866 research outputs found
Structure-preserving mesh coupling based on the Buffa-Christiansen complex
The state of the art for mesh coupling at nonconforming interfaces is
presented and reviewed. Mesh coupling is frequently applied to the modeling and
simulation of motion in electromagnetic actuators and machines. The paper
exploits Whitney elements to present the main ideas. Both interpolation- and
projection-based methods are considered. In addition to accuracy and
efficiency, we emphasize the question whether the schemes preserve the
structure of the de Rham complex, which underlies Maxwell's equations. As a new
contribution, a structure-preserving projection method is presented, in which
Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its
performance is compared with a straightforward interpolation based on Whitney
and de Rham maps, and with Galerkin projection.Comment: 17 pages, 7 figures. Some figures are omitted due to a restricted
copyright. Full paper to appear in Mathematics of Computatio
Renormalization of a Lorentz invariant doubled worldsheet theory
Manifestly T-duality covariant worldsheet string models can be constructed by
doubling the coordinate fields. We describe the underlying gauge symmetry of a
recently proposed Lorentz invariant doubled worldsheet theory that makes half
of the worldsheet degrees of freedom redundant. By shifting the Lagrange
multiplier, that enforces the gauge fixing condition, the worldsheet action can
be cast into various guises. We investigate the renormalization of this theory
using a non-linear background / quantum split by employing a normal coordinate
expansion adapted to the gauge-fixed theory. The propagator of the doubled
coordinates contains a projection operator encoding that half of them do not
propagate. We determine the doubled target space equations of motion by
requiring one-loop Weyl invariance. Some of them are generalizations of the
conventional sigma model beta-functions, while others seem to be novel to the
doubled theory: In particular, a dilaton equation seems related to the strong
constraint of double field theory. However, the other target space field
equations are not identical to those of double field theory.Comment: 32 pages; v2: motivation and discussion expanded, references adde
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