Triaxial Black-Hole Nuclei

We demonstrate that the nuclei of galaxies containing supermassive black holes can be triaxial in shape. Schwarzschild's method was first used to construct self-consistent orbital superpositions representing nuclei with axis ratios of 1:0.79:0.5 and containing a central point mass representing a black hole. Two different density laws were considered, with power-law slopes of -1 and -2. We constructed two solutions for each power law: one containing only regular orbits and the other containing both regular and chaotic orbits. Monte-Carlo realizations of the models were then advanced in time using an N-body code to verify their stability. All four models were found to retain their triaxial shapes for many crossing times. The possibility that galactic nuclei may be triaxial complicates the interpretation of stellar-kinematical data from the centers of galaxies and may alter the inferred interaction rates between stars and supermassive black holes.Comment: 4 pages, 4 postscript figures, uses emulateapj.st

Mathematical Models and Biological Meaning: Taking Trees Seriously

We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is commonly used in mathematics; the difference between them lies in the biological interpretation of their vertices and edges. Phylogenetic trees and Hennig trees carry exactly the same information, and translation between these two kinds of trees can be accomplished by a simple algorithm. On the other hand, evolutionary concepts such as monophyly are represented as different mathematical substructures are represented differently in the two models. For each phylogenetic or Hennig tree, there is a Nelson cladogram carrying the same information, but the requirement that all taxa be represented by leaves necessarily makes the representation less efficient. Moreover, we claim that it is necessary to give some interpretation to the edges and internal vertices of a Nelson cladogram in order to make it useful as a biological model. One possibility is to interpret internal vertices as sets of characters and the edges as statements of inclusion; however, this interpretation carries little more than incomplete phenetic information. We assert that from the standpoint of phylogenetics, one is forced to regard each internal vertex of a Nelson cladogram as an actual (albeit unsampled) species simply to justify the use of synapomorphies rather than symplesiomorphies.Comment: 15 pages including 6 figures [5 pdf, 1 jpg]. Converted from original MS Word manuscript to PDFLaTe

Hydrodynamics of Monolayer Domains at the Air-Water Interface

Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short- and long-range forces acting within the monolayer. The overdamped hydrodynamics of such interfacial motion is treated here in a general manner that accounts for dissipation both within the monolayer and in the subfluid. Previous results on the linear stability of interfaces are recovered and extended, and a formulation applicable to the nonlinear regime is developed. A simplified dynamical law valid when dissipation in the monolayer itself is negligible is also proposed. Throughout the analysis, special attention is paid to the dependence of the dynamical behavior on a characteristic length scale set by the ratio of the viscosities in the monolayer and in the subphase.Comment: 12 pages, RevTeX, 4 ps figures, accepted in Physics of Fluids

Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars

The Mars Orbiter Laser Altimeter (MOLA), an instrument on the Mars Global Surveyor spacecraft, has measured the topography, surface roughness, and 1.064-μm reflectivity of Mars and the heights of volatile and dust clouds. This paper discusses the function of the MOLA instrument and the acquisition, processing, and correction of observations to produce global data sets. The altimeter measurements have been converted to both gridded and spherical harmonic models for the topography and shape of Mars that have vertical and radial accuracies of ~1 m with respect to the planet's center of mass. The current global topographic grid has a resolution of 1/64° in latitude × 1/32° in longitude (1 × 2 km^2 at the equator). Reconstruction of the locations of incident laser pulses on the Martian surface appears to be at the 100-m spatial accuracy level and results in 2 orders of magnitude improvement in the global geodetic grid of Mars. Global maps of optical pulse width indicative of 100-m-scale surface roughness and 1.064-μm reflectivity with an accuracy of 5% have also been obtained

Molecular Dynamics Simulation of Ga Penetration along Grain Boundaries in Al: a Dislocation Climb Mechanism

Many systems where a liquid metal is in contact with a polycrystalline solid exhibit deep liquid grooves where the grain boundary meets the solid-liquid interface. For example, liquid Ga quickly penetrates deep into grain boundaries in Al, leading to intergranular fracture under very small stresses. We report on a series of molecular dynamics simulations of liquid Ga in contact with an Al bicrystal. We identify the mechanism for liquid metal embrittlement, develop a new model for it, and show that is in excellent agreement with both simulation and experimental data

Trends in Outcomes for Young People with Disabilities: Are We Making Progress?

This paper uses the Current Population Survey (CPS) from 1981-2000 to compare long term trends in socio-economic outcomes for youth (aged 15-21) and young adults (aged 22-29) with work limitations to those for youth and young adults without work limitations. We focus on the years 1988 and 1999: years that roughly correspond to the peaks of successive business cycles. We find that prevalence of work limitations declined for males but increased for females, mostly accounted for by growth for African American females. Despite a substantial reduction in the educational attainment gap between young adults with and without disabilities, gaps in employment, earnings, dependency on public programs and poverty widened substantially. These trends could be due to factors that determine whether individuals report themselves to be work-limited, factors that affect individual outcomes regardless of self-reported work limitation status, or both sets of factors

Concept image and concept definition in mathematics with particular reference to limits and continuity

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition. The development of limits and continuity, as taught in secondary school and university, are considered. Various investigations are reported which demonstrate individual concept images differing from the formal theory and containing factors which cause cognitive conflict

Metrics that matter for assessing the ocean biological carbon pump

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Buesseler, K. O., Boyd, P. W., Black, E. E., & Siegel, D. A. Metrics that matter for assessing the ocean biological carbon pump. Proceedings of the National Academy of Sciences of the United States of America, (2020): 201918114, doi: 10.1073/pnas.1918114117.The biological carbon pump (BCP) comprises wide-ranging processes that set carbon supply, consumption, and storage in the oceans’ interior. It is becoming increasingly evident that small changes in the efficiency of the BCP can significantly alter ocean carbon sequestration and, thus, atmospheric CO2 and climate, as well as the functioning of midwater ecosystems. Earth system models, including those used by the United Nation’s Intergovernmental Panel on Climate Change, most often assess POC (particulate organic carbon) flux into the ocean interior at a fixed reference depth. The extrapolation of these fluxes to other depths, which defines the BCP efficiencies, is often executed using an idealized and empirically based flux-vs.-depth relationship, often referred to as the “Martin curve.” We use a new compilation of POC fluxes in the upper ocean to reveal very different patterns in BCP efficiencies depending upon whether the fluxes are assessed at a fixed reference depth or relative to the depth of the sunlit euphotic zone (Ez). We find that the fixed-depth approach underestimates BCP efficiencies when the Ez is shallow, and vice versa. This adjustment alters regional assessments of BCP efficiencies as well as global carbon budgets and the interpretation of prior BCP studies. With several international studies recently underway to study the ocean BCP, there are new and unique opportunities to improve our understanding of the mechanistic controls on BCP efficiencies. However, we will only be able to compare results between studies if we use a common set of Ez-based metrics.We thank the many scientists whose ideas and contributions over the years are the foundation of this paper. This includes A. Martin, who led the organization of the BIARRITZ group (now JETZON) workshop in July 2019, discussions at which helped to motivate this article. We thank D. Karl for pointing us in the right direction for this paper format at PNAS and two thoughtful reviewers who through their comments helped to improve this manuscript. Support for writing this piece is acknowledged from several sources, including the Woods Hole Oceanographic Institution’s Ocean Twilight Zone project (K.O.B.); NASA as part of the EXport Processes in the global Ocean from RemoTe Sensing (EXPORTS) program (K.O.B. and D.A.S.). E.E.B. was supported by a postdoctoral fellowship through the Ocean Frontier Institute at Dalhousie University. P.W.B. was supported by the Australian Research Council through a Laureate (FL160100131)

Volkov-Pankratov states in topological superconductors

We study the in-gap states that appear at the boundaries of both 1D and 2D topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an s-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin-polarized on either side of the topological phase boundary. We also demonstrate that the spatial position, energy-level spacing, and spin polarization of the VP states can be modified by the introduction of in-plane electric fields.Comment: 10 pages, 8 figure

Patents and Competition in the Automobile Industry

Methane (CH4) fluxes from world rivers are still poorly constrained, with measurements restricted mainly to temperate climates. Additional river flux measurements, including spatio-temporal studies, are important to refine extrapolations. Here we assess the spatio-temporal variability of CH4 fluxes from the Amazon and its main tributaries, the Negro, Solimoes, Madeira, Tapajos, Xingu, and Para Rivers, based on direct measurements using floating chambers. Sixteen of 34 sites were measured during low and high water seasons. Significant differences were observed within sites in the same river and among different rivers, types of rivers, and seasons. Ebullition contributed to more than 50% of total emissions for some rivers. Considering only river channels, our data indicate that large rivers in the Amazon Basin release between 0.40 and 0.58 Tg CH4 yr(-1). Thus, our estimates of CH4 flux from all tropical rivers and rivers globally were, respectively, 19-51% to 31-84% higher than previous estimates, with large rivers of the Amazon accounting for 22-28% of global river CH4 emissions.Funding Agencies|FAPESP [08/58089-9, 2011/06609-1, 2011/14502-2, 2012/17359-9]</p