23,425 research outputs found

    Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations

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    Nbody simulations are used to examine the consequences of Neptune's outward migration into the Kuiper Belt, with the simulated endstates being compared rigorously and quantitatively to the observations. These simulations confirm the findings of Chiang et al. (2003), who showed that Neptune's migration into a previously stirred-up Kuiper Belt can account for the Kuiper Belt Objects (KBOs) known to librate at Neptune's 5:2 resonance. We also find that capture is possible at many other weak, high-order mean motion resonances, such as the 11:6, 13:7, 13:6, 9:4, 7:3, 12:5, 8:3, 3:1, 7:2, and the 4:1. The more distant of these resonances, such as the 9:4, 7:3, 5:2, and the 3:1, can also capture particles in stable, eccentric orbits beyond 50 AU, in the region of phase space conventionally known as the Scattered Disk. Indeed, 90% of the simulated particles that persist over the age of the Solar System in the so-called Scattered Disk zone never had a close encounter with Neptune, but instead were promoted into these eccentric orbits by Neptune's resonances during the migration epoch. This indicates that the observed Scattered Disk might not be so scattered. This model also produced only a handful of Centaurs, all of which originated at Neptune's mean motion resonances in the Kuiper Belt. We also report estimates of the abundances and masses of the Belt's various subpopulations (e.g., the resonant KBOs, the Main Belt, and the so-called Scattered Disk), and also provide upper limits on the abundance of Centaurs and Neptune's Trojans, as well as upper limits on the sizes and abundances of hypothetical KBOs that might inhabit the a>50 AU zone.Comment: 60 pages, 16 figures. Accepted for publication in the Astronomical Journa

    Measuring the convergence of Monte Carlo free energy calculations

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    The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.Comment: 14 pages, 17 figure

    Considerations on a revision of the quality factor

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    A modified analytical expression is proposed for the revised quality factor that has been suggested by a liaison group of ICRP and ICRU. With this modification one obtains, for sparsely ionizing radiation, a quality factor which is proportional to the dose average of lineal energy, y. It is shown that the proposed relation between the quality factor and lineal energy can be translated into a largely equivalent dependence on LET. The choice between the reference parameters LET or y is therefore a secondary problem in an impending revision of the quality factor

    Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and double simple Hurwitz numbers

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    We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals the strong piecewise polynomiality in the sense of Goulden–Jackson–Vakil, generalising a result of Johnson, and provides a new explicit proof of the piecewise polynomiality of the mixed case. Moreover, we derive wall-crossing formulae for the mixed case. These statements specialise to any of the three types of Hurwitz numbers, and to the mixed case of any pair
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