An ambient approach to conformal geodesics

Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third-order differential equation determined by the conformal structure. There is an alternative description via the tractor calculus. In this article, we give a third description using ideas from holography. A conformal [Formula: see text]-manifold [Formula: see text] can be seen (formally at least) as the asymptotic boundary of a Poincaré–Einstein [Formula: see text]-manifold [Formula: see text]. We show that any curve [Formula: see text] in [Formula: see text] has a uniquely determined extension to a surface [Formula: see text] in [Formula: see text], which we call the ambient surface of [Formula: see text]. This surface meets the boundary [Formula: see text] in right angles along [Formula: see text] and is singled out by the requirement that it be a critical point of renormalized area. The conformal geometry of [Formula: see text] is encoded in the Riemannian geometry of [Formula: see text]. In particular, [Formula: see text] is a conformal geodesic precisely when [Formula: see text] is asymptotically totally geodesic, i.e. its second fundamental form vanishes to one order higher than expected. We also relate this construction to tractors and the ambient metric construction of Fefferman and Graham. In the [Formula: see text]-dimensional ambient manifold, the ambient surface is a graph over the bundle of scales. The tractor calculus then identifies with the usual tensor calculus along this surface. This gives an alternative compact proof of our holographic characterization of conformal geodesics.

Thermal annealing of implanted ²⁵²Cf fission tracks in monazite

A series of isochronal heating experiments were performed to constrain monazite fission track thermal annealing properties. The 252Cf fission tracks were implanted into monazite crystals from the Devonian Harcourt granodiorite (Victoria, Australia) on polished surfaces oriented parallel to (100) pinacoidal faces and perpendicular to the crystallographic c axis. Tracks were annealed over 1, 10, 100 and 1000 h schedules at temperatures between 30 and 400 ∘C. Track lengths were measured on captured digital image stacks and then converted to calculated mean lengths of equivalent confined fission tracks that progressively decreased with increasing temperature and time. Annealing is anisotropic, with tracks on surfaces perpendicular to the crystallographic c axis consistently annealing faster than those parallel to the (100) face. To investigate how the mean track lengths decreased as a function of annealing time and temperature, one parallel and two fanning models were fitted to the empirical dataset. The temperature limits of the monazite partial annealing zone (MPAZ) were defined as length reductions to 0.95 (lowest) and 0.5 (highest) for this study. Extrapolation of the laboratory experiments to geological timescales indicates that for a heating duration of 107 years, estimated temperature ranges of the MPAZ are −44 to 101 ∘C for the parallel model and −71 to 143 ∘C (both ±6–21 ∘C, 2 standard errors) for the best-fitting linear fanning model (T0=∞). If a monazite fission track closure temperature is approximated as the midpoint of the MPAZ, these results, for tracks with similar mass and energy distributions to those involved in spontaneous fission of 238U, are consistent with previously estimated closure temperatures (calculated from substantially higher energy particles) of < 50 ∘C and perhaps not much higher than ambient surface temperatures. Based on our findings we estimate that this closure temperature (Tc) for fission tracks in monazite ranges between ∼ 45 and 25 ∘C over geological timescales of 106–107 years, making this system potentially useful as an ultra-low-temperature thermochronometer.

Combinatorial invariant of Morse-Smale diffeomorphisms on surfaces with orientable heteroclinic

In this paper we consider class of orientation-preserving Morse-Smale diffeomorphisms f, given on orientable surface M2. In their articles A.A.~Bezdenezhnich and V. Z. Grines has shown, that such diffeomorfisms contain finite number of heteroclinic orbits. Moreover, the problem of classification for such diffeomorphisms is reduced to the problem of distinguishing orientable graphs with substitutions describing the geometry of heteroclinic intersections. Howewer, these graphs generally do not allow polynomial distinguishing algorithms. In this paper, we propose a new approach to the classification of such cascades. To this end, each considered diffeomorphism f is associated with a graph whose embeddablility in the ambient surface makes it possible to construct an effective algoritm for distinguishing such graphs.

Validation of GEMS L2 products using ground-based remote sensing data including PANDORA measurements

&lt;p&gt;Launch of the Geostationary Environmental Monitoring Spectrometer (GEMS) is scheduled in early 2020 to support public service and science related to air quality and climate by providing diurnal variation of concentrations of trace gases and aerosols with high spatial/temporal resolution over Asian region. We will introduce GEMS validation methodology in parallel with a strategy for integration of existed independent measurements like as low-orbit satellite, ground-based remote sensing, and ambient surface observation data. As collections of nearly real-time and quality-assured data from existing ground-based networks are still in great needs for GEMS validation, efforts to expand observational infra-structure have been going on. Currently, two PANDORA instruments started to be in operation at Seoul and Ulsan in Korea, and PANDORA Asian Network initiated by NIER, Korea will be expanded into South East Asian region beyond Korea, China and Japan in addition. In this study, we especially try to validate the initial L2 product of GEMS gathered during IOT period by utilizing PANDORA data and other ground remote sensing data as well so that availability and feasibility of those ground observations could be assessed for GEMS validation.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;Keywords: GEMS validation, ground-based remote sensing data, PANDORA&lt;/p&gt;

Chapter 1: Gold Deposit Types: An Overview

Gold is either the only economically important metal or a major by-product in 11 well-characterized deposit types—paleoplacer, orogenic, porphyry, epithermal, Carlin, placer, reduced intrusion related, volcanogenic massive sulfide (VMS), skarn, carbonate replacement, and iron oxide-copper-gold (IOCG), arguably more than for those of any other metal; it also dominates a number of deposits of uncertain or unknown origin. Major gold concentrations formed worldwide from the Mesoarchean to the Pleistocene, from Earth’s surface to midcrustal paleodepths, alone or in association with silver, base metals, and/or uranium, and from hydrothermal fluids of predominantly metamorphic, magmatic, meteoric, seawater, or, uncommonly, basinal origins, as well as from mafic magma or ambient surface water. Most of the Neoproterozoic and Phanerozoic deposits unequivocally formed in accretionary orogens. As an introduction to this compilation of the world’s major gold deposits and provinces, this paper provides a thumbnail sketch of each gold deposit type, including geologic and economic characteristics and widely accepted genetic models, as well as briefly discusses aspects of their spatial and temporal associations and distributions.