Bridge number, Heegaard genus and non-integral Dehn surgery

We show there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1.Comment: 76 page, 48 figures; referee comments incorporated and typos fixed; accepted at TAM

Alternatives for Measuring Hazardous Waste Reduction

PTI Project number 233U-4913FRHWRIC Project Number 89006

Cabling, contact structures and mapping class monoids

In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that generalizes the standard notion of open book decomposition and allows one to more easily study surgeries on transverse knots. As a corollary to our investigation we are able to show there are Stein fillable contact structures supported by open books whose monodromies cannot be written as a product of positive Dehn twists. We also exhibit several monoids in the mapping class group of a surface that have contact geometric significance.Comment: 62 pages, 32 figures. Significant expansion of exposition and more details on some argument

A Compton telescope for remote location and identification of radioactive material

The spare detectors from NASA Compton Gamma-Ray Observatory COMPTEL instrument have been reconfigured to demonstrate the capability at ground level to remotely locate and identify sources of g radiation or the movement of material that might shield γ-ray sources. The Gamma-Ray Experimental Telescope Assembly (GRETA) employs two 28 cm diameter scintillation detectors separated by 81 cm: one 8.5 cm thick liquid scintillator detector and one 7.5 cm thick NaI(Tl) detector. The assembly electronics and real-time data acquisition system measures the energy deposits and time-of- flight for each coincident detection and compiles histograms of total energy and incident angle as computed using the kinematics of Compton scattering. The GRETA field of view is a cone with full angle approximately 120°. The sensitive energy range is 0.3 to 2.6 MeV. Energy resolution is ~10% FWHM. The angular resolution, ~19° in the simplified configuration tested, will improve to better than 5° with well-defined enhancements to the data acquisition hardware and data analysis routines. When operated in the mode that was used in space, the instrument is capable of measuring and imaging up to 30 MeV with an angular resolution of 1.5°. The response of the instrument was mapped in the laboratory with 14 Ci 22Na source 3 m from the instrument. Later, we conducted demonstrations under two measurement scenarios. In one, the remotely located instrument observed an increase of background radiation counts at 1.4 MeV when a large amount of lead was removed from a building and a corresponding decrease when the lead was replaced. In the other scenario, the location and isotope-identifying energy spectrum of a 500 μCi137Cs source 3-5 m from the instrument with two intervening walls was determined in less than one minute. We report details of the instrument design and these measurements

Position Resolution in LaBr3 and LaCl3 Scintillators Using Position-Sensitive Photomultiplier Tubes

Advanced scintillator materials such as LaBr3:Ce and LaCl3:Ce hold great promise for future hard X-ray and gamma-ray astrophysics missions due to their high density, high light output, good linearity, and fast decay times. Of particular importance for future space-based imaging instruments, such as coded-aperture telescopes, is the precise spatial location of individual gamma-ray interactions. We have investigated the position and energy resolution achievable within monolithic (5 cm × 5 cm × 1 cm) LaBr3:Ce and LaCl3:Ce crystals using position-sensitive light readout devices, including a position-sensitive photomultiplier tube and a multi-anode photomultiplier tube. We present the results of these tests and discuss the applicability of such advanced scintillators to future high-energy imaging astrophysics missions

Improved Moving Puncture Gauge Conditions for Compact Binary Evolutions

Robust gauge conditions are critically important to the stability and accuracy of numerical relativity (NR) simulations involving compact objects. Most of the NR community use the highly robust---though decade-old---moving-puncture (MP) gauge conditions for such simulations. It has been argued that in binary black hole (BBH) evolutions adopting this gauge, noise generated near adaptive-mesh-refinement (AMR) boundaries does not converge away cleanly with increasing resolution, severely limiting gravitational waveform accuracy at computationally feasible resolutions. We link this noise to a sharp (short-wavelength), initial outgoing gauge wave crossing into progressively lower resolution AMR grids, and present improvements to the standard MP gauge conditions that focus on stretching, smoothing, and more rapidly settling this outgoing wave. Our best gauge choice greatly reduces gravitational waveform noise during inspiral, yielding less fluctuation in convergence order and $\sim 40$ lower waveform phase and amplitude errors at typical resolutions. Noise in other physical quantities of interest is also reduced, and constraint violations drop by more than an order of magnitude. We expect these improvements will carry over to simulations of all types of compact binary systems, as well as other $N$+1 formulations of gravity for which MP-like gauge conditions can be chosen.Comment: 25 pages, 16 figures, 2 tables. Matches published versio