Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Technologies for biological containment of GM and Non-GM crops

International Perspective The development of GM technology continues to expand into increasing numbers of crops and conferred traits. Inevitably, the focus remains on the major field crops of soybean, maize, cotton, oilseed rape and potato with introduced genes conferring herbicide tolerance and/or pest resistance. Although there are comparatively few GM crops that have been commercialised to date, GM versions of 172 plant species have been grown in field trials in 31 countries. European Crops with Containment Issues Of the 20 main crops in the EU there are four for which GM varieties are commercially available (cotton, maize for animal feed and forage, and oilseed rape). Fourteen have GM varieties in field trials (bread wheat, barley, durum wheat, sunflower, oats, potatoes, sugar beet, grapes, alfalfa, olives, field peas, clover, apples, rice) and two have GM varieties still in development (rye, triticale). Many of these crops have hybridisation potential with wild and weedy relatives in the European flora (bread wheat, barley, oilseed rape, durum wheat, oats, sugar beet and grapes), with escapes (sunflower); and all have potential to cross-pollinate fields non-GM crops. Several fodder crops, forestry trees, grasses and ornamentals have varieties in field trials and these too may hybridise with wild relatives in the European flora (alfalfa, clover, lupin, silver birch, sweet chestnut, Norway spruce, Scots pine, poplar, elm, Agrostis canina, A. stolonifera, Festuca arundinacea, Lolium perenne, L. multiflorum, statice and rose). All these crops will require containment strategies to be in place if it is deemed necessary to prevent transgene movement to wild relatives and non-GM crops. Current Containment Strategies A wide variety of GM containment strategies are currently under development, with a particular focus on crops expressing pharmaceutical products. Physical containment in greenhouses and growth rooms is suitable for some crops (tomatoes, lettuce) and for research purposes. Aquatic bioreactors of some non-crop species (algae, moss, and duckweed) expressing pharmaceutical products have been adopted by some biotechnology companies. There are obvious limitations of the scale of physical containment strategies, addressed in part by the development of large underground facilities in the US and Canada. The additional resources required to grow plants underground incurs high costs that in the long term may negate any advantage of GM for commercial productioNatural genetic containment has been adopted by some companies through the selection of either non-food/feed crops (algae, moss, duckweed) as bio-pharming platforms or organisms with no wild relatives present in the local flora (safflower in the Americas). The expression of pharmaceutical products in leafy crops (tobacco, alfalfa, lettuce, spinach) enables growth and harvesting prior to and in the absence of flowering. Transgenically controlled containment strategies range in their approach and degree of development. Plastid transformation is relatively well developed but is not suited to all traits or crops and does not offer complete containment. Male sterility is well developed across a range of plants but has limitations in its application for fruit/seed bearing crops. It has been adopted in some commercial lines of oilseed rape despite not preventing escape via seed. Conditional lethality can be used to prevent flowering or seed development following the application of a chemical inducer, but requires 100% induction of the trait and sufficient application of the inducer to all plants. Equally, inducible expression of the GM trait requires equally stringent application conditions. Such a method will contain the trait but will allow the escape of a non-functioning transgene. Seed lethality (‘terminator’ technology) is the only strategy at present that prevents transgene movement via seed, but due to public opinion against the concept it has never been trialled in the field and is no longer under commercial development. Methods to control flowering and fruit development such as apomixis and cleistogamy will prevent crop-to-wild and wild-to-crop pollination, but in nature both of these strategies are complex and leaky. None of the genes controlling these traits have as yet been identified or characterised and therefore have not been transgenically introduced into crop species. Neither of these strategies will prevent transgene escape via seed and any feral apomicts that form are arguably more likely to become invasives. Transgene mitigation reduces the fitness of initial hybrids and so prevents stable introgression of transgenes into wild populations. However, it does not prevent initial formation of hybrids or spread to non-GM crops. Such strategies could be detrimental to wild populations and have not yet been demonstrated in the field. Similarly, auxotrophy prevents persistence of escapes and hybrids containing the transgene in an uncontrolled environment, but does not prevent transgene movement from the crop. Recoverable block of function, intein trans-splicing and transgene excision all use recombinases to modify the transgene in planta either to induce expression or to prevent it. All require optimal conditions and 100% accuracy to function and none have been tested under field conditions as yet. All will contain the GM trait but all will allow some non-native DNA to escape to wild populations or to non-GM crops. There are particular issues with GM trees and grasses as both are largely undomesticated, wind pollinated and perennial, thus providing many opportunities for hybridisation. Some species of both trees and grass are also capable of vegetative propagation without sexual reproduction. There are additional concerns regarding the weedy nature of many grass species and the long-term stability of GM traits across the life span of trees. Transgene stability and conferred sterility are difficult to trial in trees as most field trials are only conducted during the juvenile phase of tree growth. Bio-pharming of pharmaceutical and industrial compounds in plants Bio-pharming of pharmaceutical and industrial compounds in plants offers an attractive alternative to mammalian-based pharmaceutical and vaccine production. Several plantbased products are already on the market (Prodigene’s avidin, β-glucuronidase, trypsin generated in GM maize; Ventria’s lactoferrin generated in GM rice). Numerous products are in clinical trials (collagen, antibodies against tooth decay and non-Hodgkin’s lymphoma from tobacco; human gastric lipase, therapeutic enzymes, dietary supplements from maize; Hepatitis B and Norwalk virus vaccines from potato; rabies vaccines from spinach; dietary supplements from Arabidopsis). The initial production platforms for plant-based pharmaceuticals were selected from conventional crops, largely because an established knowledge base already existed. Tobacco and other leafy crops such as alfalfa, lettuce and spinach are widely used as leaves can be harvested and no flowering is required. Many of these crops can be grown in contained greenhouses. Potato is also widely used and can also be grown in contained conditions. The introduction of morphological markers may aid in the recognition and traceability of crops expressing pharmaceutical products. Plant cells or plant parts may be transformed and maintained in culture to produce recombinant products in a contained environment. Plant cells in suspension or in vitro, roots, root cells and guttation fluid from leaves may be engineered to secrete proteins that may be harvested in a continuous, non-destructive manner. Most strategies in this category remain developmental and have not been commercially adopted at present. Transient expression produces GM compounds from non-GM plants via the utilisation of bacterial or viral vectors. These vectors introduce the trait into specific tissues of whole plants or plant parts, but do not insert them into the heritable genome. There are some limitations of scale and the field release of such crops will require the regulation of the vector. However, several companies have several transiently expressed products in clinical and pre-clinical trials from crops raised in physical containment.

An automated calibration method for non-see-through head mounted displays

Accurate calibration of a head mounted display (HMD) is essential both for research on the visual system and for realistic interaction with virtual objects. Yet, existing calibration methods are time consuming and depend on human judgements, making them error prone, and are often limited to optical see-through HMDs. Building on our existing approach to HMD calibration Gilson et al. (2008), we show here how it is possible to calibrate a non-see-through HMD. A camera is placed inside a HMD displaying an image of a regular grid, which is captured by the camera. The HMD is then removed and the camera, which remains fixed in position, is used to capture images of a tracked calibration object in multiple positions. The centroids of the markers on the calibration object are recovered and their locations re-expressed in relation to the HMD grid. This allows established camera calibration techniques to be used to recover estimates of the HMD display's intrinsic parameters (width, height, focal length) and extrinsic parameters (optic centre and orientation of the principal ray). We calibrated a HMD in this manner and report the magnitude of the errors between real image features and reprojected features. Our calibration method produces low reprojection errors without the need for error-prone human judgements.

Hyper-parallel tempering Monte Carlo simulations of Ar adsorption in new models of microporous non-graphitizing activated carbon: effect of microporosity

The adsorption of gases on microporous carbons is still poorly understood, partly because the structure of these carbons is not well known. Here, a model of microporous carbons based on fullerene- like fragments is used as the basis for a theoretical study of Ar adsorption on carbon. First, a simulation box was constructed, containing a plausible arrangement of carbon fragments. Next, using a new Monte Carlo simulation algorithm, two types of carbon fragments were gradually placed into the initial structure to increase its microporosity. Thirty six different microporous carbon structures were generated in this way. Using the method proposed recently by Bhattacharya and Gubbins ( BG), the micropore size distributions of the obtained carbon models and the average micropore diameters were calculated. For ten chosen structures, Ar adsorption isotherms ( 87 K) were simulated via the hyper- parallel tempering Monte Carlo simulation method. The isotherms obtained in this way were described by widely applied methods of microporous carbon characterisation, i. e. Nguyen and Do, Horvath - Kawazoe, high- resolution alpha(a)s plots, adsorption potential distributions and the Dubinin - Astakhov ( DA) equation. From simulated isotherms described by the DA equation, the average micropore diameters were calculated using empirical relationships proposed by different authors and they were compared with those from the BG method.

Implications of non-cylindrical flux ropes for magnetic cloud reconstruction techniques and the interpretation of double flux rope events

Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) which exhibit signatures consistent with a magnetic flux rope structure. Techniques for reconstructing flux rope orientation from single-point in situ observations typically assume the flux rope is locally cylindrical, e.g., minimum variance analysis (MVA) and force-free flux rope (FFFR) fitting. In this study, we outline a non-cylindrical magnetic flux rope model, in which the flux rope radius and axial curvature can both vary along the length of the axis. This model is not necessarily intended to represent the global structure of MCs, but it can be used to quantify the error in MC reconstruction resulting from the cylindrical approximation. When the local flux rope axis is approximately perpendicular to the heliocentric radial direction, which is also the effective spacecraft trajectory through a magnetic cloud, the error in using cylindrical reconstruction methods is relatively small (≈ 10∘). However, as the local axis orientation becomes increasingly aligned with the radial direction, the spacecraft trajectory may pass close to the axis at two separate locations. This results in a magnetic field time series which deviates significantly from encounters with a force-free flux rope, and consequently the error in the axis orientation derived from cylindrical reconstructions can be as much as 90∘. Such two-axis encounters can result in an apparent ‘double flux rope’ signature in the magnetic field time series, sometimes observed in spacecraft data. Analysing each axis encounter independently produces reasonably accurate axis orientations with MVA, but larger errors with FFFR fitting.

The effectiveness of non-executive directors in Chinese state-owned enterprises

Purpose – The primary aim of this paper is to examine whether boards of directors with independent members function as effective corporate governance mechanisms in Chinese State-Owned Enterprises(SOEs), by analysing four characteristics of non-executive directors (NEDs) that impact on their effectiveness, namely their degree of independence, information, incentive, and competence. Design/methodology/approach – Being exploratory in nature, the research uses qualitative methods for data collection. It is based on an interpretivist perspective of social sciences, analysing and explaining the factors that influence the effectiveness of NEDs. Findings – The findings indicate that the NED system is weak in China as a result of the concentrated ownership structure, unique business culture, intervention of controlling shareholders and the lack of understanding of the benefits brought by NEDs. Research limitations/implications – The paper examines the salient features of and challenges to the system of NEDs of SOEs in present-day China. It provides an understanding of how the various perceptions of the board, gathered from in-depth interviews of corporate directors, leads to new interpretations of board effectiveness. The research, however, is limited owing to a relatively small sample size and the sensitive nature of the information collected. Originality/value – The study aims to fill gaps in the literature and contribute to it by assessing the “real” views and perceptions of NEDs in China in an institutional environment significantly different from that of the USA, the UK and other western economies.

Validation of ACE-FTS satellite data in the upper troposphere/lower stratosphere (UTLS) using non-coincident measurements

CO, O3, and H2O data in the upper troposphere/lower stratosphere (UTLS) measured by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer(ACE-FTS) on Canada’s SCISAT-1 satellite are validated using aircraft and ozonesonde measurements. In the UTLS, validation of chemical trace gas measurements is a challenging task due to small-scale variability in the tracer fields, strong gradients of the tracers across the tropopause, and scarcity of measurements suitable for validation purposes. Validation based on coincidences therefore suffers from geophysical noise. Two alternative methods for the validation of satellite data are introduced, which avoid the usual need for coincident measurements: tracer-tracer correlations, and vertical tracer profiles relative to tropopause height. Both are increasingly being used for model validation as they strongly suppress geophysical variability and thereby provide an “instantaneous climatology”. This allows comparison of measurements between non-coincident data sets which yields information about the precision and a statistically meaningful error-assessment of the ACE-FTS satellite data in the UTLS. By defining a trade-off factor, we show that the measurement errors can be reduced by including more measurements obtained over a wider longitude range into the comparison, despite the increased geophysical variability. Applying the methods then yields the following upper bounds to the relative differences in the mean found between the ACE-FTS and SPURT aircraft measurements in the upper troposphere (UT) and lower stratosphere (LS), respectively: for CO ±9% and ±12%, for H2O ±30% and ±18%, and for O3 ±25% and ±19%. The relative differences for O3 can be narrowed down by using a larger dataset obtained from ozonesondes, yielding a high bias in the ACEFTS measurements of 18% in the UT and relative differences of ±8% for measurements in the LS. When taking into account the smearing effect of the vertically limited spacing between measurements of the ACE-FTS instrument, the relative differences decrease by 5–15% around the tropopause, suggesting a vertical resolution of the ACE-FTS in the UTLS of around 1 km. The ACE-FTS hence offers unprecedented precision and vertical resolution for a satellite instrument, which will allow a new global perspective on UTLS tracer distributions.

Can Rachman’s indirect pathways be used to un-learn fear? A prospective paradigm to test whether children’s fears can be reduced using positive information and modelling a non-anxious response

This study investigated whether children’s fears could be un-learned using Rachman’s indirect pathways for learning fear. We hypothesised that positive information and modelling a non-anxious response are effective methods of un-learning fears acquired through verbal information. One hundred and seven children aged 6–8 years received negative information about one animal and no information about another. Fear beliefs and behavioural avoidance were measured. Children were randomised to receive positive verbal information, modelling, or a control task. Fear beliefs and behavioural avoidance were measured again. Positive information and modelling led to lower fear beliefs and behavioural avoidance than the control condition. Positive information was more effective than modelling in reducing fear beliefs and both methods significantly reduced behavioural avoidance. The results support Rachman’s indirect pathways as viable fear un-learning pathways and supports associative learning theories.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

On SETAR non-linearity and forecasting

We compare linear autoregressive (AR) models and self-exciting threshold autoregressive (SETAR) models in terms of their point forecast performance, and their ability to characterize the uncertainty surrounding those forecasts, i.e. interval or density forecasts. A two-regime SETAR process is used as the data-generating process in an extensive set of Monte Carlo simulations, and we consider the discriminatory power of recently developed methods of forecast evaluation for different degrees of non-linearity. We find that the interval and density evaluation methods are unlikely to show the linear model to be deficient on samples of the size typical for macroeconomic data

Software-based study of a non-sorting method for median calculation on a set of integer numbers

This paper presents a software-based study of a hardware-based non-sorting median calculation method on a set of integer numbers. The method divides the binary representation of each integer element in the set into bit slices in order to find the element located in the middle position. The method exhibits a linear complexity order and our analysis shows that the best performance in execution time is obtained when slices of 4-bit in size are used for 8-bit and 16-bit integers, in mostly any data set size. Results suggest that software implementation of bit slice method for median calculation outperforms sorting-based methods with increasing improvement for larger data set size. For data set sizes of N > 5, our simulations show an improvement of at least 40%.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.