Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural decomposition into subdiagrams called Heegaard cylinders, each of which has a natural shape given by the ratio of two positive integers. We characterize the Heegaard diagrams arising naturally from a twisted face-pairing description as those whose Heegaard cylinders all have integral shape. This characterization allows us to use the Kirby calculus and standard tools of Heegaard theory to attack the problem of finding which closed, orientable 3-manifolds have a twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm

MONTAGE: AGB nucleosynthesis with full s-process calculations

We present MONTAGE, a post-processing nucleosynthesis code that combines a traditional network for isotopes lighter than calcium with a rapid algorithm for calculating the s-process nucleosynthesis of the heavier isotopes. The separation of those parts of the network where only neutron-capture and beta-decay reactions are significant provides a substantial advantage in computational efficiency. We present the yields for a complete set of s-process isotopes for a 3 Mo, Z = 0.02 stellar model, as a demonstration of the utility of the approach. Future work will include a large grid of models suitable for use in calculations of Galactic chemical evolution.Comment: 9 pages, 4 figures. Accepted by PAS

The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

Presentations are computed for a braided version BV of Thompson's group V and for V itself showing that there is an Artin group/Coxeter group relation between them. The presentation for V is obtained from that for BV by declaring all that all generators are involutions.Comment: 15 page

Fixation of virgin lunar surface soil

Two systems are shown to be suitable for fixing loose particulate soils with a polymer film, without visually detectable disturbance of the soil particle spatial relationships. A two-component system is described, which uses a gas monomer condensible at the soil temperature and a gas phase catalyst acting to polymerize the monomer. A one-component system using a monomer which polymerizes spontaneously on and within the top few millimeters of the soil is also considered. The two-component system employs a simpler apparatus, but it operates over a narrower temperature range (approximately -40 to -10 C). Other two-component systems were identified which may operate at soil temperatures as high as +100 C, at relatively narrow temperature ranges of approximately 30 C. The one-component system was demonstrated to operate successfully with initial soil temperatures from -70 C or lower to +150 C

Towards Rapid Parameter Estimation on Gravitational Waves from Compact Binaries using Interpolated Waveforms

Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component masses, sky location, distance, etc.) requires computing millions of waveforms. The computational expense of parameter estimation is dominated by waveform generation and scales linearly with the waveform computational cost. Previous work showed that gravitational waveforms from non-spinning compact binary sources are amenable to a truncated singular value decomposition, which allows them to be reconstructed via interpolation at fixed computational cost. However, the accuracy requirement for parameter estimation is typically higher than for searches, so it is crucial to ascertain that interpolation does not lead to significant errors. Here we provide a proof of principle to show that interpolated waveforms can be used to recover posterior probability density functions with negligible loss in accuracy with respect to non-interpolated waveforms. This technique has the potential to significantly increase the efficiency of parameter estimation.Comment: 7 pages, 2 figure