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.

Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.

Getting pupils to 'see the point' of school subjects: history, a case study

This paper examines the factors that influence pupil take up of a subject, in this case history, at GCSE. The research indicates that pupils enjoy history but significant factors prevent many from choosing it for further study; these include factors that are beyond the control of teachers, such as government policy and the way this is interpreted by senior managers in school, and factors that are within the control of teachers. The paper suggests that there are lessons that departments can learn from more successful departments but there are also important side effects of government policy that are having unintended consequences.

In search of the aim of the free movement of persons provisions: has the Court of Justice missed the point?

The Court of Justice has, over the years, often been vilified for exceeding the limits of its jurisdiction by interpreting the provisions of Community legislation in a way not seem originally envisaged by its drafters. A recent example of this approach was a cluster of cases in the context of the free movement of workers and the freedom of establishment (Ritter-Coulais and its progeny), where the Court included within the scope of those provisions situations which, arguably, did not present a sufficient link with their (economic) aim. In particular, in that case law the Court accepted that the mere exercise of free movement for the purpose of taking up residence in the territory of another Member State whilst continuing to exercise an economic activity in the State of origin, suffices for bringing a Member State national within the scope of Articles 39 and 43 EC. It is argued that the most plausible explanation for this approach is that the Court now wishes to re-read the economic fundamental freedoms in such a way as to include within their scope all economically active Union citizens, irrespective of whether their situation presents a sufficient link with the exercise of an economic activity in a cross-border context. It is suggested that this approach is problematic for a number of reasons. It is, therefore, concluded that the Court should revert to its orthodox approach, according to which only situations that involve Union citizens who have moved between Member States for the purpose of taking up an economic activity should be included within the scope of the market freedoms.

Are the debates on water privatization missing the point? Experiences from Africa, Asia and Latin America

This paper has two principal aims: first, to unravel some of the arguments mobilized in the controversial privatization debate, and second, to review the scale and nature of private sector provision of water and sanitation in Africa, Asia and Latin America. Despite being vigorously promoted in the policy arena and having been implemented in several countries in the South in the 1990s, privatization has achieved neither the scale nor benefits anticipated. In particular, the paper is pessimistic about the role that privatization can play in achieving the Millennium Development Goals of halving the number of people without access to water and sanitation by 2015. This is not because of some inherent contradiction between private profits and the public good, but because neither publicly nor privately operated utilities are well suited to serving the majority of low-income households with inadequate water and sanitation, and because many of the barriers to service provision in poor settlements can persist whether water and sanitation utilities are publicly or privately operated. This is not to say that well-governed localities should not choose to involve private companies in water and sanitation provision, but it does imply that there is no justification for international agencies and agreements to actively promote greater private sector participation on the grounds that it can significantly reduce deficiencies in water and sanitation services in the South.

Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.