An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Application of the Lighthill-Ford theory of spontaneous imbalance to clear-air turbulence forecasting

A new method of clear-air turbulence (CAT) forecasting based on the Lighthill–Ford theory of spontaneous imbalance and emission of inertia–gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill–Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill–Ford theory to CAT forecasting for the 3 November 2005–26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational.

Caring at a distance: Gift Theory, aid chains and social movements

This paper takes as its starting point recent work on caring for distant others which is one expression of renewed interest in moral geographies. It examines relationships in aid chains connecting donors/carers in the First World or North and recipients/cared for in the Third World or South. Assuming predominance of relationships between strangers and of universalism as a basis for moral motivation I draw upon Gift Theory in order to characterize two basic forms of gift relationship. The first is purely altruistic, the other fully reciprocal and obligatory within the framework of institutions, values and social forces within specific relationships of politics and power. This conception problematizes donor-recipient relationships in the context of two modernist models of aid chains-the Resource Transfer and the Beyond Aid Paradigms. In the first, donor domination means low levels of reciprocity despite rhetoric about partnership and participation. The second identifies potential for greater reciprocity on the basis of combination between social movements and non-governmental organizations at both national and trans-national levels, although at the risk of marginalizing competencies of states. Finally, I evaluate post-structural critiques which also problematize aid chain relationships. They do so both in terms of bases-such as universals and difference-upon which it might be constructed and the means-such as forms of positionality and mutuality-by which it might be achieved.

Features of the Atlantic diet and its healthiness: Theory and evidence from social science

In order to understand diets, why and how they change and can be influenced, it is important to understand how food choices are made. The has been the subject of, considerable study within many of the social science disciplines and the humanities. The paper draws on the theoretical and empirical work of psychologists, sociologists, economists, market researchers, anthropologists, geographers and historians to understand better the forces behind food choice, derive some general empirical messages from the literature, to shed light on food choice in a European context and to address the question of whether there is, or has been, a recognisably Atlantic diet. The paper proceeds to analyse the characteristics of the food consumption patterns in the Atlantic diet countries, examines whether their food consumption patterns are homogenous (i.e. similar across the countries of this group), whether they are specific (i.e. different from the ones in other country groups) and finally evaluates the nutritional composition of the Atlantic diet against the WHO/FAO recommendations for a healthy and wholesome diet.

Understanding construction consortia: Theory, practice and opinions

Firms form consortia in order to win contracts. Once a project has been awarded to a consortium each member then concentrates on his or her own contract with the client. Therefore, consortia are marketing devices, which present the impression of teamworking, but the production process is just as fragmented as under conventional procurement methods. In this way, the consortium forms a barrier between the client and the actual construction production process. Firms form consortia, not as a simple development of normal ways of working, but because the circumstances for specific projects make it a necessary vehicle. These circumstances include projects that are too large or too complex to undertake alone or projects that require on-going services which cannot be provided by the individual firms inhouse. It is not a preferred way of working, because participants carry extra risk in the form of liability for the actions of their partners in the consortium. The behaviour of members of consortia is determined by their relative power, based on several factors, including financial commitment and ease of replacement. The level of supply chain visibility to the public sector client and to the industry is reduced by the existence of a consortium because the consortium forms an additional obstacle between the client and the firms undertaking the actual construction work. Supply chain visibility matters to the client who otherwise loses control over the process of construction or service provision, while remaining accountable for cost overruns. To overcome this separation there is a convincing argument in favour of adopting the approach put forward in the Project Partnering Contract 2000 (PPC2000) Agreement. Members of consortia do not necessarily go on to work in the same consortia again because members need to respond flexibly to opportunities as and when they arise. Decision-making processes within consortia tend to be on an ad hoc basis. Construction risk is taken by the contractor and the construction supply chain but the reputational risk is carried by all the firms associated with a consortium. There is a wide variation in the manner that consortia are formed, determined by the individual circumstances of each project; its requirements, size and complexity, and the attitude of individual project leaders. However, there are a number of close working relationships based on generic models of consortia-like arrangements for the purpose of building production, such as the Housing Corporation Guidance Notes and the PPC2000.

Second-order cybernetics and enactive perception

Purpose - To present an account of cognition integrating second-order cybernetics (SOC) together with enactive perception and dynamic systems theory. Design/methodology/approach - The paper presents a brief critique of classical models of cognition then outlines how integration of SOC, enactive perception and dynamic systems theory can overcome some weaknesses of the classical paradigm. Findings - Presents the critique of evolutionary robotics showing how the issues of teleology and autonomy are left unresolved by this paradigm although their solution fits within the proposed framework. Research limitations/implications - The paper highlights the importance of genuine autonomy in the development of artificial cognitive systems. It sets out a framework within which the robofic research of cognitive systems could succeed. Practical implications - There are no immediate practical implications but see research implications. Originality/value - It joins the discussion on the fundamental nature of cognitive systems and emphasise the importance of autonomy and embodiment.

Compression of polymer brushes: quantitative comparison of self-consistent field theory with experiment

The self-consistent field theory (SCFT) prediction for the compression force between two semi-dilute polymer brushes is compared to the benchmark experiments of Taunton et al. [Nature, 1988, 332, 712]. The comparison is done with previously established parameters, and without any fitting parameters whatsoever. The SCFT provides a significant quantitative improvement over the classical strong-stretching theory (SST), yielding excellent quantitative agreement with the experiment. Contrary to earlier suggestions, chain fluctuations cannot be ignored for normal experimental conditions. Although the analytical expressions of SST provide invaluable aids to understanding the qualitative behavior of polymeric brushes, the numerical SCFT is necessary in order to provide quantitatively accurate predictions.

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.

Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.