22,330 research outputs found
Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double
It is well known that the quantum double structure plays an important role in
three dimensional quantum gravity coupled to matter field. In this paper, we
show how this algebraic structure emerges in the context of three dimensional
Riemannian loop quantum gravity (LQG) coupled to a finite number of massive
spinless point particles. In LQG, physical states are usually constructed from
the notion of SU(2) cylindrical functions on a Riemann surface and the
Hilbert structure is defined by the Ashtekar-Lewandowski measure. In the case
where is the sphere , we show that the physical Hilbert space is
in fact isomorphic to a tensor product of simple unitary representations of the
Drinfeld double DSU(2): the masses of the particles label the simple
representations, the physical states are tensor products of vectors of simple
representations and the physical scalar product is given by intertwining
coefficients between simple representations. This result is generalized to the
case of any Riemann surface .Comment: 36 pages, published in Jour. Math. Physic
Improving Performance of Iterative Methods by Lossy Checkponting
Iterative methods are commonly used approaches to solve large, sparse linear
systems, which are fundamental operations for many modern scientific
simulations. When the large-scale iterative methods are running with a large
number of ranks in parallel, they have to checkpoint the dynamic variables
periodically in case of unavoidable fail-stop errors, requiring fast I/O
systems and large storage space. To this end, significantly reducing the
checkpointing overhead is critical to improving the overall performance of
iterative methods. Our contribution is fourfold. (1) We propose a novel lossy
checkpointing scheme that can significantly improve the checkpointing
performance of iterative methods by leveraging lossy compressors. (2) We
formulate a lossy checkpointing performance model and derive theoretically an
upper bound for the extra number of iterations caused by the distortion of data
in lossy checkpoints, in order to guarantee the performance improvement under
the lossy checkpointing scheme. (3) We analyze the impact of lossy
checkpointing (i.e., extra number of iterations caused by lossy checkpointing
files) for multiple types of iterative methods. (4)We evaluate the lossy
checkpointing scheme with optimal checkpointing intervals on a high-performance
computing environment with 2,048 cores, using a well-known scientific
computation package PETSc and a state-of-the-art checkpoint/restart toolkit.
Experiments show that our optimized lossy checkpointing scheme can
significantly reduce the fault tolerance overhead for iterative methods by
23%~70% compared with traditional checkpointing and 20%~58% compared with
lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1
Diets of shags Phalacrocorax aristotelis and cormorants P. carbo in Norway and possible implications for gadoid stock recruitment
The diets of shags and cormorants were studied in Norway through analyses of regurgitated pellets. Although this method has many limitations, indications were that both species rely heavily on small gadoids (Gadidae) and sand eels (Ammodytidae) for food throughout their range, but also eat other fish species when available. There was considerable dietary overlap between species, despite a
tendency for cormorants to eat larger fish and more benthic items than shags. Predation by shags and cormorants could be a factor limiting the recruitment of cod and saithe into what are now severely reduced, but commercially important stocks in the Norwegian and Barents Seas
An algebraic interpretation of the Wheeler-DeWitt equation
We make a direct connection between the construction of three dimensional
topological state sums from tensor categories and three dimensional quantum
gravity by noting that the discrete version of the Wheeler-DeWitt equation is
exactly the pentagon for the associator of the tensor category, the
Biedenharn-Elliott identity. A crucial role is played by an asymptotic formula
relating 6j-symbols to rotation matrices given by Edmonds.Comment: 10 pages, amstex, uses epsf.tex. New version has improved
presentatio
AS-204/LM-1 launch vehicle operational flight trajectory
Apollo Saturn-204/LM-1 launch vehicle operational flight trajector
Finiteness and Dual Variables for Lorentzian Spin Foam Models
We describe here some new results concerning the Lorentzian Barrett-Crane
model, a well-known spin foam formulation of quantum gravity. Generalizing an
existing finiteness result, we provide a concise proof of finiteness of the
partition function associated to all non-degenerate triangulations of
4-manifolds and for a class of degenerate triangulations not previously shown.
This is accomplished by a suitable re-factoring and re-ordering of integration,
through which a large set of variables can be eliminated. The resulting
formulation can be interpreted as a ``dual variables'' model that uses
hyperboloid variables associated to spin foam edges in place of representation
variables associated to faces. We outline how this method may also be useful
for numerical computations, which have so far proven to be very challenging for
Lorentzian spin foam models.Comment: 15 pages, 1 figur
Area Regge Calculus and Discontinuous Metrics
Taking the triangle areas as independent variables in the theory of Regge
calculus can lead to ambiguities in the edge lengths, which can be interpreted
as discontinuities in the metric. We construct solutions to area Regge calculus
using a triangulated lattice and find that on a spacelike hypersurface no such
discontinuity can arise. On a null hypersurface however, we can have such a
situation and the resulting metric can be interpreted as a so-called refractive
wave.Comment: 18 pages, 1 figur
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