A new Rayleigh quotient, which was introduced and briefly considered in a previous paper, is now examined in greater detail. When used in conjunction with polarised finite difference schemes established in earlier pap...
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A new Rayleigh quotient, which was introduced and briefly considered in a previous paper, is now examined in greater detail. When used in conjunction with polarised finite difference schemes established in earlier papers, it enables semivectorial E-field and H-field propagation modes of waveguide structures, which may contain any arbitrary distribution of horizontal and vertical dielectric discontinuities, to be determined without the need to solve matrix eigenvalue problems. The absence of a matrix enables the finite difference grid to incorporate substantially more points and smaller step lengths, thereby improving the accuracy of computed solutions. Results are presented for single rib waveguides and for rib waveguide directional couplers fabricated from III-V semiconductors.
Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, ...
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Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, while lacking conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks by determining multiple metrics that characterize the distribution, including their average areas and corresponding variances as well as higher-order cumulants (i.e., skewness γ1 and excess kurtosis γ2). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (γ1=3.16) and large positive excess kurtosis (γ2=16.2). The Poisson (with γ1=1.07 and γ2=1.79) and non-stealthy hyperuniform (with γ1=0.257 and γ2=0.0217) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with γ1=0.450 and γ2=−0.0384) and the highest stealthy hyperuniform distributions (with γ1=0.0272 and γ2=−0.0626) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite of the non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with N≈10,000 nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit th
The feasibility of matching templates representing map features to features in Synthetic Aperture Radar images is investigated. The performance of template matching using cross-correlation (which has no knowledge of s...
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The feasibility of matching templates representing map features to features in Synthetic Aperture Radar images is investigated. The performance of template matching using cross-correlation (which has no knowledge of speckle) is compared with a correlation measure, based on a Kolmogorov-Smirnov test of fit, which does take speckle into consideration. This is shown to perform better than cross-correlation in simulated images. However, neither method performs well on real data. This is due to the exponential speckle model being inappropriate for linear features in real data. Alternative methods for matching map features to SAR images are suggested.
This paper studies the constraint conditions for coherence destruction in tunneling by using perturbation theory and numerical simulation for an AC-field with bias and Coulomb interaction between electrons in a quantu...
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This paper studies the constraint conditions for coherence destruction in tunneling by using perturbation theory and numerical simulation for an AC-field with bias and Coulomb interaction between electrons in a quantum dot molecule. Such conditions can be described by using the roots of a Bessel function Jn（x）, where n is determined by both the bias and the Coulomb interactions, and x is the ratio of the amplitude to the frequency of the AC-field. Under such conditions, a coherent suppression of tunneling occurs between localized electronic states, which results from the dynamical localization phenomenon. All the conditions are verified with numerical simulations.
A simple accurate method, which automatically takes full account of the discontinuities in the normal electric field components across any arbitrary distribution of internal dielectric interfaces, is presented for the...
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A simple accurate method, which automatically takes full account of the discontinuities in the normal electric field components across any arbitrary distribution of internal dielectric interfaces, is presented for the determination of polarised solutions of the Helmholtz wave equation. The application of the shifted inverse power iteration method to the resulting matrices, enables any required propagation eigenvalue (not necessarily the fundamanetal mode) to be determined, together with its corresponding electric field profile. It is found that the results, which are presented for various semiconductor rib waveguide structures, compare favourably with published vector finite element and scalar results.
A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is...
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A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case. Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this observation. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves.
The implications of interpolation and resampling for the statistics of Synthetic Aperture Radar (SAR) images are analyzed. Interpolation of the complex data conserves the statistical distribution and all moments if a ...
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The paper presents a powerful method for estimating extreme probabilities of a target variable Z = h(X) which is a monotone function of a set of basic variables X = (X-1,...,X-n). To this aim, a sample of (X-1,...,X-n...
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The paper presents a powerful method for estimating extreme probabilities of a target variable Z = h(X) which is a monotone function of a set of basic variables X = (X-1,...,X-n). To this aim, a sample of (X-1,...,X-n) is simulated in such a way that the corresponding values of Z are in the corresponding tail, and used to fit a Pareto distribution to the associated exceedances. For cases where this method is difficult to apply, an alternative method is proposed, which leads to a low rejection proportion of sample values, when compared with the Monte Carlo method Both methods are shown to be very useful for sensitivity analysis in Bayesian networks or uncertainty in risk analysis, when very large confidence intervals for the marginal/conditional probabilities are required The methods are illustrated with several examples, and one example of application to a real case is used to illustrate the whole process. (C) 1997 Elsevier Science Inc.
We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effec...
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We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.
Measurements of the ocean wave directional spectrum using a dual, high-frequency (HF) radar system are presented. A modelfitting technique is used to obtain wave measurements from the radar Doppler spectra. Over 100 h...
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Measurements of the ocean wave directional spectrum using a dual, high-frequency (HF) radar system are presented. A modelfitting technique is used to obtain wave measurements from the radar Doppler spectra. Over 100 h of data, collected during NURWEC2 (Netherlands-UK Radar Wavebuoy Experimental Comparison), have been compared with measurements using a WAVEC directional wave buoy. The amplitude and directional characteristics of long wave components at frequencies of 0.07-0.1 Hz in general show good agreement. Reasonable estimates of the directional spectrum across the whole frequency range are obtained when the assumptions of the model-fitting technique are appropriate. Remaining problems in radar measurement and difficulties in assessing accuracy are discussed.
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