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

Continuous prewarping of time for multiuser interactive virtual environments

Dynamic multi-user interactions in a single networked virtual environment suffer from abrupt state transition problems due to communication delays arising from network latency--an action by one user only becoming apparent to another user after the communication delay. This results in a temporal suspension of the environment for the duration of the delay--the virtual world `hangs'--followed by an abrupt jump to make up for the time lost due to the delay so that the current state of the virtual world is displayed. These discontinuities appear unnatural and disconcerting to the users. This paper proposes a novel method of warping times associated with users to ensure that each user views a continuous version of the virtual world, such that no hangs or jumps occur despite other user interactions. Objects passed between users within the environment are parameterized, not by real time, but by a virtual local time, generated by continuously warping real time. This virtual time periodically realigns itself with real time as the virtual environment evolves. The concept of a local user dynamically warping the local time is also introduced. As a result, the users are shielded from viewing discontinuities within their virtual worlds, consequently enhancing the realism of the virtual environment.

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood. An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.

The evolution of innovation capability in multinational enterprise subsidiaries: dual network embeddedness and the divergence of subsidiary specialisation in Taiwan

This paper examines how innovation-related capabilities for production, design and marketing develop at the subsidiary level within multinational enterprises (MNEs). We focus on how subsidiary autonomy and changing opportunities to access internal (MNE) and external (host country) sources of capability contribute in a combined way to the accumulation of specialist capabilities in five Taiwan-based MNE subsidiaries in the semiconductor industry. Longitudinal analysis shows how the accumulation process is subject to discontinuities, as functional divisions are (re)opened and closed during the lifetime of the subsidiary. A composite set of innovation output measures also shows significant variations in within-function levels of capability across our sample. We conclude that subsidiary specialisation and unique subsidiary-specific advantages have evolved in a way that is strongly influenced by the above factors.

Inner plasma structure of the low-latitude reconnection layer

We report a clear transition through a reconnection layer at the low-latitude magnetopause which shows a complete traversal across all reconnected field lines during northwestward interplanetary magnetic field (IMF) conditions. The associated plasma populations confirm details of the electron and ion mixing and the time history and acceleration through the current layer. This case has low magnetic shear with a strong guide field and the reconnection layer contains a single density depletion layer on the magnetosheath side which we suggest results from nearly field-aligned magnetosheath flows. Within the reconnection boundary layer, there are two plasma boundaries, close to the inferred separatrices on the magnetosphere and magnetosheath sides (Ssp and Ssh) and two boundaries associated with the Alfvén waves (or Rotational Discontinuities, RDsp and RDsh). The data are consistent with these being launched from the reconnection site and the plasma distributions are well ordered and suggestive of the time elapsed since reconnection of the field lines observed. In each sub-layer between the boundaries the plasma distribution is different and is centered around the current sheet, responsible for magnetosheath acceleration. We show evidence for a velocity dispersion effect in the electron anisotropy that is consistent with the time elapsed since reconnection. In addition, new evidence is presented for the occurrence of partial reflection of magnetosheath electrons at the magnetopause current layer.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Turbulence dynamics near a turbulent/non-turbulent interface

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (epsilon), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), epsilon decays as z^{-6}, where z is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and epsilon display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness delta of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that delta ~ eta (where eta is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

'Eden Cinema' by Marguerite Duras

Duras’s theatre work has been profoundly neglected by UK theatre academics and practitioners, and Eden Cinema has almost no performance history in Britain. My project asked three interconnected research questions: how developing the performance contributes to understanding Duras’s theatre and specifically Eden Cinema’s problems of performability; how multimedia performance emphasising mediated sound and the live body reconfigures memory, autobiography, storytelling, gender and racial identity; how to locate a performance style appropriate for Durasian narratives of displacement and death which reflect the discontinuous and mutable form of Duras’s ‘texte/film/théâtre’. Drawing on my research interests in gender, post-colonial hybridity and performed deconstruction, I focused my staging decisions on the discontinuities and ambivalences of the text. I addressed performability by avoiding the temptation to resolve the strange ellipses in the text and instead evoked the text’s imperfect and fragmented memories, and its uncertain spatial and temporal locations, by means of a fluid theatrical form. The mise-en-scène represented imagined and remembered spaces simultaneously, and co-existing historical moments. The performance style counterpointed live and mediated action and audio-visual forms. A complex through-composed soundscape, comprising voice-over, sound and music, became a key means for evoking overlapping temporalities, interconnected narratives and fragmented memories that were dispersed across the performance. The disempowerment of the mother figure and the silent indigenous servant in the text was demonstrated through their spatial centrality but physical stillness. The servant’s colonial subaltern identity was paralleled and linked with the mother’s disenfranchisement through their proxemic relationships. I elicited a performance style which evoked ‘characters’, whose being was deferred across different regimes of reality and who ‘haunted’ the stage rather than inhabited it. I developed the project further in the additional written outcomes and presentations, and the subsequent performance of Savannah Bay where problems of performability intensify until embodiment is almost erased except via voice.

The heliospheric magnetic field

The heliospheric magnetic field (HMF) is the extension of the coronal magnetic field carried out into the solar system by the solar wind. It is the means by which the Sun interacts with planetary magnetospheres and channels charged particles propagating through the heliosphere. As the HMF remains rooted at the solar photosphere as the Sun rotates, the large-scale HMF traces out an Archimedean spiral. This pattern is distorted by the interaction of fast and slow solar wind streams, as well as the interplanetary manifestations of transient solar eruptions called coronal mass ejections. On the smaller scale, the HMF exhibits an array of waves, discontinuities, and turbulence, which give hints to the solar wind formation process. This review aims to summarise observations and theory of the small- and large-scale structure of the HMF. Solar-cycle and cycle-to-cycle evolution of the HMF is discussed in terms of recent spacecraft observations and pre-spaceage proxies for the HMF in geomagnetic and galactic cosmic ray records.

Comparing the fit between BREEAM assessment and design processes

This paper explores the mapping of the environmental assessment process onto design and construction processes. A comparative case study method is used to identify and account for variations in the ‘fit’ between these two processes. The analysis compares eight BREEAM projects (although relevant to LEED, GreenStar, etc.) and distinguishes project-level characteristics and dynamics. Drawing on insights from literature on sustainable construction and assessment methods, an analytic framework is developed to examine the effect of clusters of project and assessment level elements on different types of fit (tight, punctual and bolt-on). Key elements distinguishing between types include: prior working experience with project team members, individual commitment to sustainable construction, experience with sustainable construction, project continuity, project-level ownership of the assessment process, and the nature and continuity of assessor involvement. Professionals with ‘sustainable’ experience used BREEAM judiciously to support their designs (along with other frameworks), but less committed professionals tended to treat it purely as an assessment method. More attention needs to be paid to individual levels of engagement with, and understanding of, sustainability in general (rather than knowledge of technical solutions to individual credits), to ownership of the assessment process and to the potential effect of discontinuities at the project level on sustainable design.

Modelling signatures of pulsed magnetopause reconnection in cusp ion dispersion signatures seen at middle altitudes

It is shown that the open magnetosphere model can reproduce both the down-going and the up-going magnetosheath ions seen in the cusp and mantle regions by the Polar satellite at middle altitudes. ?he pass studied shows a series of discontinuities in the ion dispersion, most of which are shown to arise from pulses of magnetopause reconnection rate. A total of 9 pulses are detected in an interval estimated to be about 30 min long, giving a mean repetition period of about 3 min: they vary in length between 0.5 min and 3.5 min and are separated by periods of much slower reconnection of duration 1-3 min. One step is not as predicted for reconnection rate pulses but is explained in terms of compressive motions caused by a pulse of solar wind dynamic pressure. The reconnection site is found to be 16 +/- 3 R-E from the ionosphere along the separatrix field line, placing it at low latitudes on the dayside magnetopause.

Habitat fragmentation reduces genetic diversity and connectivity among toad populations in the Brazilian Atlantic Coastal Forest

Tropical rainforests are becoming increasingly fragmented and understanding the genetic consequences of fragmentation is crucial for conservation of their flora and fauna. We examined populations of the toad Rhinella ornata, a species endemic to Atlantic Coastal Forest in Brazil, and compared genetic diversity among small and medium forest fragments that were either isolated or connected to large forest areas by corridors. Genetic differentiation, as measured by F(ST), was not related to geographic distance among study sites and the size of the fragments did not significantly alter patterns of genetic connectivity. However, population genetic diversity was positively related to fragment size, thus haplotype diversity was lowest in the smallest fragments, likely due to decreases in population sizes. Spatial analyses of genetic discontinuities among groups of populations showed a higher proportion of barriers to gene flow among small and medium fragments than between populations in continuous forest. Our results underscore that even species with relatively high dispersal capacities may, over time, suffer the negative genetic effects of fragmentation, possibly leading to reduced fitness of population and cases of localized extinction. (C) 2008 Elsevier Ltd. All rights reserved.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

First-principles calculation of the AlAs/GaAs interface band structure using a self-energy-corrected local density approximation

We apply a self-energy-corrected local density approximation (LDA) to obtain corrected bulk band gaps and to study the band offsets of AlAs grown on GaAs (AlAs/GaAs). We also investigate the Al(x)Ga(1-x)As/GaAs alloy interface, commonly employed in band gap engineering. The calculations are fully ab initio, with no adjustable parameters or experimental input, and at a computational cost comparable to traditional LDA. Our results are in good agreement with experimental values and other theoretical studies. Copyright (C) EPLA, 2011

Morphology and composition of gold in a lateritic profile, Fazenda Pison ""Garimpo"", Amazon, Brazil

This study describes the morphological evolution of gold grains in a lateritic weathering profile in an equatorial rainforest climate. Primary sources of gold are quartz veins associated with shallow granophyric intrusion. Gold grains were found in fresh ore, saprolite, transition zones, ferruginous duricrust, red latosol, and yellow latosol. Irregularly shaped grains predominate, with smaller proportions of dendritic and prismatic forms. Gold grains are weathered in the uppermost 10 m of the regolith. Mean gold grain size is maximum in the duricrust (> 125 mu m) and decreases progressively upward into the yellow latosol (<90 mu m). Voids and corrosion pits appear on grain surfaces, and progressive rounding is observed from the bottom of the profile to the top. Gold grains can be classified as either homogeneous or zoned with respect to their chemical composition. Homogeneous grains contain 2-15% Ag (mean 8.3%). Zoned grains have more variable Ag contents; grain cores have means of approximately 10% or 23% Ag, with Ag-poor zones of approximately 3.7% Ag along internal discontinuities and/or outer rims. Formation of Ag-poor rims is due to preferential depletion of silver. Processes responsible for duricrust formation may preserve some grains as large aggregates, but subsequent transformation into latosol further modifies them. (c) 2007 Elsevier Ltd. All rights reserved.