High frequency homogenization for travelling waves in periodic media

We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{\"o}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector \Bk and frequency $\omega_1$ plus a modulated Bloch carrier wave having crystal wave vector \Bm and frequency $\omega_2$. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless $\omega_1=\omega_2$ and (\Bk-\Bm)\odot\Lambda \in 2\pi \mathbb Z^d, where $\Lambda=(\lambda_1\lambda_2\dots\lambda_d)$ is the periodicity cell of the medium and for any two vectors $a=(a_1,a_2,\dots,a_d), b=(b_1,b_2,\dots,b_d)\in\mathbb R^d,$ the product $a\odot b$ is defined to be the vector $(a_1b_1,a_2b_2,\dots,a_db_d).$ This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.Comment: 30 pages, Proceedings of the Royal Society A, 201

Use of satellite images for broad-scale modelling of conservation areas for wolves in the Carpathian Mountains, central Europe

This study analysed the spatial structure of the Carpathian Mountains, in Central Europe, considering it a unit that extends across national boundaries, and assessing the suitability of areas were wolves could be conserved. Physical characteristics of the area were extracted from NOAA-AVHRR NDVI. A set of 9 images from different periods of the year was used to parameterise the phenological variability of the area. Digital maps of road networks, human settlements and a DEM were integrated in a GIS. Locations of wolf presence were used to extract “optimal” environmental characteristics that served as reference for estimating the degree of suitability over the whole area. Results show that most of the Carpathian Mountains are highly suitable for the wolf and that highly suitable areas are actually inhabited by the present population of wolf. These are also the area most phenologically stable

Wavelength-dependent spatial variation in the reflectance of 'homogeneous' ground calibration targets (Paper presented at XIX ISPRS Congress, 16-22 July, 2000, Amsterdam, The Netherlands)

Remotely sensed data are most useful if calibrated to spectral reflectance of known features. One simple method of calibration is regression of remote data on the reflectance of several ground targets as measured in the field, the so called empirical line method (ELM). The ideal situation would be one where a range of ground targets representing all the features of interest in the remote image were available for ground measurements (Lawless et al., 1998). The identification of suitable ground targets is constrained by several limitations, such as their size (to minimise edge effects), their absolute reflectance (to represent spectral characteristics of the image) and their effective spatial variability (to extract reflectance characteristics representative of the target). The size of a ground target is dependent on the spatial resolution of the image that must be calibrated (Justice & Townshend, 1981) and the number of observations needed to represent features in the image has been suggested to depend upon the spatial resolution of the remotely sensed image (Justice & Townshend, 1981) and on the spatial variability of the ground target (Harlan et al., 1979; Curran & Williamson, 1986). Although ground targets used for calibration should be spectrally “bland” and spatially uniform by definition (Clark et al., 1999), it is sometimes very difficult to find such places available for calibrating remotely sensed images. When surfaces that apparently satisfy these conditions are available in suitable size, their sampling needs to be designed to optimise representation of the whole surface and available resources (e.g., effort and time). Surfaces that look spatially uniform by eye may actually contain spatial variation, and this spatial variation may depends on wavelength (Atkinson & Emery, 1999). Such variability can be detected using geostatistics, which is concerned with issues such as spatial correlation and analyses of spatial data. Geostatistical tools have been used in a variety of studies and the variogram has been applied in remote sensing and ecology to design optimal sampling strategies for variables sampled in space (Atkinson, 1991; Rossi et al., 1992) and time (Salvatori et al., 1999). This study investigates the spatial variability of potentially suitable ground calibration targets (GCT) using a geostatistical approach, which gives results that can be used to design optimal sampling strategies for such surfaces. The targets were selected from an area where an Itres Instruments Compact Airborne Spectral Imager (casi) with ground resolution of about 1.5 metres was flown at the same time as ground data were acquired

Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors

We show that any pair of real symmetric tensors \BGve and \BGm can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{\'e} and Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.Comment: 12 pages, no figure

Energy conditions outside a dielectric ball

We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.Comment: 12 pages, RevTex

Civil society coalitions as pathways to PSB reform in Southern Africa

Democracy requires open public service broadcasting (PSB) institutions that constantly interact with active informed citizens. This article posits that a more proactive network of civil society across Southern Africa can produce an impact on PSB institutions in these countries enhancing reform and accountability to the public. We enter this topic by identifying pathways towards increased cooperation among public service broadcasters, civil society coalitions and other stakeholders in South Africa and Zimbabwe. The main focus is on the interaction between broadcasters, policy-makers and civil society groups, namely SOS: Support Public Broadcasting in South Africa and the Media Alliance of Zimbabwe, two leading media activist organizations in Southern Africa. The engagement by such networks can deepen public interest and reconnect PSB institutions and PSB staff to the PSB mandate and mission. Civil society coalitions working collaboratively with PSB will engender a context within which a collaboratively defined PSB mission, institutional structure and programme outcomes are constantly foregrounded in the operations and performance of the broadcasters

Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in previous version corrected, giving a zero Casimir energy for a tenuous cylinde