The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

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.

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

A survey on sampling and probe methods for inverse problems

The goal of the review is to provide a state-of-the-art survey on sampling and probe methods for the solution of inverse problems. Further, a configuration approach to some of the problems will be presented. We study the concepts and analytical results for several recent sampling and probe methods. We will give an introduction to the basic idea behind each method using a simple model problem and then provide some general formulation in terms of particular configurations to study the range of the arguments which are used to set up the method. This provides a novel way to present the algorithms and the analytic arguments for their investigation in a variety of different settings. In detail we investigate the probe method (Ikehata), linear sampling method (Colton-Kirsch) and the factorization method (Kirsch), singular sources Method (Potthast), no response test (Luke-Potthast), range test (Kusiak, Potthast and Sylvester) and the enclosure method (Ikehata) for the solution of inverse acoustic and electromagnetic scattering problems. The main ideas, approaches and convergence results of the methods are presented. For each method, we provide a historical survey about applications to different situations.

Origin and structure of Devensian depressions at Letton, Herefordshire

Groups of circular to oval enclosed depressions in soft sediments of Pleistocene age are relatively common in north-west Europe. These features are normally interpreted as being either glacial or periglacial in origin. Where these features are developed in glacial sediments, a glacial (and specifically ‘kettle hole’) genesis is considered most likely. Some groups of features, however, have been re-interpreted as being periglacial in origin and are thought to be the remains of cryogenic mounds (former pingos or palsas/lithalsas). The problem at many sites, of course, is correct identification and previously this was often resolved through extensive trenching of the sediments. The use of geophysics in the form of electrical resistivity tomography and ground probing radar, however, can aid investigation and interpretation and is less invasive. A group of enclosed depressions in the Letton area of Herefordshire within the Last Glacial Maximum ice limit (Late Devensian) have been investigated in this way. The morphology and internal structure of the features and their existence in glaciolacustrine sediments of Late Devensian age strongly suggests that these depressions are kettle holes resulting from ice block discharge into a shallow lakes or lakes, and hence a glacial origin is supported. The lack of any ramparts surrounding the depressions (at the surface or any evidence of these at depth) and the fact that they do not overlap (‘mutually interfere’) indicates that they are not the remains of cryogenic mounds.

Modelling complex systems for project planning - A semiotics motivated method

A large and complex IT project may involve multiple organizations and be constrained within a temporal period. An organization is a system comprising of people, activities, processes, information, resources and goals. Understanding and modelling such a project and its interrelationship with relevant organizations are essential for organizational project planning. This paper introduces the problem articulation method (PAM) as a semiotic method for organizational infrastructure modelling. PAM offers a suite of techniques, which enables the articulation of the business, technical and organizational requirements, delivering an infrastructural framework to support the organization. It works by eliciting and formalizing (e. g. processes, activities, relationships, responsibilities, communications, resources, agents, dependencies and constraints) and mapping these abstractions to represent the manifestation of the "actual" organization. Many analysts forgo organizational modelling methods and use localized ad hoc and point solutions, but this is not amenable for organizational infrastructures modelling. A case study of the infrared atmospheric sounding interferometer (IASI) will be used to demonstrate the applicability of PAM, and to examine its relevancy and significance in dealing with the innovation and changes in the organizations.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

Measuring productivity growth when technological change is biased - a new index and an application to UK agriculture

Productivity growth is conventionally measured by indices representing discreet approximations of the Divisia TFP index under the assumption that technological change is Hicks-neutral. When this assumption is violated, these indices are no longer meaningful because they conflate the effects of factor accumulation and technological change. We propose a way of adjusting the conventional TFP index that solves this problem. The method adopts a latent variable approach to the measurement of technical change biases that provides a simple means of correcting product and factor shares in the standard Tornqvist-Theil TFP index. An application to UK agriculture over the period 1953-2000 demonstrates that technical progress is strongly biased. The implications of that bias for productivity measurement are shown to be very large, with the conventional TFP index severely underestimating productivity growth. The result is explained primarily by the fact that technological change has favoured the rapidly accumulating factors against labour, the factor leaving the sector. (C) 2004 Elsevier B.V. All rights reserved.

Modified rare earth semiconductor oxide as a new nucleotide probe

Recent rapid developments in biological analysis, medical diagnosis, pharmaceutical industry, and environmental control fuel the urgent need for recognition of particular DNA sequences from samples. Currently, DNA detection techniques use radiochemical, enzymatic, fluorescent, or electrochemiluminescent methods; however, these techniques require costly labeled DNA and highly skilled and cumbersome procedure, which prohibit any in-situ monitoring. Here, we report that hybridization of surface-immobilized single-stranded oligonucleotide on praseodymium oxide (evaluated as a biosensor surface for the first time) with complimentary strands in solution provokes a significant shift of electrical impedance curve. This shift is attributed to a change in electrical characteristics through modification of surface charge of the underlying modified praseodymium oxide upon hybridization with the complementary oligonucelotide strand. On the other hand, using a noncomplementary single strand in solution does not create an equivalent change in the impedance value. This result clearly suggests that a new and simple electrochemical technique based on the change in electrical properties of the modified praseodymium oxide semiconductor surface upon recognition and transduction of a biological event without using labeled species is revealed.

Semiotic modelling for complex enterprise systems

An enterprise is viewed as a complex system which can be engineered to accomplish organisational objectives. Systems analysis and modelling will enable to the planning and development of the enterprise and IT systems. Many IT systems design methods focus on functional and non-functional requirements of the IT systems. Most methods are normally capable of one but leave out other aspects. Analysing and modelling of both business and IT systems may often have to call on techniques from various suites of methods which may be placed on different philosophic and methodological underpinnings. Coherence and consistency between the analyses are hard to ensure. This paper introduces the Problem Articulation Method (PAM) which facilitates the design of an enterprise system infrastructure on which an IT system is built. Outcomes of this analysis represent requirements which can be further used for planning and designing a technical system. As a case study, a finance system, Agresso, for e-procurement has been used in this paper to illustrate the applicability of PAM in modelling complex systems.

A design of e-procurement infrastructure model for public service sector

Procurement is one of major business operations in public service sector. The advance of information and communication technology (ICT) pushes this business operation to increase its efficiency and foster collaborations between the organization and its suppliers. This leads to a shift from the traditional procurement transactions to an e-procurement paradigm. Such change impacts on business process, information management and decision making. E-procurement involves various stakeholders who engage in activities based on different social and cultural practices. Therefore, a design of e-procurement system may involve complex situations analysis. This paper describes an approach of using the problem articulation method to support such analysis. This approach is applied to a case study from UAE.

Articulation of stakeholders requirements for complex e-government systems development

Requirements analysis focuses on stakeholders concerns and their influence towards e-government systems. Some characteristics of stakeholders concerns clearly show the complexity and conflicts. This imposes a number of questions in the requirements analysis, such as how are they relevant to stakeholders? What are their needs? How conflicts among the different stakeholders can be resolved? And what coherent requirements can be methodologically produced? This paper describes the problem articulation method in organizational semiotics which can be used to conduct such complex requirements analysis. The outcomes of the analysis enable e-government systems development and management to meet userspsila needs. A case study of Yantai Citizen Card is chosen to illustrate a process of analysing stakeholders in the lifecycle of requirements analysis.