Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Homogeneous and heterogeneous distributed classification for pocket data mining

Pocket Data Mining (PDM) describes the full process of analysing data streams in mobile ad hoc distributed environments. Advances in mobile devices like smart phones and tablet computers have made it possible for a wide range of applications to run in such an environment. In this paper, we propose the adoption of data stream classification techniques for PDM. Evident by a thorough experimental study, it has been proved that running heterogeneous/different, or homogeneous/similar data stream classification techniques over vertically partitioned data (data partitioned according to the feature space) results in comparable performance to batch and centralised learning techniques.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

The Phantom Carriage (1921)

The reputation of The Phantom Carriage (Körkarlen) as one of the major films of Swedish silent cinema is in some respects securely established. Yet the film has attracted surprisingly little detailed discussion. It may be that its most striking stylistic features have deflected or discouraged closer scrutiny. Tom Gunning, for instance, in making the case for Sjöström’s Masterman, argues that ‘Körkarlen wears its technique on its sleeve, overtly displays its unquestionable mastery of superimposition and complex narrative structure. Mästerman tucks its mastery of editing and composition up its sleeve, so to speak’. This article makes an argument for a different evaluation of The Phantom Carriage, bringing a critical and interpretative understanding of the film’s style into conversation with the historical accounts of film form which predominate in the scholarship around silent cinema. It suggests that the film achieves ‘mastery of editing and composition’ with a flexibility and fluidity in the construction of dramatic space that is in itself remarkable for its period, but that Sjöström’s achievements extend well beyond his handling of film space. Specifically, it discusses a segment which is in several respects at the heart of the film: the first meeting between the two central characters, David Holm (Victor Sjöström) and Sister Edit (Astrid Holm); it spans the film’s exact mid-point; and at almost twelve and a half minutes it is the longest uninterrupted passage to take place in a single setting. The chapter argues that the dramatic and structural centrality of the hostel segment is paralleled by its remarkably rich articulation of the relationships between action, character and space. We show how Sjöström’s creation of a three-dimensional filmic space - with no hint of frontality - becomes the basis for a reciprocal relationship between spatial naturalism and performance style, and for a mise-en-scene that can take on discrete interpretive force. The argument also places the hostel sequences within the film as a whole in order to show how relationships articulated through the detailed decisions in this section take on their full resonance within patterns and motifs that develop across the film.

The Phantom Carriage: a revaluation

This is a two-part audiovisual essay on Victor Sjöström’s extraordinary film The Phantom Carriage (Körkarlen), which was released on New Year’s Day 1921. Part 1 explores a sequence in detail, revealing a mastery of three-dimensional film space which is remarkable for its period; the essay then look at the ways in which this handling of space is integral to the film’s rich articulation of character and action. Part 2 considers aspects of the film’s mise-en-scène and shows how the features of the sequence explored in Part 1 take on their full resonance within patterns and motifs that develop across the film. Published by Movie: a journal of film criticism, the essay complements our chapter on the film in the volume Silent Features, edited by Steve Neale (Exeter University Press, 2016).

Evolution of primordial black holes in a radiation and phantom energy environment

In this work we extend previous work on the evolution of a primordial black hole (PBH) to address the presence of a dark energy component with a super-negative equation of state as a background, investigating the competition between the radiation accretion, the Hawking evaporation and the phantom accretion, the latter two causing a decrease on black hole mass. It is found that there is an instant during the matter-dominated era after which the radiation accretion becomes negligible compared to the phantom accretion. The Hawking evaporation may become important again depending on a mass threshold. The evaporation of PBHs is quite modified at late times by these effects, but only if the generalized second law of thermodynamics is violated.

On phantom thermodynamics

The thermodynamic properties of dark energy fluids described by an equation of state parameter omega = p/rho are rediscussed in the context of FRW type geometries. Contrarily to previous claims, it is argued here that the phantom regime omega < -1 is not physically possible since that both the temperature and the entropy of every physical fluids must be always positive definite. This means that one cannot appeal to negative temperature in order to save the phantom dark energy hypothesis as has been recently done in the literature. Such a result remains true as long as the chemical potential is zero. However, if the phantom fluid is endowed with a non-null chemical potential, the phantom field hypothesis becomes thermodynamically consistent, that is, there are macroscopic equilibrium states with T > 0 and S > 0 in the course of the Universe expansion. (C) 2008 Elsevier B.V. All rights reserved.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.

Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

Phantom accretion by black holes and the generalized second law of thermodynamics

The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the generalized second law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by the generalized second law. (C) 2010 Elsevier B.V. All rights reserved.

Non-homogeneous liver distribution of photosensitizer and its consequence for photodynamic therapy outcome

Background: Photodynamic therapy is mainly used for treatment of malignant lesions, and is based on selective location of a photosensitizer in the tumor tissue, followed by light at wavelengths matching the photosensitizer absorption spectrum. In molecular oxygen presence, reactive oxygen species are generated, inducing cells to die. One of the limitations of photodynamic therapy is the variability of photosensitizer concentration observed in systemically photosensitized tissues, mainly due to differences of the tissue architecture, cell lines, and pharmacokinetics. This study aim was to demonstrate the spatial distribution of a hematoporphyrin derivative, Photogem(R), in the healthy liver tissue of Wistar rats via fluorescence spectroscopy, and to understand its implications on photodynamic response. Methods: Fifteen male Wistar rats were intravenously photosensitized with 1.5 mg/kg body weight of Photogem(R). Laser-induced fluorescence spectroscopy at 532nm-excitation was performed on ex vivo liver slices. The influence of photosensitizer surface distribution detected by fluorescence and the induced depth of necrosis were investigated in five animals. Results: Photosensitizer distribution on rat liver showed to be greatly non-homogeneous. This may affect photodynamic therapy response as shown in the results of depth of necrosis. Conclusions: As a consequence of these results, this study suggests that photosensitizer surface spatial distribution should be taken into account in photodynamic therapy dosimetry, as this will help to better predict clinical results. (C) 2010 Elsevier B.V. All rights reserved.