11,774 research outputs found
Period and toroidal knot mosaics
Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on
`Quantum knots and mosaics' to give a precise and workable definition of
quantum knots, intended to represent an actual physical quantum system. A knot
(m,n)-mosaic is an matrix whose entries are eleven mosaic
tiles, representing a knot or a link by adjoining properly. In this paper we
introduce two variants of knot mosaics: period knot mosaics and toroidal knot
mosaics, which are common features in physics and mathematics. We present an
algorithm producing the exact enumeration of period knot (m,n)-mosaics for any
positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m
and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We
also analyze the asymptotics of the growth rates of their cardinality
Pulsed Laser Deposition of Rocksalt Magnetic Binary Oxides
Here we systematically explore the use of pulsed laser deposition technique
(PLD) to grow three basic oxides that have rocksalt structure but different
chemical stability in the ambient atmosphere: NiO (stable), MnO (metastable)
and EuO (unstable). By tuning laser fluence, an epitaxial single-phase nickel
oxide thin-film growth can be achieved in a wide range of temperatures from 10
to 750 {\deg}C. At the lowest growth temperature, the out-of-plane strain
raises to 1.5%, which is five times bigger than that in a NiO film grown at 750
{\deg}C. MnO thin films that had long-range ordered were successfully deposited
on the MgO substrates after appropriate tuning of deposition parameters. The
growth of MnO phase was strongly influenced by substrate temperature and laser
fluence. EuO films with satisfactory quality were deposited by PLD after oxygen
availability had been minimized. Synthesis of EuO thin films at rather low
growth temperature prevented thermally-driven lattice relaxation and allowed
growth of strained films. Overall, PLD was a quick and reliable method to grow
binary oxides with rocksalt structure in high quality that can satisfy
requirements for applications and for basic research
Performance of SSE and AVX Instruction Sets
SSE (streaming SIMD extensions) and AVX (advanced vector extensions) are SIMD
(single instruction multiple data streams) instruction sets supported by recent
CPUs manufactured in Intel and AMD. This SIMD programming allows parallel
processing by multiple cores in a single CPU. Basic arithmetic and data
transfer operations such as sum, multiplication and square root can be
processed simultaneously. Although popular compilers such as GNU compilers and
Intel compilers provide automatic SIMD optimization options, one can obtain
better performance by a manual SIMD programming with proper optimization: data
packing, data reuse and asynchronous data transfer. In particular, linear
algebraic operations of vectors and matrices can be easily optimized by the
SIMD programming. Typical calculations in lattice gauge theory are composed of
linear algebraic operations of gauge link matrices and fermion vectors, and so
can adopt the manual SIMD programming to improve the performance.Comment: 7 pages, 5 figures, 4 tables, Contribution to proceedings of the 30th
International Symposium on Lattice Field Theory (Lattice 2012), June 24-29,
201
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