1,308 research outputs found
Inward and Outward Integral Equations and the KKR Method for Photons
In the case of electromagnetic waves it is necessary to distinguish between
inward and outward on-shell integral equations. Both kinds of equation are
derived. A correct implementation of the photonic KKR method then requires the
inward equations and it follows directly from them. A derivation of the KKR
method from a variational principle is also outlined. Rather surprisingly, the
variational KKR method cannot be entirely written in terms of surface integrals
unless permeabilities are piecewise constant. Both kinds of photonic KKR method
use the standard structure constants of the electronic KKR method and hence
allow for a direct numerical application. As a by-product, matching rules are
obtained for derivatives of fields on different sides of the discontinuity of
permeabilities.
Key words: The Maxwell equations, photonic band gap calculationsComment: (to appear in J. Phys. : Cond. Matter), Latex 17 pp, PRA-HEP 93/10
(exclusively English and unimportant misprints corrected
The Malkus–Robbins dynamo with a linear series motor
Hide [1997] has introduced a number of different nonlinear models to describe the behavior of n-coupled self-exciting Faraday disk homopolar dynamos. The hierarchy of dynamos based upon the Hide et al. [1996] study has already received much attention in the literature (see [Moroz, 2001] for a review). In this paper we focus upon the remaining dynamo, namely Case 3 of [Hide, 1997] for the particular limit in which the Malkus–Robbins dynamo [Malkus, 1972; Robbins, 1997] obtains, but now modified by the presence of a linear series motor. We compare and contrast the linear and the nonlinear behaviors of the two types of dynamo
When are projections also embeddings?
We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents that satisfy , so the Lyapunov dimension is in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from to . In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other
A Comparison of Tests for Embeddings
It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions
Sequential inverse problems Bayesian principles and the\ud logistic map example
Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection
Voice morphing using the generative topographic mapping
In this paper we address the problem of Voice Morphing. We attempt to transform the spectral characteristics of a source speaker's speech signal so that the listener would believe that the speech was uttered by a target speaker. The voice morphing system transforms the spectral envelope as represented by a Linear Prediction model. The transformation is achieved by codebook mapping using the Generative Topographic Mapping, a non-linear, latent variable, parametrically constrained, Gaussian Mixture Model
Wavelet-based voice morphing
This paper presents a new multi-scale voice morphing algorithm. This algorithm enables a user to transform one person's speech pattern into another person's pattern with distinct characteristics, giving it a new identity, while preserving the original content. The voice morphing algorithm performs the morphing at different subbands by using the theory of wavelets and models the spectral conversion using the theory of Radial Basis Function Neural Networks. The results obtained on the TIMIT speech database demonstrate effective transformation of the speaker identity
Data assimilation using bayesian filters and B-spline geological models
This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir
Resonance-Induced Effects in Photonic Crystals
For the case of a simple face-centered-cubic photonic crystal of homogeneous
dielectric spheres, we examine to what extent single-sphere Mie resonance
frequencies are related to band gaps and whether the width of a gap can be
enlarged due to nearby resonances. Contrary to some suggestions, no spectacular
effects may be expected. When the dielectric constant of the spheres
is greater than the dielectric constant of the
background medium, then for any filling fraction there exists a critical
above which the lowest lying Mie resonance frequency falls inside
the lowest stop gap in the (111) crystal direction, close to its midgap
frequency. If , the correspondence between Mie
resonances and both the (111) stop gap and a full gap does not follow such a
regular pattern. If the Mie resonance frequency is close to a gap edge, one can
observe a resonance-induced widening of a relative gap width by .Comment: 14 pages, 3 figs., RevTex. For more info look at
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
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