crossing orbits is one new Earth-crosser every 880 y

The WARPS survey - IV: The X-ray luminosity-temperature relation of high redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity-temperature relation out to high redshift (z~0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fit in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high redshift L-T relation not previously sampled, are compared to existing measurements at low redshift in order to constrain the evolution of the L-T relation. We find a best fit to low redshift (z1 keV, to be L proportional to T^(3.15\pm0.06). Our data are consistent with no evolution in the normalisation of the L-T relation up to z~0.8. Combining our results with ASCA measurements taken from the literature, we find eta=0.19\pm0.38 (for Omega_0=1, with 1 sigma errors) where L_Bol is proportional to (1 + z)^eta T^3.15, or eta=0.60\pm0.38 for Omega_0=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.Comment: 11 pages, 7 figures, accepted for publication in MNRA