The Planet Nine Hypothesis

Over the course of the past two decades, observational surveys have unveiled the intricate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital behavior, the emerging census of trans-Neptunian objects displays dynamical phenomena that cannot be accounted for by interactions with the known eight-planet solar system alone. Specifically, explanations for the observed physical clustering of orbits with semi-major axes in excess of $\sim250\,$AU, the detachment of perihelia of select Kuiper belt objects from Neptune, as well as the dynamical origin of highly inclined/retrograde long-period orbits remain elusive within the context of the classical view of the solar system. This newly outlined dynamical architecture of the distant solar system points to the existence of a new planet with mass of $m_9\sim 5-10\,M_{\oplus}$, residing on a moderately inclined orbit ($i_9\sim15-25\deg$) with semi-major axis $a_9\sim 400 - 800\,$AU and eccentricity between $e_9 \sim 0.2 - 0.5$. This paper reviews the observational motivation, dynamical constraints, and prospects for detection of this proposed object known as Planet Nine.Comment: 92 pages, 28 figures, published in Physics Report

Poincare duality for K-theory of equivariant complex projective spaces

We make explicit Poincare duality for the equivariant K-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the K-theory orientation

Monte Carlo simulation of phase separation during thin‐film codeposition

Copyright 1993 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The article originally appeared in Journal of Applied Physics 74, 1707 (1993) and may be found at http://jap.aip.org/resource/1/japiau/v74/i3/p1707_s1.The results of Monte Carlo simulation of phase separation during binary film coevaporation are presented for a range of deposition conditions. The model employed assumes that phase separation occurs through surface interdiffusion during deposition, while the bulk of the film remains frozen. Simulations were performed on A‐B alloy films having compositions of 10 and 50 vol % solute. For both film compositions, the lateral scale of the domains at the film surface evolves to a steady‐state size during deposition. A power‐law dependence of the steady‐state domain size on the inverse deposition rate is obtained. Simulation microstructures at 50 vol % compare favorably with those obtained in a previous experimental study of phase separation during coevaporation of Al‐Ge films of the same composition. Results of simulations performed at 10 vol % are compared with the predictions of a theoretical model based on the above assumptions. The power‐law exponent obtained from simulations at 10 vol % is different than that predicted by the theoretical model. The reasons for this difference are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69953/2/JAPIAU-74-3-1707-1.pd

Beyond Flux-Limited Diffusion: Parallel Algorithms for Multidimensional Radiation Hydrodynamics

This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here encapsulate the physics provided by the serial algorithm of Stone et. al (ApJSupp, vol 80, pp. 819-845), but add new functionality with regard to physics and numerics. Physics enhancments include the addition of time dependence to the computation of the variable tensor Eddington factor (VTEF) closure term, and a matter-radiation coupling scheme which is particularly robust for nonequilibrium problems. Numerical highlights include a discussion of how our code is implemented for parallel execution and a description of our scalable linear solver module. We present a suite of numerical tests from which the virtues and vices of our method may be gleaned; these include nonequilibrium Marshak waves, 2-D "shadow" tests showing the one-sided illumination of an opaque cloud, and full RHD+VTEF simulations of radiating shocks. We conclude that radiation moment solutions closed with variable tensor Eddington factors show a dramatic qualitative improvement over results obtained with flux-limited diffusion, and further that this approach has a bright future in the context of parallel RHD simulations in astrophysics.Comment: 57 pages (including 18 eps figures); submitted to the ApJ Supplement; prepared with AASTEX 5.

Consumer Racial Discrimination in Tipping: A Replication and Extension

This study examines the effects of server race, customer race and their interaction on restaurant tips while statistically controlling for the customers’ perceptions of service quality and other variables. The findings indicate that consumers of both races discriminate against black service providers by tipping them less than white service providers. Furthermore, this server race effect on tipping is moderated by perceived service quality and dining party size. The theoretical and practical implications of these findings are discussed. Particularly noteworthy is the possibility that the server race effect on tipping represents an adverse impact against black servers that makes the use of tipping to compensate employees a violation of employment discrimination law in the United States