Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Structural transformation of graphite by arc-discharge

The formation of novel structures by the passage of an electric current through graphite is described. These structures apparently consist of hollow three-dimensional graphitic shells bounded by curved and faceted planes, typically made up of two graphene layers. The curved structures were frequently decorated with nano-scale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and the nanotubes is intimately connected. Small nanotubes or nanoparticles were also sometimes found encapsulated inside the hollow structures, while fullerene-like particles were often seen attached to the outside surfaces. With their high surface areas and structural perfection, the new carbon structures may have applications as anodes of lithium ion batteries or as components of composite materials.

Molecular dynamics simulation insight into the mechanism of phenol adsorption at low coverages from aqueous solutions on microporous carbons

MD simulation studies showing the influence of porosity and carbon surface oxidation on phenol adsorption from aqueous solutions on carbons are reported. Based on a realistic model of activated carbon, three carbon structures with gradually changed microporosity were created. Next, a different number of surface oxygen groups was introduced. The pores with diameters around 0.6 nm are optimal for phenol adsorption and after the introduction of surface oxygen functionalities, adsorption of phenol decreases (in accordance with experimental data) for all studied models. This decrease is caused by a pore blocking effect due to the saturation of surface oxygen groups by highly hydrogen-bounded water molecules.

Ultrathin graphitic structures and carbon nanotubes in a purified synthetic graphite

A new class of carbon structure is reported, which consists of microscale graphitic shells bounded by curved and faceted planes containing two to five layers. These structures were originally found in a commercial graphite produced by the Acheson process, followed by a purification treatment. The particles, which could be several hundreds of nanometres in size, were frequently decorated with nanoscale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and that of the nanotubes are intimately connected. The structures are believed to form during a purification process which involves passing an electric current through the graphite in the presence of a reactive gas. In support of this, it is shown that similar particles can be produced in a standard carbon arc apparatus. With their extremely thin graphene walls and high surface areas, the new structures may have a range of useful properties.

Boundary integral methods for singularly perturbed boundary value problems

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Characterization of a highly biodiverse floodplain meadow using hyperspectral remote sensing within a plant functional trait framework

We assessed the potential for using optical functional types as effective markers to monitor changes in vegetation in floodplain meadows associated with changes in their local environment. Floodplain meadows are challenging ecosystems for monitoring and conservation because of their highly biodiverse nature. Our aim was to understand and explain spectral differences among key members of floodplain meadows and also characterize differences with respect to functional traits. The study was conducted on a typical floodplain meadow in UK (MG4-type, mesotrophic grassland type 4, according to British National Vegetation Classification). We compared two approaches to characterize floodplain communities using field spectroscopy. The first approach was sub-community based, in which we collected spectral signatures for species groupings indicating two distinct eco-hydrological conditions (dry and wet soil indicator species). The other approach was “species-specific”, in which we focused on the spectral reflectance of three key species found on the meadow. One herb species is a typical member of the MG4 floodplain meadow community, while the other two species, sedge and rush, represent wetland vegetation. We also monitored vegetation biophysical and functional properties as well as soil nutrients and ground water levels. We found that the vegetation classes representing meadow sub-communities could not be spectrally distinguished from each other, whereas the individual herb species was found to have a distinctly different spectral signature from the sedge and rush species. The spectral differences between these three species could be explained by their observed differences in plant biophysical parameters, as corroborated through radiative transfer model simulations. These parameters, such as leaf area index, leaf dry matter content, leaf water content, and specific leaf area, along with other functional parameters, such as maximum carboxylation capacity and leaf nitrogen content, also helped explain the species’ differences in functional dynamics. Groundwater level and soil nitrogen availability, which are important factors governing plant nutrient status, were also found to be significantly different for the herb/wetland species’ locations. The study concludes that spectrally distinguishable species, typical for a highly biodiverse site such as a floodplain meadow, could potentially be used as target species to monitor vegetation dynamics under changing environmental conditions.

School effectiveness and the displacement of equity discourses in education

An essential aspect of school effectiveness theory is the shift from the social to the organisational context, from the macro- to the micro-culture. The school is represented largely as a bounded institution, set apart, but also in a precarious relationship with the broader social context. It is ironic that at a time when social disadvantage appears to be increasing in Britain and elsewhere, school effectiveness theory places less emphasis on poverty, deprivation and social exclusion. Instead, it places more emphasis on organisational factors such as professional leadership, home/school partnerships, the monitoring of academic progress, shared vision and goals. In this article, the authors evaluate the extent to which notions of effectiveness have displaced concerns about equity in theories of educational change. They explore the extent to which the social structures of gender, ethnicity, sexualities, special needs, social class, poverty and other historical forms of inequality have been incorporated into or distorted and excluded from effectiveness thinking.

Innovation in construction: a sociology of technology approach

An alternative approach to understanding innovation is made using two intersecting ideas. The first is that successful innovation requires consideration of the social and organizational contexts in which it is located. The complex context of construction work is characterized by inter-organizational collaboration, a project-based approach and power distributed amongst collaborating organizations. The second is that innovations can be divided into two modes: ‘bounded’, where the implications of innovation are restricted within a single, coherent sphere of influence, and ‘unbounded’, where the effects of implementation spill over beyond this. Bounded innovations are adequately explained within the construction literature. However, less discussed are unbounded innovations, where many firms' collaboration is required for successful implementation, even though many innovations can be considered unbounded within construction's inter-organizational context. It is argued that unbounded innovations require an approach to understand and facilitate the interactions both within a range of actors and between the actors and technological artefacts. The insights from a sociology of technology approach can be applied to the multiplicity of negotiations and alignments that constitute the implementation of unbounded innovation. The utility of concepts from the sociology of technology, including ‘system building’ and ‘heterogeneous engineering’, is demonstrated by applying them to an empirical study of an unbounded innovation on a major construction project (the new terminal at Heathrow Airport, London, UK). This study suggests that ‘system building’ contains outcomes that are not only transformations of practices, processes and systems, but also the potential transformation of technologies themselves.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Fibrils and nanotubes assembled from a modified amyloid-β peptide fragment differ in the packing of the same β-sheet building blocks

The peptide AAKLVFF assembles into fibrils in water and nanotubes in methanol. Solid-state NMR data are consistent with fibrils constructed from β-sheet bilayers and nanotubes bounded by a wall of offset β-sheet monolayers. Remarkably distinct morphologies are thus traced to subtle differences in the arrangement of the same fundamental building blocks.

Causal volumes in distributed virtual reality

Research to date has tended to concentrate on bandwidth considerations to increase scalability in distributed interactive simulation and virtual reality systems. This paper proposes that the major concern for latency in user interaction is that of the fundamental limit of communication rate due to the speed of light. Causal volumes and surfaces are introduced as a model of the limitations of causality caused by this fundamental delay. The concept of virtual world critical speed is introduced, which can be determined from the causal surface. The implications of the critical speed are discussed, and relativistic dynamics are used to constrain the object speed, in the same way speeds are bounded in the real world.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.