4,439 research outputs found
Projective Ponzano-Regge spin networks and their symmetries
We present a novel hierarchical construction of projective spin networks of
the Ponzano-Regge type from an assembling of five quadrangles up to the
combinatorial 4-simplex compatible with a geometrical realization in Euclidean
4-space. The key ingrendients are the projective Desargues configuration and
the incidence structure given by its space-dual, on the one hand, and the
Biedenharn--Elliott identity for the 6j symbol of SU(2), on the other. The
interplay between projective-combinatorial and algebraic features relies on the
recoupling theory of angular momenta, an approach to discrete quantum gravity
models carried out successfully over the last few decades. The role of Regge
symmetry --an intriguing discrete symmetry of the which goes beyond the
standard tetrahedral symmetry of this symbol-- will be also discussed in brief
to highlight its role in providing a natural regularization of projective spin
networks that somehow mimics the standard regularization through a
q-deformation of SU(2).Comment: 14 pages, 19 figure
Singer quadrangles
[no abstract available
Point regular groups of automorphisms of generalised quadrangles
We study the point regular groups of automorphisms of some of the known
generalised quadrangles. In particular we determine all point regular groups of
automorphisms of the thick classical generalised quadrangles. We also construct
point regular groups of automorphisms of the generalised quadrangle of order
obtained by Payne derivation from the classical symplectic
quadrangle . For with we obtain at least two
nonisomorphic groups when and at least three nonisomorphic groups
when or . Our groups include nonabelian 2-groups, groups of exponent 9
and nonspecial -groups. We also enumerate all point regular groups of
automorphisms of some small generalised quadrangles.Comment: some minor changes (including to title) after referee's comment
Dense near octagons with four points on each line, III
This is the third paper dealing with the classification of the dense near octagons of order (3, t). Using the partial classification of the valuations of the possible hexes obtained in [12], we are able to show that almost all such near octagons admit a big hex. Combining this with the results in [11], where we classified the dense near octagons of order (3, t) with a big hex, we get an incomplete classification for the dense near octagons of order (3, t): There are 28 known examples and a few open cases. For each open case, we have a rather detailed description of the structure of the near octagons involved
On the conformational structure of a stiff homopolymer
In this paper we complete the study of the phase diagram and conformational
states of a stiff homopolymer. It is known that folding of a sufficiently stiff
chain results in formation of a torus. We find that the phase diagram obtained
from the Gaussian variational treatment actually contains not one, but several
distinct toroidal states distinguished by the winding number. Such states are
separated by first order transition curves terminating in critical points at
low values of the stiffness. These findings are further supported by
off-lattice Monte Carlo simulation. Moreover, the simulation shows that the
kinetics of folding of a stiff chain passes through various metastable states
corresponding to hairpin conformations with abrupt U-turns.Comment: 9 pages, 16 PS figures. Journal of Chemical Physics, in pres
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