131,418 research outputs found
Hypercubes, Leonard triples and the anticommutator spin algebra
This paper is about three classes of objects: Leonard triples,
distance-regular graphs and the modules for the anticommutator spin algebra.
Let \K denote an algebraically closed field of characteristic zero. Let
denote a vector space over \K with finite positive dimension. A Leonard
triple on is an ordered triple of linear transformations in
such that for each of these transformations there exists a
basis for with respect to which the matrix representing that transformation
is diagonal and the matrices representing the other two transformations are
irreducible tridiagonal. The Leonard triples of interest to us are said to be
totally B/AB and of Bannai/Ito type.
Totally B/AB Leonard triples of Bannai/Ito type arise in conjunction with the
anticommutator spin algebra , the unital associative \K-algebra
defined by generators and relations
Let denote an integer, let denote the hypercube of diameter
and let denote the antipodal quotient. Let (resp.
) denote the Terwilliger algebra for (resp.
).
We obtain the following. When is even (resp. odd), we show that there
exists a unique -module structure on (resp.
) such that act as the adjacency and dual adjacency
matrices respectively. We classify the resulting irreducible
-modules up to isomorphism. We introduce weighted adjacency
matrices for , . When is even (resp. odd) we show
that actions of the adjacency, dual adjacency and weighted adjacency matrices
for (resp. ) on any irreducible -module (resp.
-module) form a totally bipartite (resp. almost bipartite) Leonard
triple of Bannai/Ito type and classify the Leonard triple up to isomorphism.Comment: arXiv admin note: text overlap with arXiv:0705.0518 by other author
Solving the electrical control of magnetic coercive field paradox
The ability to tune magnetic properties of solids via electric voltages instead of external magnetic fields is a physics curiosity of great scientific and technological importance. Today, there is strong published experimental evidence of electrical control of magnetic coercive fields in composite multiferroic solids. Unfortunately, the literature indicates highly contradictory results. In some studies, an applied voltage increases the magnetic coercive field and in other studies the applied voltage decreases the coercive field of composite multiferroics. Here, we provide an elegant explanation to this paradox and we demonstrate why all reported results are in fact correct. It is shown that for a given polarity of the applied voltage, the magnetic coercive field depends on the sign of two tensor components of the multiferroic solid: magnetostrictive and piezoelectric coefficient. For a negative applied voltage, the magnetic coercive field decreases when the two material parameters have the same sign and increases when they have opposite signs, respectively. The effect of the material parameters is reversed when the same multiferroic solid is subjected to a positive applied voltage
An analytical and experimental assessment of flexible road ironwork support structures
This paper describes work undertaken to investigate the mechanical performance of road ironwork installations in highways, concentrating on the chamber construction. The principal aim was to provide the background research which would allow improved designs to be developed to reduce the incidence of failures through improvements to the structural continuity between the installation and the surrounding pavement. In doing this, recycled polymeric construction materials (Jig Brix) were studied with a view to including them in future designs and specifications. This paper concentrates on the Finite Element (FE) analysis of traditional (masonry) and flexible road ironwork structures incorporating Jig Brix. The global and local buckling capacity of the Jig Brix elements was investigated and results compared well with laboratory measurements. FE models have also been developed for full-scale traditional (masonry) and flexible installations in a surrounding flexible (asphalt) pavement structure. Predictions of response to wheel loading were compared with full-scale laboratory measurements. Good agreement was achieved with the traditional (masonry) construction but poorer agreement for the flexible construction. Predictions from the FE model indicated that the use of flexible elements significantly reduces the tensile horizontal strain on the surface of the surrounding asphaltic material which is likely to reduce the incidence of surface cracking
Comparison of Models of Critical Opacity in the Quark-Gluon Plasma
In this work we discuss two methods of calculation of quark propagation in
the quark-gluon plasma. Both methods make use of the Nambu-Jona-Lasinio model.
The essential difference of these calculations is the treatment of
deconfinement. A model of confinement is not included in the work of Gastineau,
Blanquier and Aichelin [hep-ph/0404207], however, the meson states they
consider are still bound for temperatures greater than the deconfinement
temperature T_c. On the other hand, our model deals with unconfined quarks and
includes a description of the q(bar)q resonances found in lattice QCD studies
that make use of the maximum entropy method (MEM). We compare the q{bar)q cross
sections calculated in these models.Comment: 7 pages and 4 figures RevTe
Impact of global structure on diffusive exploration of organelle networks
We investigate diffusive search on planar networks, motivated by tubular
organelle networks in cell biology that contain molecules searching for
reaction partners and binding sites. Exact calculation of the diffusive mean
first-passage time on a spatial network is used to characterize the typical
search time as a function of network connectivity. We find that global
structural properties --- the total edge length and number of loops --- are
sufficient to largely determine network exploration times for a variety of both
synthetic planar networks and organelle morphologies extracted from living
cells. For synthetic networks on a lattice, we predict the search time
dependence on these global structural parameters by connecting with percolation
theory, providing a bridge from irregular real-world networks to a simpler
physical model. The dependence of search time on global network structural
properties suggests that network architecture can be designed for efficient
search without controlling the precise arrangement of connections.
Specifically, increasing the number of loops substantially decreases search
times, pointing to a potential physical mechanism for regulating reaction rates
within organelle network structures.Comment: 13 pages, 4 figures. Accepted for publication in Scientific Report
On arithmetic and asymptotic properties of up-down numbers
Let , where , and let
denote the number of permutations of whose
up-down signature , for .
We prove that the set of all up-down numbers can be expressed by
a single universal polynomial , whose coefficients are products of
numbers from the Taylor series of the hyperbolic tangent function. We prove
that is a modified exponential, and deduce some remarkable congruence
properties for the set of all numbers , for fixed . We prove a
concise upper-bound for , which describes the asymptotic behaviour
of the up-down function in the limit .Comment: Recommended for publication in Discrete Mathematics subject to
revision
Cooling of the crust in the neutron star low-mass X-ray binary MXB 1659-29
In quasi-persistent neutron star transients, long outbursts cause the neutron
star crust to be heated out of thermal equilibrium with the rest of the star.
During quiescence, the crust then cools back down. Such crustal cooling has
been observed in two quasi-persistent sources: KS 1731-260 and MXB 1659-29.
Here we present an additional Chandra observation of MXB 1659-29 in quiescence,
which extends the baseline of monitoring to 6.6 yr after the end of the
outburst. This new observation strongly suggests that the crust has thermally
relaxed, with the temperature remaining consistent over 1000 days. Fitting the
temperature cooling curve with an exponential plus constant model we determine
an e-folding timescale of 465 +/- 25 days, with the crust cooling to a constant
surface temperature of kT = 54 +/- 2 eV (assuming D=10 kpc). From this, we
infer a core temperature in the range 3.5E7-8.3E7 K (assuming D=10 kpc), with
the uncertainty due to the surface composition. Importantly, we tested two
neutron star atmosphere models as well as a blackbody model, and found that the
thermal relaxation time of the crust is independent of the chosen model and the
assumed distance.Comment: accepted for publication in ApJL, 4 pages, 1 figure
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