Canonical solution of the two critical argument problem

The solution by Sessin and Ferraz-Mello (Celes. Mech. 32, 307–332) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 21 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem.     

The age of the Roter Kamm impact crater,Namibia: Constraints from 40Ar-39Ar,K-Ar,Rb-Sr,fission track,and 10Be-26Al studies

Abstract The well-preserved 2.5 km diameter Roter Kamm impact crater is located in the Namib desert in Namibia. The impact has occurred in Precambrian granitic and granodioritic orthogneisses of the 1200–900 Ma old Namaqualand Metamorphic Complex which were partly covered by Gariep metasediments; the granites are invaded by quartz veins and quartz-feldspar-pegmatites. Previous geological field evidence suggested a crater age of about 5–10 Ma. In order to constrain this age, we selected a set of basement rocks (granites, granodiorites) exposed at the crater rim and studied the Rb-Sr, K-Ar, ⁴⁰Ar-³⁹Ar, and ¹⁰Be-²⁶Al isotopic systems as well as apatite fission track ages of these samples. The Rb-Sr isotopic systematics confirm the derivation of these samples from the Namaqualand basement (age about 1.29 Ga), which underwent Damaran orogenesis at about 650 Ma. No basement rocks with Rb-Sr ages younger than about 410 Ma were identified. The K-Ar ages of pseudotachylite and melt breccia samples show that these samples are dominated by incompletely degassed fragments of basement rocks, with some retaining their original metamorphic ages of about 470 Ma. The apatite fission track ages range from 20–28 Ma, which may be interpreted as an extension of the 25 Ma Burdigalian peneplanation event, or as incomplete resetting of the apatite fission tracks during the impact event. The ¹⁰Be and ²⁶Al exposure age of a quartz sample isolated from a quartz-pegmatite was found to be 150 ka; it is likely that the exposure of the sample began after material covering it had been removed by erosion 150 ka ago. Two glassy fractions extracted from a rim granite were dated by ⁴⁰Ar-³⁹Ar analysis. One sample gives practically a plateau age of 3.7 ± 0.3 Ma, while the other gives a minimum age of 3.6 Ma. The best available age estimate for the Roter Kamm crater is therefore 3.7 ± 0.3 Ma.     

Theoretical meteor radiants of Apollo,Amor, and Aten asteroids

A compilation of theoretical meteor radiants is presented for all numbered (through 2525) asteroids which approach the Earth's orbit to within 0.20 AU. On the basis of orbital similarity, asteroids associated with current meteor streams and Prairie Network fireballs are listed; plausible associations with medieval fireball radiants are also given. The best defunct comet candidates in terms of meteoric evidence appear to be 2101 Adonis and 2201 1947XC. Asteroids which may be either extinct comets or perturbed main belt asteroids accompanied by collisional debris (represented by fireballs) are 1917 Cuyo, 2202 Pele, 2061 Anza, and 2340 Hathor. 1566 Icarus and 1981 Midas are the only asteroids whose orbits approach to less than 0.07 AU of the Earth's orbit, have a northern radiant, and still show no certain meteoric activity. The majority of Atens, Apollos, and Amors do not pass sufficiently close (<0.07 AU) to the Earth's orbit for a reasonable expectation of meteoric activity, or have radiants south of ?20° declination, requiring southern hemisphere observations.     

Chaotic behavior and the origin of the 31 Kirkwood gap

The sudden eccentricity increases discovered by J. Wisdom (Astron J.87, 577–593, 1982) are reproduced in numerical integrations of the planar-elliptic restricted three-body problem, verifying that this phenomenon is real. Maximum Lyapunov characteristic exponents for trajectories near the $\text{3}\text{1}$ commensurability are computed both with the mappings presented in Wisdom (1982) and by numerical integration of the planar-elliptic problem. In all cases the agreement is excellent, indicating that the mappings accurately reflect whether trajectories are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the $\text{3}\text{1}$ commensurability, both in the planar-elliptic problem and to a more limited extent in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the $\text{3}\text{1}$ Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.     

New 1982 — 1990 photometry of λ Andromedae and its 11-year cycle

We present photoelectric photometry of λ And never before published, obtained between February 1982 and December 1990 at 29 different observatories. Then we combine it with all other photometry available to us (previously published, contained in the I.A.U. Commission 27 Archives, and obtained with the Vanderbilt 16-inch automatic telescope but not yet published), to yield a 14.8-year data base. Analysis reveals a long-term cycle in mean brightness, with a full range of 0^m.15 and a period of 11.4 ± 0.4 years. Because most of our new photometry was concentrated in the 1983-84 observing season, we analyze that one well-defined light curve with a two-spot model. Spot A keeps a 0^m.04 amplitude throughout four rotation cycles whereas the amplitude of spot B diminishes from 0^m.09 down almost to 0^m.03. The spot rotation periods were 55^d.9 ± 0^d.6 and 520^d.8 ± 1^d.0, respectively.     

Hydraulic Performance of the Horizontal Reactive Media Treatment Well: Pilot and Numerical Study

This study is focused on a passive treatment system known as the horizontal reactive treatment well (HRX Well®) installed parallel to groundwater flow, which operates on the principle of flow focusing that results from the hydraulic conductivity (K) ratio of the well and aquifer media. Passive flow and capture in the HRX Well are described by simplified equations adapted from Darcy's Law. A field pilot-scale study (PSS) and numerical simulations using a finite element method (FEM) were conducted to verify the HRX Well concept and test the validity of the HRX Well-simplified equations. The hydraulic performance results from both studies were observed to be within a close agreement to the simplified equations and their hydraulic capture width approximately five times greater than the well diameter (0.20 m). Key parameters affecting capture included the aquifer thickness, well diameter, and permeability ratio of the HRX Well treatment media and aquifer material. During pilot testing, the HRX Well captured 39% of flow while representing 0.5% of the test pit cross-sectional volume, indicating that the well captures a substantial amount of surrounding groundwater. While uncertainty in the aquifer and well properties (porosity, K, well losses), including the effects of boundary conditions, may have caused minor differences in the results, data from this study indicate that the simplified equations are valid for the conceptual design of a field study. A full-scale HRX Well was installed at Site SS003 at Vanderberg Air Force Base, California, in July/August 2018 based on outcomes from this study.     

Searching for nanoflares

The evolution of hydrodynamic shocks generated by nanoflares in coronal loops is investigated in order to suggest requirements for future observations. The shocks produced by nanoflares of 10²⁴ ergs decay within a few seconds, which sets stringent requirements for Doppler or transverse velocity measurements. With feasible improvements, the Normal Incidence X-ray Telescope could observe the time-averaged emission from a nanoflare, however. We also consider collisions between shocks and show that these could also be observed.Operated by the Association of Universities for Research in Astronomy (AURA) under agreement with the Natinal Science Foundation.     

Field Demonstration of the Horizontal Treatment Well (HRX Well®) for Passive In Situ Remediation

The horizontal reactive media treatment well (HRX Well®) uses directionally drilled horizontal wells filled with a treatment media to induce flow-focusing behavior created by the well-to-aquifer permeability contrast to passively capture proportionally large volumes of groundwater. Groundwater is treated in situ as it flows through the HRX Well and downgradient portions of the aquifer are cleaned via elution as these zones are flushed with clean water discharging from the HRX Well. The HRX Well concept is particularly well suited for sites where long-term mass discharge control is a primary performance objective. This concept is appropriate for recalcitrant and difficult-to-treat constituents, including chlorinated solvents, per- and polyfluoroalkyl substances (PFAS), 1,4-dioxane, and metals. A full-scale HRX Well was installed and operated to treat trichloroethene (TCE) with zero valent iron (ZVI). The model-predicted enhanced flow through the HRX Well (compared to the flow in and equivalent cross-sectional area orthogonal to flow in the natural formation before HRX Well installation) and treatment zone width was consistent with flows and widths estimated independently by point velocity probe (PVP) testing, HRX Well tracer testing, and observed treatment in downgradient monitoring wells. The actual average capture zone width was estimated to be between 45 and 69 feet. Total TCE mass discharge reduction was maintained through the duration of the performance monitoring period and exceeded 99.99% (%). Decreases in TCE concentrations were observed at all four downgradient monitoring wells within the treatment zone (ranging from 50 to 74% at day 436), and the first arrival of treated water was consistent with model predictions. The field demonstration confirmed the HRX Well technology is best suited for long-term mass discharge control, can be installed under active infrastructure, requires limited ongoing operation and maintenance, and has low life cycle energy and water requirements.