Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Planning for the reuse of redundant defence estate: disposal processes, policy frameworks and development impacts

This paper reviews recent research and other literature concerning the planning and development of redundant defence estate. It concentrates on UK sources but includes reference to material from Europe and the North America were it is relevant for comparative purposes. It introduces the topic by providing a brief review of the recent restructuring of the UK defence estate and then proceeds to examine the various planning policy issues generated by this process; the policy frameworks used to guide it; comparable approaches to surplus land disposal and the appraisal of impacts; and ending the main body of the review with an analyse of the economic, social and environmental impacts of military base closure and redevelopment. It concludes that there is a significant body of work focusing on the reuse and redevelopment of redundant defence estate in the UK and abroad, but that much of this work is based on limited research or on personal experience. One particular weakness of the current literature is that it does not fully reflect the institutional difficulties posed by the disposal process and the day-to-day pressures which MOD personnel have to deal with. In doing this, it also under-emphasises the embedded cultures of individuals and professional groups who are required to operationalise the policies, procedures and practices for planning and redeveloping redundant defence estate.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

Hydrochemical processes in lowland rivers: insights from in situ, high-resolution monitoring

This paper introduces new insights into the hydrochemical functioning of lowland river systems using field-based spectrophotometric and electrode technologies. The streamwater concentrations of nitrogen species and phosphorus fractions were measured at hourly intervals on a continuous basis at two contrasting sites on tributaries of the River Thames – one draining a rural catchment, the River Enborne, and one draining a more urban system, The Cut. The measurements complement those from an existing network of multi-parameter water quality sondes maintained across the Thames catchment and weekly monitoring based on grab samples. The results of the sub-daily monitoring show that streamwater phosphorus concentrations display highly complex dynamics under storm conditions dependent on the antecedent catchment wetness, and that diurnal phosphorus and nitrogen cycles occur under low flow conditions. The diurnal patterns highlight the dominance of sewage inputs in controlling the streamwater phosphorus and nitrogen concentrations at low flows, even at a distance of 7 km from the nearest sewage treatment works in the rural River Enborne. The time of sample collection is important when judging water quality against ecological thresholds or standards. An exhaustion of the supply of phosphorus from diffuse and multiple septic tank sources during storm events was evident and load estimation was not improved by sub-daily monitoring beyond that achieved by daily sampling because of the eventual reduction in the phosphorus mass entering the stream during events. The results highlight the utility of sub-daily water quality measurements and the discussion considers the practicalities and challenges of in situ, sub-daily monitoring.

Negotiating social identities: the influence of gender, age and ethnicity on young people’s ‘Street Careers’ in Tanzania

This paper explores the diverse ways that children and young people negotiate their social identities and construct their life course trajectories on the street, based on ethnographic research with street children in Tanzania. Drawing on the concept of a ‘street career’, I show how differences of age, gender and ethnicity intersect with the time spent on the street, to influence young people’s livelihood strategies, use of public space, access to services, and adherence to cultural rites of passage. Using the notion of ‘gender performativity’, I analyse how young people actively reconfigure gender norms and the concept of ‘the family’ on the street.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Globalizing Mediterranean identities: the overlapping spheres of Egyptian, Greek and Roman worlds at Trimithis

This article furthers recent gains made in applying globalization perspectives to the Roman world by exploring two Romano-Egyptian houses that used Roman material culture in different ways within the city known as Trimithis (modern day Amheida, in Egypt). In so doing, I suggest that concepts drawn from globalization theory will help us to disentangle and interpret how homogeneous Roman Mediterranean goods may appear heterogeneous on the local level. This theoretical vantage is broadly applicable to other regions in the Roman Mediterranean, as well as other environments in which individuals reflected a multifaceted relationship with their local identity and the broader social milieu.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.