Hubble Space Telescope Observations of 3200 Phaethon At Closest Approach

We present Hubble Space Telescope observations of the active asteroid (and Geminid stream parent) 3200 Phaethon when at its closest approach to Earth (separation 0.07 AU) in 2017 December. Images were recorded within $\sim$1\degr~of the orbital plane, providing extra sensitivity to low surface brightness caused by scattering from a large-particle trail. We placed an upper limit to the apparent surface brightness of such a trail at 27.2 magnitudes arcsecond$^{-2}$, corresponding to an in-plane optical depth $\le 3\times10^{-9}$. No co-moving sources brighter than absolute magnitude 26.3, corresponding to circular equivalent radius $\sim$12 m (albedo 0.12 assumed), were detected. Phaethon is too hot for near-surface ice to survive. We briefly consider the thermodynamic stability of deeply-buried ice, finding that its survival would require either a very small (regolith-like) thermal diffusivity ($< 10^{-8}$ m$^2$ s$^{-1}$), or the unexpectedly recent injection of Phaethon (timescale $\lesssim$ 10$^6$ yr) into its present orbit, or both.Comment: Improved the discussion of optical depth calculation and corrected an error in the previous version. 28 pages, 5 figures, Astronomical Journal, in pres

Distributed control of a fault tolerant modular multilevel inverter for direct-drive wind turbine grid interfacing

Modular generator and converter topologies are being pursued for large offshore wind turbines to achieve fault tolerance and high reliability. A centralized controller presents a single critical point of failure which has prevented a truly modular and fault tolerant system from being obtained. This study analyses the inverter circuit control requirements during normal operation and grid fault ride-through, and proposes a distributed controller design to allow inverter modules to operate independently of each other. All the modules independently estimate the grid voltage magnitude and position, and the modules are synchronised together over a CAN bus. The CAN bus is also used to interleave the PWM switching of the modules and synchronise the ADC sampling. The controller structure and algorithms are tested by laboratory experiments with respect to normal operation, initial synchronization to the grid, module fault tolerance and grid fault ride-through

Anatomy of an Asteroid Break-Up: The Case of P/2013 R3

We present an analysis of new and published data on P/2013 R3, the first asteroid detected while disintegrating. Thirteen discrete components are measured in the interval between UT 2013 October 01 and 2014 February 13. We determine a mean, pair-wise velocity dispersion amongst these components of $\Delta v = 0.33\pm0.03$ m s$^{-1}$ and find that their separation times are staggered over an interval of $\sim$5 months. Dust enveloping the system has, in the first observations, a cross-section $\sim$30 km$^2$ but fades monotonically at a rate consistent with the action of radiation pressure sweeping. The individual components exhibit comet-like morphologies and also fade except where secondary fragmentation is accompanied by the release of additional dust. We find only upper limits to the radii of any embedded solid nuclei, typically $\sim$100 to 200 m (geometric albedo 0.05 assumed). Combined, the components of P/2013 R3 would form a single spherical body with radius $\lesssim$400 m, which is our best estimate of the size of the precursor object. The observations are consistent with rotational disruption of a weak (cohesive strength $\sim$50 to 100 N m$^{-2}$) parent body, $\sim$400 m in radius. Estimated radiation (YORP) spin-up times of this parent are $\lesssim$1 Myr, shorter than the collisional lifetime. If present, water ice sublimating at as little as 10$^{-3}$ kg s$^{-1}$ could generate a torque on the parent body rivaling the YORP torque. Under conservative assumptions about the frequency of similar disruptions, the inferred asteroid debris production rate is $\gtrsim$10$^3$ kg s$^{-1}$, which is at least 4% of the rate needed to maintain the Zodiacal Cloud.Comment: 44 pages, 13 figures, accepted by Astronomical Journa

Disintegrating Asteroid P/2013 R3

Splitting of the nuclei of comets into multiple components has been frequently observed but, to date, no main-belt asteroid has been observed to break-up. Using the Hubble Space Telescope, we find that main-belt asteroid P/2013 R3 consists of 10 or more distinct components, the largest up to 200 m in radius (assumed geometric albedo of 0.05) each of which produces a coma and comet-like dust tail. A diffuse debris cloud with total mass roughly 2x10^8 kg further envelopes the entire system. The velocity dispersion among the components is about V = 0.2 to 0.5 m/s, is comparable to the gravitational escape speeds of the largest members, while their extrapolated plane-of-sky motions suggest break-up between February and September 2013. The broadband optical colors are those of a C-type asteroid. We find no spectral evidence for gaseous emission, placing model-dependent upper limits to the water production rate near 1 kg/s. Breakup may be due to a rotationally induced structural failure of the precursor body.Comment: 16 pages, 3 figures; accepted by ApJ

Phantom energy from graded algebras

We construct a model of phantom energy using the graded Lie algebra SU(2/1). The negative kinetic energy of the phantom field emerges naturally from the graded Lie algebra, resulting in an equation of state with w<-1. The model also contains ordinary scalar fields and anti-commuting (Grassmann) vector fields which can be taken as two component dark matter. A potential term is generated for both the phantom fields and the ordinary scalar fields via a postulated condensate of the Grassmann vector fields. Since the phantom energy and dark matter arise from the same Lagrangian the phantom energy and dark matter of this model are coupled via the Grassman vector fields. In the model presented here phantom energy and dark matter come from a gauge principle rather than being introduced in an ad hoc manner.Comment: 8 pages no figures; references added and discussion on condensate of vector grassman fields added. To be published MPL