The influence of surface tension upon trapped waves and hydraulic falls

We consider steady two-dimensional free-surface flows past submerged obstructions on the bottom of a channel. The flow is assumed to be irrotational, and the fluid inviscid and incompressible. Both the effects of gravity and surface tension are considered. Critical flow solutions with subcritical flow upstream and supercritical flow downstream are sought using fully nonlinear boundary integral equation techniques based on the Cauchy integral formula. When a second submerged obstruction is included further upstream in the flow configuration in the absence of surface tension, solutions which have a train of waves trapped between the two obstacles before the critical flow have already been found (Dias and Vanden-Broeck 2004). We extend this work by including the effects of surface tension. Trapped wave solutions are found upstream for small values of the Bond number, for some values of the Froude number. Other types of trapped waves are found for stronger tension when the second obstruction is placed downstream of the hydraulic fall generated by the first obstacle

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument

A Systematic Analysis of Errors in the Simplification of a Rational Expression

Exploring the errors that mathematics students frequently make is a means by which teachers can gain a better understanding of students’ difficulties. Reported here are the process by which the algebraic working of 95 undergraduate students who incorrectly simplified a rational expression was analysed and the results of the analysis. Initially, a deductive approach to analysing the errors was planned, categorising students’ mistakes using the error types identified, named and described in the literature. In reviewing the literature, however, it became clear that this would be no simple task. The large body of literature, while rich in examples of “typical errors” that could be expected in students’ working, had two limitations. Firstly, the error types lacked precise descriptions and were mainly described by example only. Secondly, insufficient details of the procedures used to categorise the errors prevented replication of the categorising process. Consequently, a mainly inductive approach, that categorised the errors by their location and inferred student operation was devised. This systematic approach resulted in generating descriptions of three error categories

European Capacity for Monitoring and Assimilating Space-based Climate Change Observations - Status and Prospects

This report, which is based on the findings of a workshop at Ispra in March 2009, provides the scientific background to a forthcoming Commission response to the Space and Competitiveness councils requests that the commission assess the needs for full access to standardised climate change data, the means to provide these data and together with ESA, EUMETSAT and the scientific community define how GMES services can contribute effectively to providing these data. The report therefore focuses primarily, but not exclusively, on space-based Climate data sources. Standardised climate data are needed for climate monitoring, prediction and research, while climate information informs the policy cycle at four key points - Policy definition; Management and scenario building; Reporting requirements; Alarm functions. The workshop identified the 44 Essential Climate Variables defined by GCOS as the minimum set of standardised climate data that the commission should be considering and a gap analysis for the provision of these observations was undertaken. In addition European capacity is analysed according to maturity, differentiating between sustained operational capacity (Envelope Missions/EUMETSAT), non-operationally funded repetitive capacity and additional infrastructure needs in order to fill the gaps are identified. Finally the report discusses co-ordination and governance issues and how to overcome them. The key findings and recommendations are contained in an executive summary.JRC.DDG.H.2-Climate chang

Investigating students’ perceptions of graduate learning outcomes in mathematics

The purpose of this study is to explore the perceptions mathematics students have of the knowledge and skills they develop throughout their programme of study. It addresses current concerns about the employability of mathematics graduates by contributing much needed insight into how degree programmes are developing broader learning outcomes for students majoring in mathematics. Specifically, the study asked students who were close to completing amathematics major (n=144) to indicate the extent to which opportunities to develop mathematical knowledge along with more transferable skills (communication to experts and non-experts, writing, working in teams and thinking ethically) were included and assessed in their major. Their perceptions were compared to the importance they assign to each of these outcomes, their own assessment of improvement during the programme and their confidence in applying these outcomes. Overall, the findings reveal a pattern of high levels of students'agreement that these outcomes are important, but evidence a startling gap when compared to students' perceptions of the extent to which many of these - communication, writing, teamwork and ethical thinking - are actually included and assessed in the curriculum, and their confidence in using such learning

Habitat conversion and global avian biodiversity loss

The magnitude of the impacts of human activities on global biodiversity has been documented at several organizational levels. However, although there have been numerous studies of the effects of local-scale changes in land use (e.g. logging) on the abundance of groups of organisms, broader continental or global-scale analyses addressing the same basic issues remain largely wanting. None the less, changing patterns of land use, associated with the appropriation of increasing proportions of net primary productivity by the human population, seem likely not simply to have reduced the diversity of life, but also to have reduced the carrying capacity of the environment in terms of the numbers of other organisms that it can sustain. Here, we estimate the size of the existing global breeding bird population, and then make a first approximation as to how much this has been modified as a consequence of land-use changes wrought by human activities. Summing numbers across different land-use classes gives a best current estimate of a global population of less than 100 billion breeding bird individuals. Applying the same methodology to estimates of original land-use distributions suggests that conservatively this may represent a loss of between a fifth and a quarter of pre-agricultural bird numbers. This loss is shared across a range of temperate and tropical land-use types

Drought events and their effects on vegetation productivity in China

Many parts of the world have experienced frequent and severe droughts during the last few decades. Most previous studies examined the effects of specific drought events on vegetation productivity. In this study, we characterized the drought events in China from 1982 to 2012 and assessed their effects on vegetation productivity inferred from satellite data. We first assessed the occurrence, spatial extent, frequency, and severity of drought using the Palmer Drought Severity Index (PDSI). We then examined the impacts of droughts on China\u27s terrestrial ecosystems using the Normalized Difference Vegetation Index (NDVI). During the period 1982–2012, China\u27s land area (%) experiencing drought showed an insignificant trend. However, the drought conditions had been more severe over most regions in northern parts of China since the end of the 1990s, indicating that droughts hit these regions more frequently due to the drier climate. The severe droughts substantially reduced annual and seasonal NDVI. The magnitude and direction of the detrended NDVI under drought stress varied with season and vegetation type. The inconsistency between the regional means of PDSI and detrended NDVI could be attributed to different responses of vegetation to drought and the timing, duration, severity, and lag effects of droughts. The negative effects of droughts on vegetation productivity were partly offset by the enhancement of plant growth resulting from factors such as lower cloudiness, warming climate, and human activities (e.g., afforestation, improved agricultural management practices)

The use of AVHRR data for large area vegetation studies

This thesis compares the attributes and limitations of the various Advanced Very High Resolution Radiometer (AVHRR) data types for large area vegetation studies in the context of global change research. In chapter 1, some of the major scientific issues customarily associated with the Global Change concept are outlined, and the specific role of vegetation dynamics in the earth's energy, hydrological and biogeochemical cycles is discussed. Deficiencies in currently available global vegetation data sets and the role of remote sensing as a new source of information are reviewed. This review is supplemented by detailed discussion of the spectral properties of vegetation, soil and water in chapter 2. In chapter 3 the Normalised Difference Vegetation Index (NDVI) and the Perpendicular Vegetation Index (PVI) from 1 km resolution AVHRR High Resolution Picture Transmission (HRPT) data are compared as a means of providing biomass estimates for large geographical areas. The PVI provides better measures of biomass than NDVI, particularly where cover is sparse. Caution in the use of NDVI is recommended. Problems of accurate ground location because of the AVHRR's coarse resolution are highlighted. High resolution (80 m) satellite imagery from the Landsat Multi Spectral Scanner (MSS) is shown to be an effective intermediate step. Comparison with MSS also shows the effect of landscape structure on areal estimates of vegetation cover from the AVHRR HRPT. In chapter 4, MSS and HRPT comparisons show that sensor-induced spatial autocorrelation in AVHRR HRPT data can limit the use of these data for the identification of spatial structure and pattern at full resolution. The same limitation on the use of full resolution data is also found to apply to the spatially sampled AVHRR Global Area Coverage (GAC) archives. In this case local variance induced by sampling in GAC data generation is thought to be the cause. In chapter 5 the structural analysis is extended across a range of resolutions. Sampling artefacts are found for all West African ecosystems at full GAC resolution (4 km), though at coarse resolutions spatial patterns observed with the GAC and the unsampled AVHRR HRPT are very similar. Differences between the two are most pronounced where landscape features are either points or lines. A resolution of 12 km is found to suppress the negative effects of the sampling for all West African ecosystems. At resolutions coarser than 12 km, the GAC data are just as good a measure of landscape structure as the unsampled data. The relevance of these coarse measurement scales to global change research is discussed. Chapter 6 shows that transitions across major ecological zones can be detected at resolutions coarser than 12 km, though the agreement between the sampled and unsampled AVHRR changes both with geographical location and time. This is particularly so for ecosystems affected by fire. Fire is increasingly recognised as a key factor in both the study of global vegetation dynamics directly, and for global change research. This is the focus of chapter 7. Problems relating to the poor sensitivity of the AVHRR's middle-infrared and thermal channels are identified and resolved. The GAC sampling method is shown to affect the sensitivity of these data for fire detection in relation to ecosystem and season. Regional stratification is highlighted as a means of improving fire analysis over large areas, improving land cover classification, and helping in the definition of new cover classes (particularly at continental and global scales) Finally, the results of the previous chapters are discussed with reference to the existing and planned processed AVHRR data archives. The importance of the 12 km limit with reference to the GAC archives is stressed, the need for circumspection in the use of NDVI reiterated, particularly with reference to the derivation of physical measurements from AVHRR, and the requirement for new synergistic approaches to the use of AVHRR with other data emphasised.Ph

Reoptimisation strategies for dynamic vehicle routing problems with proximity-dependent nodes

Autonomous vehicles create new opportunities as well as new challenges to dynamic vehicle routing. The introduction of autonomous vehicles as information-collecting agents results in scenarios, where dynamic nodes are found by proximity. This paper presents a novel dynamic vehicle-routing problem variant with proximity-dependent nodes. Here, we introduced a novel variable, detectability, which determines whether a proximal dynamic node will be detected, based on the sight radius of the vehicle. The problem considered is motivated by autonomous weed-spraying vehicles in large agricultural operations. This work is generalisable to many other autonomous vehicle applications. The first step to crafting a solution approach for the problem is to decide when reoptimisation should be triggered. Two reoptimisation trigger strategies are considered—exogenous and endogenous. Computational experiments compared the strategies for both the classical dynamic vehicle routing problem as well as the introduced variant. Experiments used extensive standardised vehicle-routing problem benchmarks with varying degrees of dynamism and geographical node distributions. The results showed that for both the classical problem and the novel variant, an endogenous trigger strategy is better in most cases, while an exogenous trigger strategy is only suitable when both detectability and dynamism are low. Furthermore, the optimal level of detectability was shown to be dependent on the combination of trigger, degree of dynamism, and geographical node distribution, meaning practitioners may determine the required detectability based on the attributes of their specific problem