6,004 research outputs found
Finite element eigenvalue enclosures for the Maxwell operator
We propose employing the extension of the Lehmann-Maehly-Goerisch method
developed by Zimmermann and Mertins, as a highly effective tool for the
pollution-free finite element computation of the eigenfrequencies of the
resonant cavity problem on a bounded region. This method gives complementary
bounds for the eigenfrequencies which are adjacent to a given real parameter.
We present a concrete numerical scheme which provides certified enclosures in a
suitable asymptotic regime. We illustrate the applicability of this scheme by
means of some numerical experiments on benchmark data using Lagrange elements
and unstructured meshes.Comment: arXiv admin note: substantial text overlap with arXiv:1306.535
Negative modes and the thermodynamics of Reissner-Nordstr\"om black holes
We analyse the problem of negative modes of the Euclidean section of the
Reissner-Nordstr\"om black hole in four dimensions. We find analytically that a
negative mode disappears when the specific heat at constant charge becomes
positive. The sector of perturbations analysed here is included in the
canonical partition function of the magnetically charged black hole. The result
obeys the usual rule that the partition function is only well-defined when
there is local thermodynamical equilibrium. We point out the difficulty in
quantising Einstein-Maxwell theory, where the so-called conformal factor
problem is considerably more intricate. Our method, inspired by hep-th/0608001,
allows us to decouple the divergent gauge volume and treat the metric
perturbations sector in a gauge-invariant way.Comment: 24 pages, 1 figure; v2 minor changes to fit published versio
Small Collaboration: Numerical Analysis of Electromagnetic Problems (hybrid meeting)
The classical theory of electromagnetism describes the interaction of electrically charged particles through electromagnetic forces, which are carried by the electric and magnetic fields. The propagation of the electromagnetic fields can be described by Maxwell's equations. Solving Maxwell's equations numerically is a challenging problem which appears in many different technical applications. Difficulties arise for instance from material interfaces or if the geometrical features are much larger than or much smaller than a typical wavelength. The spatial discretization needs to combine good geometrical flexibility with a relatively high order of accuracy.
The aim of this small-scale, week-long interactive mini-workshop jointly organized by the University of Duisburg-Essen and the University of Twente, and kindly hosted at the MFO, is to bring together experts in non-standard and mixed finite elements methods with experts in the field of electromagnetism
Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques
We describe a numerical method to compute Casimir forces in arbitrary
geometries, for arbitrary dielectric and metallic materials, with arbitrary
accuracy (given sufficient computational resources). Our approach, based on
well-established integration of the mean stress tensor evaluated via the
fluctuation-dissipation theorem, is designed to directly exploit fast methods
developed for classical computational electromagnetism, since it only involves
repeated evaluation of the Green's function for imaginary frequencies
(equivalently, real frequencies in imaginary time). We develop the approach by
systematically examining various formulations of Casimir forces from the
previous decades and evaluating them according to their suitability for
numerical computation. We illustrate our approach with a simple
finite-difference frequency-domain implementation, test it for known geometries
such as a cylinder and a plate, and apply it to new geometries. In particular,
we show that a piston-like geometry of two squares sliding between metal walls,
in both two and three dimensions with both perfect and realistic metallic
materials, exhibits a surprising non-monotonic ``lateral'' force from the
walls.Comment: Published in Physical Review A, vol. 76, page 032106 (2007
Modes of Random Lasers
In conventional lasers, the optical cavity that confines the photons also
determines essential characteristics of the lasing modes such as wavelength,
emission pattern, ... In random lasers, which do not have mirrors or a
well-defined cavity, light is confined within the gain medium by means of
multiple scattering. The sharp peaks in the emission spectra of semiconductor
powders, first observed in 1999, has therefore lead to an intense debate about
the nature of the lasing modes in these so-called lasers with resonant
feedback. In this paper, we review numerical and theoretical studies aimed at
clarifying the nature of the lasing modes in disordered scattering systems with
gain. We will discuss in particular the link between random laser modes near
threshold (TLM) and the resonances or quasi-bound (QB) states of the passive
system without gain. For random lasers in the localized regime, QB states and
threshold lasing modes were found to be nearly identical within the scattering
medium. These studies were later extended to the case of more lossy systems
such as random systems in the diffusive regime where differences between
quasi-bound states and lasing modes were measured. Very recently, a theory able
to treat lasers with arbitrarily complex and open cavities such as random
lasers established that the TLM are better described in terms of the so-called
constant-flux states.Comment: Review paper submitted to Advances in Optics and Photonic
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