6,799 research outputs found
Huygens' principle and Dirac-Weyl equation
We investigate the validity of Huygens' principle for forward propagation in
the massless Dirac-Weyl equation. The principle holds for odd space dimension
n, while it is invalid for even n. We explicitly solve the cases n=1,2 and 3
and discuss generic . We compare with the massless Klein-Gordon equation and
comment on possible generalizations and applications.Comment: 7 pages, 1 figur
The cost of continuity: performance of iterative solvers on isogeometric finite elements
In this paper we study how the use of a more continuous set of basis
functions affects the cost of solving systems of linear equations resulting
from a discretized Galerkin weak form. Specifically, we compare performance of
linear solvers when discretizing using B-splines, which span traditional
finite element spaces, and B-splines, which represent maximum
continuity. We provide theoretical estimates for the increase in cost of the
matrix-vector product as well as for the construction and application of
black-box preconditioners. We accompany these estimates with numerical results
and study their sensitivity to various grid parameters such as element size
and polynomial order of approximation . Finally, we present timing results
for a range of preconditioning options for the Laplace problem. We conclude
that the matrix-vector product operation is at most \slfrac{33p^2}{8} times
more expensive for the more continuous space, although for moderately low ,
this number is significantly reduced. Moreover, if static condensation is not
employed, this number further reduces to at most a value of 8, even for high
. Preconditioning options can be up to times more expensive to setup,
although this difference significantly decreases for some popular
preconditioners such as Incomplete LU factorization
Electronic structure of VO: charge ordering, metal-insulator transition and magnetism
The low and high-temperature phases of VO have been studied by
\textit{ab initio} calculations. At high temperature, all V atoms are
electronically equivalent and the material is metallic. Charge and orbital
ordering, associated with the distortions in the V pseudo-rutile chains, occur
below the metal-insulator transition. Orbital ordering in the low-temperature
phase, different in V and V chains, allows to explain the
distortion pattern in the insulating phase of VO. The in-chain magnetic
couplings in the low-temperature phase turn out to be antiferromagnetic, but
very different in the various V and V bonds. The V dimers
formed below the transition temperature form spin singlets, but V ions,
despite dimerization, apparently participate in magnetic ordering.Comment: 10 pages, 6 figures, 2 table
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