Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

Annular variability and eddy-zonal flow interactions in a simplified atmospheric GCM. Part 1: Characterization of high and low frequency behaviour

Experiments have been performed using a simplified, Newtonian forced, global circulation model to investigate how variability of the tropospheric jet can be characterized by examining the combined fluctuations of the two leading modes of annular variability. Eddy forcing of this variability is analyzed in the phase space of the leading modes using the vertically integrated momentum budget. The nature of the annular variability and eddy forcing depends on the time scale. At low frequencies the zonal flow and baroclinic eddies are in quasi equilibrium and anomalies propagate poleward. The eddies are shown primarily to reinforce the anomalous state and are closely balanced by the linear damping, leaving slow evolution as a residual. At high frequencies the flow is strongly evolving and anomalies are initiated on the poleward side of the tropospheric jet and propagate equatorward. The eddies are shown to drive this evolution strongly: eddy location and amplitude reflect the past baroclinicity, while eddy feedback on the zonal flow may be interpreted in terms of wave breaking associated with baroclinic life cycles in lateral shear.

Performance and prediction: Bayesian modelling of fallible choice in chess

Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.

A potential energy surface for the ground state of formaldehyde, H2CO(1A1)

A model potential energy function for the ground state of H2CO has been derived which covers the whole space of the six internal coordinates. This potential reproduces the experimental energy, geometry and quadratic force field of formaldehyde, and dissociates correctly to all possible atom, diatom and triatom fragments. Thus there are good reasons for believing it to be close to the true potential energy surface except in regions where both hydrogen atoms are close to the oxygen. It leads to the prediction that there should be a metastable singlet hydroxycarbene HCOH which has a planar trans structure and an energy of 2•31 eV above that of equilibrium formaldehyde. The reaction path for dissociation into H2 + CO is predicted to pass through a low symmetry transition state with an activation energy of 4•8 eV. Both of these predictions are in good agreement with recently published ab initio calculations.

Conceptualizing change in the Portuguese footwear industry: regional voices and cognitive spaces of agency

Expanding national services sectors and global competition aggravate current and perceived future market pressures on traditional manufacturing industries. These perceptions of change have provoked a growing intensification of geo-political discourses on technological innovation and ‘learning’, and calls for competency in design among other professional skills. However, these political discourses on innovation and learning have paralleled public concerns with the apparent ‘growth pains’ from factory closures and subsequent increases in unemployment, and its debilitating social and economic implications for local and regional development. In this respect the following investigation sets out to conceptualize change through the complementary and differing perceptions of industry and regional actors’ experiences or narratives, linking these perceptions to their structure-determined spheres of agent-environment interactivity. It aims to determine whether agents’ differing perceptions of industry transformation can have a role in the legitimization of their interests in, and in sustaining their organizational influence over the process of industry-regional transformation. It argues that industry and regional agent perceptions are among the cognitive aspects of agent-environment interactivity that permeate agency. It stresses agents’ ability to reason and manipulate their work environments to preserve their self-regulating interests in, and task representative influence over the multi-jurisdictional space of industry-regional transformation. The contributions of this investigation suggest that agents’ varied perceptions of industry and regional change inform or compete for influence over the redirection of regional, industry and business strategies. This claim offers a greater appreciation for the reflexive and complex institutional dimensions of industry planning and development, and the political responsibility to socially just forms of regional development. It positions the outcomes of this investigation at the nexus of intensifying geo-political discourses on the efficiency and equity of territorial development in Europe.

Post-frying oil drainage from potato chips and french fries: a comparative study of atmospheric and vacuum drainage

This paper represents a study of the transient changes occurring in temperature, and moisture and oil contents during the so called “post-frying drainage”—which is the duration for which a product is held in the head space of the fryer after it is removed from the oil. Since most of the oil adhering to the product penetrates into the structure during this period, this paper examines the effects of applying vacuum during drainage (1.33 kPa) to maintain the product temperature consistently above the water saturation temperature corresponding to the prevailing pressure (11 °C), which potentially eliminates water condensation and prevents the occluded surface oil from penetrating into the product structure. Draining under vacuum significantly lowers the oil content of potato chips by 38% compared to atmospheric drainage. This phenomenon can be further confirmed by confocal laser scanning microscopy (CLSM) images, which show that the boundary between the core and the crust regions is clearly visible in the case of vacuum drainage, whereas in the case of atmospheric drainage, the oil is distributed throughout the structure. Unfortunately, the same approach did not reduce the oil content of French fries—the oil content of vacuum-drained product was found similar to the product obtained by draining under atmospheric pressure. This is because the reduction in oil content only occurs when there is net moisture evaporation from the product and the evaporation rate is sufficient to force out the oil from the product; this was clearly not the case with French fries. The CLSM images show that the oil distribution in the products drained under atmospheric pressure and vacuum was similar.

The Life of Galileo and Brechtian television drama

Bertolt Brecht's dramaturgy was as influential upon the development of British drama on television between the 1950s and the 1970s as it was in the theatre. His influence was made manifest through the work of writers, directors and producers such as Tony Garnett, Ken Loach, John McGrath and Dennis Potter, whose attempts to create original Brechtian forms of television drama were reflected in the frequent reference to Brecht in contemporary debate concerning the political and aesthetic direction and value of television drama. While this discussion has been framed thus far around how Brechtian techniques and theory were applied to the newer media of television, this article examines these arguments from another perspective. Through detailed analysis of a 1964 BBC production of The Life of Galileo, I assess how the primary, canonical sources of Brecht's stage plays were realised on television during this period, locating Brecht's drama in the wider context of British television drama in general during the 1960s and 1970s. I pay particular attention to the use of the television studio as a site that could replicate or reinvent the theatrical space of the stage, and the responsiveness of the television audience towards Brechtian dramaturgy.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

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.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].