On the traceless SU(2) character variety of the 6-punctured 2-sphere

We exhibit the traceless $SU(2)$ character variety of a 6-punctured 2-sphere as a 2-fold branched cover of ${\mathbb{C}}P^3$ , branched over the singular Kummer surface, with the branch locus in $R(S^2,6)$ corresponding to the binary dihedral representations. This follows from an analysis of the map induced on $SU(2)$ character varieties by the 2-fold branched cover $F_{n-1}\to S^2$ branched over $2n$ points, combined with the theorem of Narasimhan–Ramanan which identifies $R(F_2)$ with ${\mathbb{C}}P^3$ . The singular points of $R(S^2,6)$ correspond to abelian representations, and we prove that each has a neighborhood in $R(S^2,6)$ homeomorphic to a cone on $S^2\times S^3$

Gauge Theoretic Invariants of, Dehn Surgeries on Knots

New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of the odd signature operator, and the rho invariants of irreducible SU(2) representations. These quantities are calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k Dehn surgery on (2,q) torus knots. The methods are then applied to compute the SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7 and 9.Comment: Version 3: minor corrections from version 2. Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.htm

Pair plasma cushions in the hole-boring scenario

Pulses from a 10 PW laser are predicted to produce large numbers of gamma-rays and electron-positron pairs on hitting a solid target. However, a pair plasma, if it accumulates in front of the target, may partially shield it from the pulse. Using stationary, one-dimensional solutions of the two-fluid (electron-positron) and Maxwell equations, including a classical radiation reaction term, we examine this effect in the hole-boring scenario. We find the collective effects of a pair plasma "cushion" substantially reduce the reflectivity, converting the absorbed flux into high-energy gamma-rays. There is also a modest increase in the laser intensity needed to achieve threshold for a non-linear pair cascade.Comment: 17 pages, 5 figures. Accepted for publication in Plasma Physics and Controlled Fusion. Typos corrected, reference update

Evaluation of modern hydrogen masers

The masers were tested for environmental sensitivities (magnetic field, temperature, barometric pressure) and long-term aging. Allan variance runs of 72 days were made in order to attain averaging times from several seconds to 1 million seconds. Auto- and cross-correlation techniques were used to determine the effects of uncontrolled parameters such as humidity. Three-cornered-hat and other data reduction techniques were used to determine the characteristics of the individual masers

Results of using the global positioning system to maintain the time and frequency synchronization in the Deep Space Network

There are two hydrogen maser clocks located at each signal processing center (SPC) in the DSN. Close coordination of the time and frequency of the SPC clocks is needed to navigate spacecraft to the outer planets. A recent example was the Voyager spacecraft's encounter with Uranus in January 1986. The clocks were adjusted with the goal of minimizing time and frequency offsets between the SPCs at encounter. How time and frequency at each SPC is estimated using data acquired from the Global Positioning System Timing Receivers operating on the NBS-BIH (National Bureau of Standards-Bureau International de l'Heure) tracking schedule is described. These data are combined with other available timing receiver data to calculate the time offset estimates. The adjustment of the clocks is described. It was determined that long range hydrogen maser drift is quite predictable and adjustable within limits. This enables one to minimize time and frequency differences between the three SPCs for many months by matching the drift rates of the three standards. Data acquisition and processing techniques using a Kalman filter to make estimates of time and frequency offsets between the clocks at the SPCs and UTC(NBS) (Coordinated Universal Time realized at NBS) are described