Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for $m$ between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when $0.54\leq m\leq 1$, and are linearly unstable when $0<m\leq0.53$.Comment: 6 figure

Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.Comment: 16 pages, 4 figure

Deformations arising during air-knife stripping in the galvanization of steel

During sheet steel production, the steel surface is usually coated with metal alloy for corrosion protection. This can be done by passing the steel through a bath of the molten metal coating, and controlling thickness with a pair of air knives on either side of the ascending steel strip. Surface quality problem, have arisen with recent developments in production. The process was considered at the 2009 Mathematics-and-Statistics-in-Industry Study Group in Wollongong (MIS09) and in subsequent investigations. Previous analyses are extended by the addition of shear terms and by exploring the effect of increased air-jet speeds. A first-order partial differential equation governs the system. This may be used to determine the steady-state coating shape and to study the evolution of any defects that may form

Deformations during jet-stripping in the galvanizing process

The problem of coating steel by passing it through a molten alloy and then stripping off excess coating using an air jet is considered. The work revisits the analysis of Tuck (Phys Fluids 26:2352, 1983) with the addition of extra shear terms and a consideration of the effect of increased air-jet speeds. A first-order partial differential equation is derived and solved both to obtain the steady-state coating shape and to determine the evolution of any defects that may form

MOA-2013-BLG-220Lb:massive planetary companion to galactic-disk host

We report the discovery of MOA-2013-BLG-220Lb, which has a super-Jupiter mass ratio q = 3.01 ± 0.02 × 10-3 relative to its host. The proper motion, μ = 12.5 ± 1 mas yr-1, is one of the highest for microlensing planets yet discovered, implying that it will be possible to separately resolve the host within ∼7 yr. Two separate lines of evidence imply that the planet and host are in the Galactic disk. The planet could have been detected and characterized purely with follow-up data, which has important implications for microlensing surveys, both current and into the Large Synoptic Survey Telescope (LSST) era.</p

MOA-2011-BLG-262Lb:a sub-earth-mass moon orbiting a gas giant primary or a high velocity planetary system in the galactic bulge

We present the first microlensing candidate for a free-floating exoplanet-exomoon system, MOA-2011-BLG-262, with a primary lens mass of M host ~ 4 Jupiter masses hosting a sub-Earth mass moon. The argument for an exomoon hinges on the system being relatively close to the Sun. The data constrain the product MLπrel where ML is the lens system mass and πrel is the lens-source relative parallax. If the lens system is nearby (large πrel), then ML is small (a few Jupiter masses) and the companion is a sub-Earth-mass exomoon. The best-fit solution has a large lens-source relative proper motion, μrel = 19.6 ± 1.6 mas yr–1, which would rule out a distant lens system unless the source star has an unusually high proper motion. However, data from the OGLE collaboration nearly rule out a high source proper motion, so the exoplanet+exomoon model is the favored interpretation for the best fit model. However, there is an alternate solution that has a lower proper motion and fits the data almost as well. This solution is compatible with a distant (so stellar) host. A Bayesian analysis does not favor the exoplanet+exomoon interpretation, so Occam's razor favors a lens system in the bulge with host and companion masses of M host = 0.12 +0.19-0.06 MΘ and mcomp = 18+28-10M⊕, at a projected separation of a⊥ = 0.84+0.25−0.14 AU. The existence of this degeneracy is an unlucky accident, so current microlensing experiments are in principle sensitive to exomoons. In some circumstances, it will be possible to definitively establish the mass of such lens systems through the microlensing parallax effect. Future experiments will be sensitive to less extreme exomoons.</p

A super-Jupiter orbiting a late-type star:a refined analysis of microlensing event OGLE-2012-BLG-0406

We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG-0406 based on data obtained from 10 different observatories. Intensive coverage of the light curve, especially the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects, we estimate the physical parameters of the lens system. We find that the event was caused by a 2.73 ± 0.43 M J planet orbiting a 0.44 ± 0.07 M ☉ early M-type star. The distance to the lens is 4.97 ± 0.29 kpc and the projected separation between the host star and its planet at the time of the event is 3.45 ± 0.26 AU. We find that the additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to a more accurate determination of the physical parameters of the lens.</p