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

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

The Secular Evolution of the Primordial Kuiper Belt

A model that computes the secular evolution of a gravitating disk-planet system is developed. The disk is treated as a set of gravitating rings, with the rings'/planets' time-evolution governed by the classical Laplace-Lagrange solution for secular evolution but modified to account for the disk's finite thickness h. This system's Lagrange planetary equations yield a particular class of spiral wave solutions, usually denoted as apsidal density waves and nodal bending waves. There are two varieties of apsidal waves:long waves and short waves. Planets typically launch long density waves at the disk's nearer edge or else at a secular resonance in the disk, and these waves ultimately reflect downstream at a more distant disk edge or else at a Q-barrier in the disk, whereupon they return as short density waves. Planets also launch nodal bending waves, and these have the property that they can stall in the disk, that is, their group velocity plummets to zero upon approaching a disk region too thick to support the continued propagation of bending waves. The rings model is used to compute the secular evolution of a Kuiper Belt having a variety of masses, and it is shown that the early massive Belt was very susceptible to the propagation of low-amplitude apsidal and nodal waves launched by the giant planets.Comment: 45 pages, 6 figure

Bayesian Nonparametric Feature and Policy Learning for Decision-Making

Learning from demonstrations has gained increasing interest in the recent past, enabling an agent to learn how to make decisions by observing an experienced teacher. While many approaches have been proposed to solve this problem, there is only little work that focuses on reasoning about the observed behavior. We assume that, in many practical problems, an agent makes its decision based on latent features, indicating a certain action. Therefore, we propose a generative model for the states and actions. Inference reveals the number of features, the features, and the policies, allowing us to learn and to analyze the underlying structure of the observed behavior. Further, our approach enables prediction of actions for new states. Simulations are used to assess the performance of the algorithm based upon this model. Moreover, the problem of learning a driver's behavior is investigated, demonstrating the performance of the proposed model in a real-world scenario

Bayesian Nonparametric Unmixing of Hyperspectral Images

Hyperspectral imaging is an important tool in remote sensing, allowing for accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a hyperspectral image rarely represents a single material, but rather a mixture of different spectra. HSU aims at estimating the pure spectra present in the scene of interest, referred to as endmembers, and their fractions in each pixel, referred to as abundances. Today, many HSU algorithms have been proposed, based either on a geometrical or statistical model. While most methods assume that the number of endmembers present in the scene is known, there is only little work about estimating this number from the observed data. In this work, we propose a Bayesian nonparametric framework that jointly estimates the number of endmembers, the endmembers itself, and their abundances, by making use of the Indian Buffet Process as a prior for the endmembers. Simulation results and experiments on real data demonstrate the effectiveness of the proposed algorithm, yielding results comparable with state-of-the-art methods while being able to reliably infer the number of endmembers. In scenarios with strong noise, where other algorithms provide only poor results, the proposed approach tends to overestimate the number of endmembers slightly. The additional endmembers, however, often simply represent noisy replicas of present endmembers and could easily be merged in a post-processing step

Measuring the convergence of Monte Carlo free energy calculations

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

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

An N-body Integrator for Gravitating Planetary Rings, and the Outer Edge of Saturn's B Ring

A new symplectic N-body integrator is introduced, one designed to calculate the global 360 degree evolution of a self-gravitating planetary ring that is in orbit about an oblate planet. This freely-available code is called epi_int, and it is distinct from other such codes in its use of streamlines to calculate the effects of ring self-gravity. The great advantage of this approach is that the perturbing forces arise from smooth wires of ring matter rather than discreet particles, so there is very little gravitational scattering and so only a modest number of particles are needed to simulate, say, the scalloped edge of a resonantly confined ring or the propagation of spiral density waves. The code is applied to the outer edge of Saturn's B ring, and a comparison of Cassini measurements of the ring's forced response to simulations of Mimas' resonant perturbations reveals that the B ring's surface density at its outer edge is 195+-60 gm/cm^2 which, if the same everywhere across the ring would mean that the B ring's mass is about 90% of Mimas' mass. Cassini observations show that the B ring-edge has several free normal modes, which are long-lived disturbances of the ring-edge that are not driven by any known satellite resonances. Although the mechanism that excites or sustains these normal modes is unknown, we can plant such a disturbance at a simulated ring's edge, and find that these modes persist without any damping for more than ~10^5 orbits or ~100 yrs despite the simulated ring's viscosity of 100 cm^2/sec. These simulations also indicate that impulsive disturbances at a ring can excite long-lived normal modes, which suggests that an impact in the recent past by perhaps a cloud of cometary debris might have excited these disturbances which are quite common to many of Saturn's sharp-edged rings.Comment: 55 pages, 13 figures, accepted for publication in the Astrophysical Journa