A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Behavioural compensation by drivers of a simulator when using a vision enhancement system

Technological progress is suggesting dramatic changes to the tasks of the driver, with the general aim of making driving environment safer. Before any of these technologies are implemented, empirical research is required to establish if these devices do, in fact, bring about the anticipated improvements. Initially, at least, simulated driving environments offer a means of conducting this research. The study reported here concentrates on the application of a vision enhancement (VE) system within the risk homeostasis paradigm. It was anticipated, in line with risk homeostasis theory, that drivers would compensate for the reduction in risk by increasing speed. The results support the hypothesis although, after a simulated failure of the VE system, drivers did reduce their speed due to reduced confidence in the reliability of the system

The Phase Transition to a Square Vortex Lattice in Type-II Superconductors with Fourfold Anisotropy

We investigate the stability of the square vortex lattice which has been recently observed in experiments on the borocarbide family of superconductors. Taking into account the tetragonal symmetry of these systems, we add fourfold symmetric fourth-derivative terms to the Ginzburg-Landau(GL) free energy. At $H_{c2}$ these terms may be treated perturbatively to lowest order to locate the transition from a distorted hexagonal to a square vortex lattice. We also solve for this phase boundary numerically in the strongly type-II limit, finding large corrections to the lowest-order perturbative results. We calculate the relative fourfold $H_{c2}$ anisotropy for field in the $xy$ plane to be 4.5% at the temperature, $T_c^{\Box}$, where the transition occurs at $H_{c2}$ for field along the $z$ axis. This is to be compared to the 3.6% obtained in the perturbative calculation. Furthermore, we find that the phase boundary in the $H-T$ phase diagram has positive slope near $H_{c2}$.Comment: 15 pages including 2 figures, LaTe

The perceived barriers to the inclusion of rainwater harvesting systems by UK house building companies

This work investigates the barriers that exist to deter the implementation of rainwater harvesting into new UK housing. A postal questionnaire was sent to a selection of large, medium and small house-builders distributed across the UK. Questions were asked concerning potential barriers to the inclusion of rainwater harvesting in homes separated into five sections; (1) institutional and regulatory gaps, (2) economic and financial constraints, (3) absence of incentives, (4) lack of information and technical knowledge, and (5) house-builder attitudes. The study concludes that although the knowledge of rainwater systems has increased these barriers are deterring house-builders from installing rainwater harvesting systems in new homes. It is further acknowledged that the implementation of rainwater harvesting will continue to be limited whilst these barriers remain and unless resolved, rainwater harvesting's potential to reduce the consumption of potable water in houses will continue to be limited

Four-fold basal plane anisotropy of the nonlocal magnetization of YNi2B2C

Studies of single crystal YNi2B2C have revealed a four-fold anisotropy of the equilibrium magnetization in the square crystallographic basal plane. This pi/2 periodicity occurs deep in the superconductive mixed state. In this crystal symmetry, an ordinary superconductive mass anisotropy (as in usual London theory) allows only a constant, isotropic response. In contrast, the experimental results are well described by generalized London theory incorporating non-local electrodynamics, as needed for this clean, intermediate-k superconductor.Comment: 4 pages, 4 figure

The olfactory coreceptor IR8a governs larval feces-mediated competition avoidance in a hawkmoth

Finding a suitable oviposition site is a challenging task for a gravid female moth. At the same time, it is of paramount importance considering the limited capability of most caterpillars to relocate to alternative host plants. The hawkmoth, Manduca sexta, oviposits on solanaceous plants. Larvae hatching on a plant that is already attacked by conspecific caterpillars face food competition. Here, we show that feces from conspecific caterpillars are sufficient to deter a female M. sexta from ovipositing on a plant. Furthermore, we not only identify the responsible compound in the feces but also localize the population of sensory neurons that governs the female’s avoidance. Hence, our work increases the understanding of how animals cope with a competitive environment

Lithotectonic elements and geological events in the Hengshan-Wutai-Fuping belt: A synthesis and implications for the evolution of the Trans-North China Orogen

The Hengshan-Wutai-Fuping belt is located in the middle segment of the Trans-North China Orogen, a Palaeoproterozoic continental collisional belt along which the Eastern and Western blocks amalgamated to form the North China Craton. The belt consists of the medium- to high-grade Hengshan and Fuping gneiss complexes and the intervening low- to medium-grade Wutai granite-greenstone terrane, and most igneous rocks in the belt are calc-alkaline and have affinities to magmatic arcs. Previous tectonic models assumed that the Hengshan and Fuping gneiss assemblages were an older basement to the Wutai supracrustal rocks, but recent studies indicate that the three complexes constitute a single, long-lived Neoarchaean to Palaeoproterozoic magmatic arc where the Wutai Complex represents an upper crustal domain, whereas the Hengshan and Fuping gneisses represent the lower crustal components forming the root of the arc. The earliest arc-related magmatism in the belt occurred at 2560-2520 Ma, marked by the emplacement of the Wutai granitoids, which was followed by arc volcanism at 2530-2515 Ma, forming the Wutai greenstones. Extension driven by widespread arc volcanism led to the development of a back-arc basin or a marginal sea, which divided the belt into the Hengshan-Wutai island arc (Japan-type) and the Fuping relict arc. At 2520-2480 Ma, subduction beneath the Hengshan-Wutai island arc caused partial melting of the lower crust to form the Hengshan tonalitic-trondhjemitic-granodioritic (TTG) suites, whereas eastward-directed subduction of the marginal sea led to the reactivation of the Fuping relict arc, where the Fuping tonalitic-trondhjemitic-granodioritic suite was emplaced. In the period 2360-2000 Ma, sporadic phases of isolated granitoid magmatism occurred in the Hengshan-Wutai-Fuping region, forming 2360 Ma, c. 2250 Ma and 2000-2100 Ma granitoids in the Hengshan Complex, the c. 2100 Ma Wangjiahui and Dawaliang granites in the Wutai Complex, and the 2100-2000 Ma Nanying granitoids in the Fuping Complex. At c. 1920 Ma, the Hengshan-Wutai island arc underwent an extensional event, possibly due to the subduction of an oceanic ridge, leading to the emplacement of pre-tectonic gabbroic dykes that were subsequently metamorphosed, together with their host rocks, to form medium- to high-pressure granulites. At 1880-1820 Ma, the Hengshan-Wutai-Fuping arc system was juxtaposed, intensely deformed and metamorphosed during a major and regionally extensive orogenic event, the Lüliang Orogeny, which generated the Trans-North China Orogen through collision of the Eastern and Western blocks. The Hengshan-Wutai-Fuping belt was finally stabilized after emplacement of a mafic dyke swarm at 1780-1750 Ma. © 2007 Cambridge University Press.published_or_final_versio