On the numerical evaluation of finite-part integrals involving an algebraic singularity

Thesis (PhD)--Stellenbosch University, 1975.ENGLISH ABSTRACT: Some problems of applied mathematics, for instance in the fields of aerodynamics or electron optics, involve certain singular integrals which do not exist classically. The problems can, however, be solved pLovided that such integrals are interpreted as finite-part integrals. Although the concept of a finite-part integral has existed for about fifty years, it was possible to define it rigorously only by means of distribution theory, developed about twenty-five years ago. But, to the best of our knowledge, no quadrature formula for the numerical eva= luation of finite-part integrals ha~ been given in the literature. The main concern of this thesis is the study and discussion of.two kinds of quadrature formulae for evaluating finite-part integrals in= volving an algebraic singularity. Apart from a historical introduction, the first chapter contains some physical examples of finite-part integrals and their definition based on distribution theory. The second chapter treats the most im= portant properties of finite-part integrals; in particular we study their behaviour under the most common rules for ordinary integrals. In chapters three and four we derive a quadrature formula for equispaced stations and one which is optimal in the sense of the Gauss-type quadra= ture. In connection with the latter formula, we also study a new class of orthogonal polynomials. In the fifth and.last chapter we give a derivative-free error bound for the equispaced quadrature formula. The error quantities which are independent of the integrand were computed for the equispaced quadrature formula and are also given. In the case of some examples, we compare the computed error bounds with the actual errors. ~esides this theoretical investigation df finite-part integrals, we also computed - for several orders of the algebraic singularity the coefficients for both of the aforesaid quadrature formulae, in which the number of stations ranges from three up to twenty. In the case of the equispaced quadrature fortnu1a,we give the weights and - for int~ger order of the singularity - the coefficients for a numerical derivative of the integrand function. For the Gauss-type quadrature, we give the stations, the corresponding weights and the coefficients of the orthogonal polynomials. These data are being published in a separate report [18] which also contains detailed instructions on the use of the tables

Theory of coherent acoustic phonons in InGaN/GaN multi-quantum wells

A microscopic theory for the generation and propagation of coherent LA phonons in pseudomorphically strained wurzite (0001) InGaN/GaN multi-quantum well (MQW) p-i-n diodes is presented. The generation of coherent LA phonons is driven by photoexcitation of electron-hole pairs by an ultrafast Gaussian pump laser and is treated theoretically using the density matrix formalism. We use realistic wurzite bandstructures taking valence-band mixing and strain-induced piezo- electric fields into account. In addition, the many-body Coulomb ineraction is treated in the screened time-dependent Hartree-Fock approximation. We find that under typical experimental conditions, our microscopic theory can be simplified and mapped onto a loaded string problem which can be easily solved.Comment: 20 pages, 17 figure

Coherent Phonons in Carbon Nanotubes and Graphene

We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.Comment: 48 pages, 41 figure

Establishing effective conservation management strategies for a poorly known endangered species: A case study using Australia’s night parrot (Pezoporus occidentalis)

An evidence-based approach to the conservation management of a species requires knowledge of that species’ status, distribution, ecology, and threats. Coupled with budgets for specific conservation strategies, this knowledge allows prioritisation of funding toward activities that maximise benefit for the species. However, many threatened species are poorly known, and determining which conservation strategies will achieve this is difficult. Such cases require approaches that allow decision-making under uncertainty. Here we used structured expert elicitation to estimate the likely benefit of potential management strategies for the Critically Endangered and, until recently, poorly known Night Parrot (Pezoporus occidentalis). Experts considered cat management the single most effective management strategy for the Night Parrot. However, a combination of protecting and actively managing existing intact Night Parrot habitat through management of grazing, controlling feral cats, and managing fire specifically to maintain Night Parrot habitat was thought to result in the greatest conservation gains. The most cost-effective strategies were thought to be fire management to maintain Night Parrot habitat, and intensive cat management using control methods that exploit local knowledge of cat movements and ecology. Protecting and restoring potentially suitable, but degraded, Night Parrot habitat was considered the least effective and least cost-effective strategy. These expert judgements provide an informed starting point for land managers implementing on-ground programs targeting the Night Parrot, and those developing policy aimed at the species’ longer-term conservation. As a set of hypotheses, they should be implemented, assessed, and improved within an adaptive management framework that also considers the likely co-benefits of these strategies for other species and ecosystems. The broader methodology is applicable to conservation planning for the management and conservation of other poorly known threatened species

Eaten out of house and home:impacts of grazing on ground-dwelling reptiles in Australian grasslands and grassy woodlands

Large mammalian grazers can alter the biotic and abiotic features of their environment through their impacts on vegetation. Grazing at moderate intensity has been recommended for biodiversity conservation. Few studies, however, have empirically tested the benefits of moderate grazing intensity in systems dominated by native grazers. Here we investigated the relationship between (1) density of native eastern grey kangaroos, Macropus giganteus, and grass structure, and (2) grass structure and reptiles (i.e. abundance, richness, diversity and occurrence) across 18 grassland and grassy Eucalyptus woodland properties in south-eastern Australia. There was a strong negative relationship between kangaroo density and grass structure after controlling for tree canopy cover. We therefore used grass structure as a surrogate for grazing intensity. Changes in grazing intensity (i.e. grass structure) significantly affected reptile abundance, reptile species richness, reptile species diversity, and the occurrence of several ground-dwelling reptiles. Reptile abundance, species richness and diversity were highest where grazing intensity was low. Importantly, no species of reptile was more likely to occur at high grazing intensities. Legless lizards (Delma impar, D. inornata) were more likely to be detected in areas subject to moderate grazing intensity, whereas one species (Hemiergis talbingoensis) was less likely to be detected in areas subject to intense grazing and three species (Menetia greyii, Morethia boulengeri, and Lampropholis delicata) did not appear to be affected by grazing intensity. Our data indicate that to maximize reptile abundance, species richness, species diversity, and occurrence of several individual species of reptile, managers will need to subject different areas of the landscape to moderate and low grazing intensities and limit the occurrence and extent of high grazing

Computational Approaches to Explainable Artificial Intelligence:Advances in Theory, Applications and Trends

Deep Learning (DL), a groundbreaking branch of Machine Learning (ML), has emerged as a driving force in both theoretical and applied Artificial Intelligence (AI). DL algorithms, rooted in complex and non-linear artificial neural systems, excel at extracting high-level features from data. DL has demonstrated human-level performance in real-world tasks, including clinical diagnostics, and has unlocked solutions to previously intractable problems in virtual agent design, robotics, genomics, neuroimaging, computer vision, and industrial automation. In this paper, the most relevant advances from the last few years in Artificial Intelligence (AI) and several applications to neuroscience, neuroimaging, computer vision, and robotics are presented, reviewed and discussed. In this way, we summarize the state-of-the-art in AI methods, models and applications within a collection of works presented at the 9 International Conference on the Interplay between Natural and Artificial Computation (IWINAC). The works presented in this paper are excellent examples of new scientific discoveries made in laboratories that have successfully transitioned to real-life applications

The HERMES Spectrometer

The HERMES experiment is collecting data on inclusive and semi-inclusive deep inelastic scattering of polarised positrons from polarised targets of Il, D, and He-3. These data give information on the spin structure of the nucleon. This paper describes the forward angle spectrometer built for this purpose. The spectrometer includes numerous tracking chambers (micro-strip gas chambers, drift and proportional chambers) in front of and behind a 1.3 T.m magnetic field, as well as an extensive set of detectors for particle identification (a lead-glass calorimeter, a pre-shower detector, a transition radiation detector, and a threshold Cherenkov detector). Two of the main features of the spectrometer are its good acceptance and identification of both positrons and hadrons, in particular pions. These characteristics, together with the purity of the targets, are allowing HERMES to make unique contributions to the understanding of how the spins of the quarks contribute to the spin of the nucleon. (C) 1998 Elsevier Science B.V. All rights reserved