A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

On the 'downward control' of extratropical diabatic circulations by eddy-induced mean zonal forces

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force F̄, conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force F̄ may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the F̄ distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport. The robustness of the principle is examined when F̄ is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in F̄ confined to a shallow layer LF̄ is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when F̄ is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τr−1 divided by {1 + (4H2/HR2)}. This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above LF̄ without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τr−1 HR2/H. For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from LF̄ and closing via the boundary layer. Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective F̄ in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.

On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

On collective intentions: collective action in economics and philosophy

Philosophers and economists write about collective action from distinct but related points of view. This paper aims to bridge these perspectives. Economists have been concerned with rationality in a strategic context. There, problems posed by “coordination games” seem to point to a form of rational action, “team thinking,” which is not individualistic. Philosophers’ analyses of collective intention, however, sometimes reduce collective action to a set of individually instrumental actions. They do not, therefore, capture the first person plural perspective characteristic of team thinking. Other analyses, problematically, depict intentions ranging over others’ actions. I offer an analysis of collective intention which avoids these problems. A collective intention aims only at causing an individual action, but its propositional content stipulates its mirroring in other minds.

Interpersonal interaction and economic theory: the case of public goods

Interpersonal interaction in public goods contexts is very different in character to its depiction in economic theory, despite the fact that the standard model is based on a small number of apparently plausible assumptions. Approaches to the problem are reviewed both from within and outside economics. It is argued that quick fixes such as a taste for giving do not provide a way forward. An improved understanding of why people contribute to such goods seems to require a different picture of the relationships between individuals than obtains in standard microeconomic theory, where they are usually depicted as asocial. No single economic model at present is consistent with all the relevant field and laboratory data. It is argued that there are defensible ideas from outside the discipline which ought to be explored, relying on different conceptions of rationality and/or more radically social agents. Three such suggestions are considered, one concerning the expressive/communicative aspect of behaviour, a second the possibility of a part-whole relationship between interacting agents and the third a version of conformism.

An evolutionary innovation perspective on the selection of low and zero carbon technologies in new housing

The Code for Sustainable Homes (the Code) will require new homes in the United Kingdom to be ‘zero carbon’ from 2016. Drawing upon an evolutionary innovation perspective, this paper contributes to a gap in the literature by investigating which low and zero carbon technologies are actually being used by house builders, rather than the prevailing emphasis on the potentiality of these technologies. Using the results from a questionnaire three empirical contributions are made. First, house builders are selecting a narrow range of technologies. Second, these choices are made to minimise the disruption to their standard design and production templates (SDPTs). Finally, the coalescence around a small group of technologies is expected to intensify with solar-based technologies predicted to become more important. This paper challenges the dominant technical rationality in the literature that technical efficiency and cost benefits are the primary drivers for technology selection. These drivers play an important role but one which is mediated by the logic of maintaining the SDPTs of the house builders. This emphasises the need for construction diffusion of innovation theory to be problematized and developed within the context of business and market regimes constrained and reproduced by resilient technological trajectories.

The creativity of action: Property, Kin and the social in African artisanal mining

Analyses of neo-liberal change in African mining tend to frame discussion through the lens of an overarching structural perspective. Far less attention has been paid to the way change is enacted within social relations in mining communities. To this end, our chapter considers how development in the Tanzanian mineral sector transforms people’s relationships and stimulates new iterations of power and agency within local trajectories of development, focusing on the case of artisanal gold mining in Mgusu village in Geita region, Tanzania. The aim is to trace how neo-liberal change configures market rationality and property relations in ways that can fundamentally alter social relationships within the local community, occupational groups and families, raising both opportunities for wealth accumulation and the potential to entrench poverty. The creative action involved in these processes generates new associational ties and repertoires of practice, as miners’ respond to change and the need to protect their livelihoods.

The end of the opportunism vs trust debate: bounded reliability as a new envelope concept in research on MNE governance

Modern transaction cost economics (TCE) thinking has developed into a key intellectual foundation of international business (IB) research, but the Williamsonian version has faced substantial criticism for adopting the behavioral assumption of opportunism. In this paper we assess both the opportunism concept and existing alternatives such as trust within the context of IB research, especially work on multinational enterprise (MNE) governance. Case analyses of nine global MNEs illustrate an alternative to the opportunism assumption that captures more fully the mechanisms underlying failed commitments inside the MNE. As a substitute for the often-criticized assumption of opportunism, we propose the envelope concept of bounded reliability (BRel), an assumption that represents more accurately and more completely the reasons for failed commitments, without invalidating the other critical assumption in conventional TCE (and internalization theory) thinking, namely the widely accepted envelope concept of bounded rationality (BRat). Bounded reliability as an envelope concept includes two main components, within the context of global MNE management: opportunism as intentional deceit, and benevolent preference reversal. The implications for IB research of adopting the bounded reliability concept are far reaching, as this concept may increase the legitimacy of comparative institutional analysis in the social sciences.

The Brownian traveller on manifolds

We study the inuence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the at case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the at case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

Max Weber in the thought of Edward Shils (1910–1995) and Ernest Gellner (1925–1995): the paradox of two Weberian approaches to the understanding of nations and nationalism?

This article traces the paradoxical impact of Weber's oeuvre on two major scholars of nationalism, Ernest Gellner and Edward Shils. Both these scholars died in 1995, leaving behind a rich corpus of writings on the nation and nationalism, much of which was inspired by Max Weber. The paradox is that although neither scholar accepted Weber's sceptical attitude to the concept of ‘nation’, they both used his other major concepts, such as ‘rationality’, ‘disenchantment’, ‘unintended consequences’, the ‘ethic of responsibility’ and ‘charisma’, in their very analyses of the nation and nationalism. And they both saw, each in his own way, the nation and nationalism as constitutive elements of modern societies. However, the paradox ceases being a paradox if one sees the integration, by Shils and Gellner, of concepts of the nation and of nationalism in the analysis of modernity, as a development of Weber's ideas.

Organisational politics: reconciling leadership's rational-emotional paradox

Purpose – Effective leadership action requires managers to harness power that is intrinsically political. This paper aims to study and characterise the political nature of a manager's behaviour when taking leadership action. Design/methodology/approach – The methodological approach is qualitative and examines three organisations over a three-year period when these entities experienced a major product failure. The paper analyses the actual managerial behaviour of managers and provides insight into the factors that most strongly influence the effectiveness of managers when taking leadership action. Findings – Political behaviour when taking leadership action can be conceptualised in terms of rationality and emotionality. In so doing, it can be clarified how behaviour must be modified to ensure that leadership action is consistently effective. Research limitations/implications – A case study of three multinational engineering companies engaged in the design, development and manufacturing of turbomachinery provides the platform for the research. The concepts presented in the paper will require validating in other organisations of different demographic profiles. Practical implications – The concepts presented and the implications discussed provide insight into the political nature of managerial behaviour when taking leadership action. The paper highlights the practical steps individual managers can embrace to ensure that their behaviour is appropriate to context, even under the most traumatic situations. Thus, the paper provides managers with a model that facilitates effective leadership action. Originality/value – This paper provides insight into how managers behaved in circumstances that mattered to them. Through immersion in events at the time they took place, the authors captured situations in which managers were under real pressure and, in so doing, avoided the bias inherent when interviewing a manager about past events. As such, the paper concludes that the political behaviour in which managers engage when taking leadership action is rooted in the reality of the adversity that the most capable managers have both experienced and overcome. This detailed study reports behaviour in a situation where managers' business and future prospects were in jeopardy. This paper identifies why some managers were able to use the experience positively, helping them to adopt politically intrinsic behaviour to facilitate effective leadership action.

Health care rights and NHS rationing: turning theory into practice

How should we understand the nature of patients’ right in public health care systems? Are health care rights different to rights under a private contract for car insurance? This article distinguishes between public and private rights and the relevance of community interests and notions of social solidarity. It discusses the distinction between political and civil rights, and social and economic rights and the inherently political and redistributive nature of the latter. Nevertheless, social and economic rights certainly give rise to “rights” enforceable by the courts. In the UK (as in many other jurisdictions), the courts have favoured a “procedural” approach to the question, in which the courts closely scrutinise decisions and demand high standards of rationality from decision-makers. However, although this is the general rule, the article also discusses a number of exceptional cases where “substantive” remedies are available which guarantee patients access to the care they need.