11,715 research outputs found
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
- …