Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

Beyond the sphere of the English facial approximation literature: Ramifications of German papers on western method concepts

In the English literature, facial approximation methods have been commonly classified into three types: Russian, American, or Combination. These categorizations are based on the protocols used, for example, whether methods use average soft-tissue depths (American methods) or require face muscle construction (Russian methods). However, literature searches outside the usual realm of English publications reveal key papers that demonstrate that the Russian category above has been founded on distorted views. In reality, Russian methods are based on limited face muscle construction, with heavy reliance on modified average soft-tissue depths. A closer inspection of the American method also reveals inconsistencies with the recognized classification scheme. This investigation thus demonstrates that all major methods of facial approximation depend on both face anatomy and average soft-tissue depths, rendering common method classification schemes redundant. The best way forward appears to be for practitioners to describe the methods they use (including the weight each one gives to average soft-tissue depths and deep face tissue construction) without placing them in any categorical classificatory group or giving them an ambiguous name. The state of this situation may need to be reviewed in the future in light of new research results and paradigms.

Assessing facial approximation accuracy: How do resemblance ratings of disparate faces compare to recognition tests?

In the past, the accuracy of facial approximations has been assessed by resemblance ratings (i.e., the comparison of a facial approximation directly to a target individual) and recognition tests (e.g., the comparison of a facial approximation to a photo array of faces including foils and a target individual). Recently, several research studies have indicated that recognition tests hold major strengths in contrast to resemblance ratings. However, resemblance ratings remain popularly employed and/or are given weighting when judging facial approximations, thus indicating that no consensus has been reached. This study aims to further investigate the matter by comparing the results of resemblance ratings and recognition tests for two facial approximations which clearly differed in their morphological appearance. One facial approximation was constructed by an experienced practitioner privy to the appearance of the target individual (practitioner had direct access to an antemortem frontal photograph during face construction), while the other facial approximation was constructed by a novice under blind conditions. Both facial approximations, whilst clearly morphologically different, were given similar resemblance scores even though recognition test results produced vastly different results. One facial approximation was correctly recognized almost without exception while the other was not correctly recognized above chance rates. These results suggest that resemblance ratings are insensitive measures of the accuracy of facial approximations and lend further weight to the use of recognition tests in facial approximation assessment. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

On the multicomponent polynomial solution models

The present study addresses the problem of predicting the properties of multicomponent systems from those of corresponding binary systems. Two types of multicomponent polynomial models have been analysed. A probabilistic interpretation of the parameters of the Polynomial model, which explicitly relates them with the Gibbs free energies of the generalised quasichemical reactions, is proposed. The presented treatment provides a theoretical justification for such parameters. A methodology of estimating the ternary interaction parameter from the binary ones is presented. The methodology provides a way in which the power series multicomponent models, where no projection is required, could be incorporated into the Calphad approach.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimensioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation which improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Derivations of variational gaussian process approximation framework

Recently, within the VISDEM project (EPSRC funded EP/C005848/1), a novel variational approximation framework has been developed for inference in partially observed, continuous space-time, diffusion processes. In this technical report all the derivations of the variational framework, from the initial work, are provided in detail to help the reader better understand the framework and its assumptions.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

A new variational radial basis function approximation for inference in multivariate diffusions

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.