A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

Validation of data analysis routines for a thermal probe apparatus using numerical data sets

Most thermal properties of construction materials used in the analysis of building performance have been measured under laboratory conditions, using a guarded hot box or hot plate apparatus. As a consequence, these properties seldom reflect the impact of actual conditions (especially moisture content) on the values of conductivity and diffusivity. Hence there is a need to develop techniques that allow to take into account local conditions, and measure building material properties in situ. One option available is the use of a thermal probe. The thermal probe technique is based on creating a line source in a material sample, and measuring the temperature rise in the sample in reaction to heat being applied. Obviously the data analysis routines used to calculate thermal conductivity and thermal diffusivity based on the temperature rise observed are crucial to the success of the technique. Transient thermal simulation of a of a model representing a line source in an infinite material sample has been used to generate a set of numerical data sets to validate analysis routines in conjunction with an experimental thermal probe apparatus. Findings show that by careful application of these routines, a close agreement with simulation input values can be achieved, with errors of less than one percent. This validates the analysis routines and provides a deeper appreciation of the theoretical behaviour of a thermal probe

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high frequency asymptotics of the solution. Our numerical results suggest that fi�xed accuracy can be achieved at arbitrarily high frequencies with a frequency-independent computational cost. Our analysis does not capture this observed behaviour completely, but we provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom $N$ increases, and that to achieve any desired accuracy it is sufficient to increase $N$ in proportion to the square of the logarithm of the frequency as the frequency increases (standard boundary element methods require $N$ to increase at least linearly with frequency to retain accuracy). We also show how our method can be applied to the complementary "breakwater" problem of propagation through an aperture in an infinite sound-hard screen

An assessment of the potential returns of energy certificates for the UK household sector

Purpose – This article seeks to investigate the interconnections between the expectations of the impact of energy certificates issued within the UK domestic building sector through the Energy Performance of Buildings Directive (EPBD) and the actual number and financial implications of the energy saving measures (ESMs) achieved. Design/methodology/approach – The methodology uses two previously published surveys and compares these with a third independent survey by the authors focusing upon the discrepancies between planned action and implemented action, introducing the term human factor element (hfe). Findings – The article concludes that annual carbon savings arising from implementation of the Energy Performance Certificate (EPC) may be as low as 73.4?ktC over the five year term of the Kyoto Protocol even though 44 per cent of energy saving measure costs of £200 million are recouped within the same time period and savings will continue for up to 40 years. Achieving annual savings of only 14.7?ktC by 2010, such a figure represents a mere 0.3 per cent of the annual domestic 4.8?MtC savings announced by the government in its 2006 Climate Change Programme. Practical implications – Since the principal determinant in the uptake of ESMs is initial cost, it is considered that the EPBD is likely to remain an under-performing instrument in the promotion of energy sufficiency until such time as other complementary provisions are introduced. Originality/value – Sheds light upon the likely financial impact upon energy efficiency in domestic buildings by energy certificates

Stochastic resonance in Gaussian quantum channels

We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a "forbidden interval". We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel, and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case the symmetry between sender and receiver is broken and the "forbidden interval" may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.Comment: 17 pages, 6 figures. Manuscript improved in many ways. New results on private communication adde

Quantum Channel Capacities Per Unit Cost

Communication over a noisy channel is often conducted in a setting in which different input symbols to the channel incur a certain cost. For example, for bosonic quantum channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a quantum channel such as classical communication, entanglement-assisted classical communication, private communication, and quantum communication. For each task, we define the corresponding capacity per unit cost and derive a formula for it analogous to that of the usual capacity. Furthermore, for the special and natural case in which there is a zero-cost state, we obtain expressions in terms of an optimized relative entropy involving the zero-cost state. For each communication task, we construct an explicit pulse-position-modulation coding scheme that achieves the capacity per unit cost. Finally, we compute capacities per unit cost for various bosonic Gaussian channels and introduce the notion of a blocklength constraint as a proposed solution to the long-standing issue of infinite capacities per unit cost. This motivates the idea of a blocklength-cost duality, on which we elaborate in depth.Comment: v3: 18 pages, 2 figure

Thermal probe technology for buildings: the transition from laboratory to field measurements

This article reports the results of an investigation into the transfer of thermal probe measurement technology from laboratory use to actual buildings in order to undertake the in situ determination of thermal material properties. The imperative for using in situ measurements is 1) the impact of moisture content on thermal properties, 2) the possible wide range of variation of properties across most materials used in construction, and 3) the lack of data for new and innovative materials. Thermal probe technology offers the prospect of taking building specific data, addressing these issues. Based on commercially available thermal probes a portable measurement kit and accompanying measurement procedure have been developed. Three case study buildings, each having different materials, have been studied to ascertain whether or not the technique can be transferred to relatively uncontrolled environments while remaining capable of achieving a precision that is similar to an ASTM standard that can be related to thermal conductivity measurements of building materials. The results show that this is indeed the case, and that the use of thermal probe technology may yield thermal properties that vary significantly from the laboratory values currently used in building thermal engineering calculations