4,874 research outputs found
Affine semigroups having a unique Betti element
We characterize affine semigroups having one Betti element and we compute
some relevant non-unique factorization invariants for these semigroups. As an
example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its
Application
Helico-conical optical beams self-heal
An optical beam is said to be self-healing when, distorted by an obstacle,
the beam corrects itself upon propagation. In this letter, we show through
experiments supported by numerical simulations, that Helico-conical optical
beams (HCOBs) self-heal. We observe the strong resilience of these beams with
different types of obstructions, and relate this to the characteristics of
their transverse energy flow.Comment: 4 pages, 5 figure
Three-sublattice Skyrmion crystal in the antiferromagnetic triangular lattice
The frustrated classical antiferromagnetic Heisenberg model with
Dzyaloshinskii-Moriya (DM) interactions on the triangular lattice is studied
under a magnetic field by means of semiclassical calculations and large-scale
Monte Carlo simulations. We show that even a small DM interaction induces the
formation of an Antiferromagnetic Skyrmion crystal (AF-SkX) state. Unlike what
is observed in ferromagnetic materials, we show that the AF-SkX state consists
of three interpenetrating Skyrmion crystals (one by sublattice), and most
importantly, the AF-SkX state seems to survive in the limit of zero
temperature. To characterize the phase diagram we compute the average of the
topological order parameter which can be associated to the number of
topological charges or Skyrmions. As the magnetic field increases this
parameter presents a clear jump, indicating a discontinuous transition from a
spiral phase into the AF-SkX phase, where multiple Bragg peaks coexist in the
spin structure factor. For higher fields, a second (probably continuous)
transition occurs into a featureless paramagnetic phase.Comment: 8 pages, 8 figure
Supergroup BF action for supergravity
General relativity can be formulated as a SU(2) BF-theory with constraints,
as has been shown, by Pleba\'nski. The cosmological constant term can be
obtained from the constraint term, following from the consistency of the
equations of motion, as recently shown by Krasnov. We consider an
invariant, supergravity extension of this theory, for which the consistency of
the equations of motion and the constraints contribute as well to the
cosmological constant terms of Townsend's supergravity. The Kalb-Ramond
invariance is shortly discussed.Comment: 14 page
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