Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Morphology induced spinodal decomposition at the surface of symmetric diblock copolymer films

Atomic force microscopy is used to study the ordering dynamics of symmetric diblock copolymer films. The films order to form a lamellar structure which results in a frustration when the film thickness is incommensurate with the lamellae. By probing the morphology of incommensurate films in the early ordering stages, we discover an intermediate phase of lamellae arranged perpendicular to the film surface. This morphology is accompanied by a continuous growth in amplitude of the film surface topography with a characteristic wavelength, indicative of a spinodal process. Using selfconsistent field theory, we show that the observation of perpendicular lamellae suggests an intermediate state with parallel lamellae at the substrate and perpendicular lamellae at the free surface. The calculations confirm that the intermediate state is unstable to thickness fluctuations, thereby driving the spinodal growth of surface structures.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

People or machines? Assessing the impacts of smart meters and load controllers in Italian office spaces

Government initiatives in several developed and developing countries to roll-out smart meters call for research on the sustainability impacts of these devices. In principle smart meters bring about higher control over energy theft and lower consumption, but require a high level of engagement by end-users. An alternative consists of load controllers, which control the load according to pre-set parameters. To date, research has focused on the impacts of these two alternatives separately. This study compares the sustainability impacts of smart meters and load controllers in an occupied office building in Italy. The assessment is carried out on three different floors of the same building. Findings show that demand reductions associated with a smart meter device are 5.2% higher than demand reductions associated with the load controller.

Parameter spaces of environmental fields responsible for cyclone development from tropics to extratropics

Objective cyclone tracking applied to a 30-yr reanalysis dataset shows that cyclone development in the summer and autumn seasons is active in the tropics and extratropics and inactive in the subtropics. To understand this geographically bimodal distribution of cyclone development associated with tropical and extratropical cyclones quantitatively, the direct relationship between cyclone types and their environments are assessed by using a parameter space of environmental variables [environmental parameter space (EPS)]. The number of cyclones is analyzed in terms of two different factors: the environmental conditions favorable for cyclone development and the area size that satisfies the favorable condition. The EPS analysis is mainly conducted for two representative environmental parameters that are commonly used for cyclone analysis: potential intensity for tropical cyclones and baroclinicity for extratropical cyclones. The geographically bimodal distribution is attributed to the high sensitivity of the cyclone development to the change in the environmental fields from tropics to extratropics. In addition, the bimodal distribution is partly attributed to the rapid change in the environmental fields from tropics to extratropics. The EPS analysis also shows that other environmental parameters, including relative humidity and vertical velocity, may enhance the contrast between the tropics (extratropics) and subtropics, whereas they are not essential for determining cyclone types. The relationship between cyclones and their environments is found to be similar between the hemispheres in the EPS, although the geographical distribution, particularly the longitudinal uniformity, is markedly different between the hemispheres.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

The spaces of the Wednesday Play (BBC TV 1964–1970): production, technology and style

The BBC television drama anthology The Wednesday Play, broadcast from 1964-70 on the BBC1 channel, was high-profile and often controversial in its time and has since been central to accounts of British television’s ‘golden age’. This article demonstrates that production technologies and methods were more diverse at that time than is now acknowledged, and that The Wednesday Play dramas drew both approving but also very critical responses from contemporary viewers and professional reviewers. This article analyses the ways that the physical spaces of production for different dramas in the series, and the different technologies of shooting and recording that were adopted in these production spaces, are associated with but do not determine aesthetic style. The adoption of single-camera location filming rather than the established production method of multi-camera studio videotaping in some of the dramas in the series has been important to The Wednesday Play’s significance, but each production method was used in different ways. The dramas drew their dramatic forms and aesthetic emphases from both theatre and cinema, as well as connecting with debates about the nature of drama for television. Institutional and regulatory frameworks such as control over staff working away from base, budgetary considerations and union agreements also impacted on decisions about how programmes were made. The article makes use of records from the BBC Written Archives Centre, as well as published scholarship. By placing The Wednesday Play in a range of overlapping historical contexts, its identity can be understood as transitional, differentiated and contested.

Writers' rooms: theories of contemporary authorship in portraits of creative spaces

This article analyzes two series of photographs and essays on writers’ rooms published in England and Canada in 2007 and 2008. The Guardian’s Writers Rooms series, with photographs by Eamon McCabe, ran in 2007. In the summer of 2008, The Vancouver International Writers and Readers Festival began to post its own version of The Guardian column on its website by displaying, each week leading up to the Festival in September, a different writer’s “writing space” and an accompanying paragraph. I argue that these images of writers’ rooms, which suggest a cultural fascination with authors’ private compositional practices and materials, reveal a great deal about theoretical constructions of authorship implicit in contemporary literary culture. Far from possessing the museum quality of dead authors’ spaces, rooms that are still being used, incorporating new forms of writing technology, and having drafts of manuscripts scattered around them, can offer insight into such well-worn and ineffable areas of speculation as inspiration, singular authorial genius, and literary productivity.

State-resolved gas-surface reactivity of methane in the symmetric C-H stretch vibration on Ni(100)

The state-resolved reactivity of CH4 in its totally symmetric C-H stretch vibration (�1) has been measured on a Ni(100) surface. Methane molecules were accelerated to kinetic energies of 49 and 63:5 kJ=mol in a molecular beam and vibrationally excited to �1 by stimulated Raman pumping before surface impact at normal incidence. The reactivity of the symmetric-stretch excited CH4 is about an order of magnitude higher than that of methane excited to the antisymmetric stretch (�3) reported by Juurlink et al. [Phys. Rev. Lett. 83, 868 (1999)] and is similar to that we have previously observed for the excitation of the first overtone (2�3). The difference between the state-resolved reactivity for �1 and �3 is consistent with predictions of a vibrationally adiabatic model of the methane reaction dynamics and indicates that statistical models cannot correctly describe the chemisorption of CH4 on nickel.

Local spaces: open minds - inspirational ideas for managing lowland commons and other green spaces

The Chiltern commons are typical of those in the south east of England: small and numerous, but with the potential to provide important natural green space whilst contributing to environmental sustainability. In order to keep commons in good heart, they need to be managed. However, as activities such as grazing and coppicing become unviable on the commons, owners need to find sustainable roles beyond traditional agricultural and silvicultural practices. This paper examines ways of making management pay. It begins by exploring the economic, social and environmental challenges of sustainable management within the context of contemporary life. Section 2 identifies the different ways in which revenue contributions might be made towards the management of commons. Section 3 examines the relevant legal and other restrictions and Section 4 offers insights into where management proposals might offer multiple positive benefits, but also where there is the potential to cause conflict with environmental and social interests. Section 5 explores alternative funding streams for commons. Finally, Section 6 concludes with practical tips for the owners and managers of commons in the Chilterns and identifies areas for further research. Full references, links and resources are provided in the footnotes and appendix.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.