Showing papers by "University of Exeter published in 1991"

The Philosophy of Mathematics Education

Abstract: This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

The Physics of Phonons

Abstract: Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.

Optical excitation of surface plasmons: An introduction

Abstract: Beginning from low level concepts the basic understanding for the optical excitation of surface plasmons is developed. Prism coupling using the attenuated total reflection technique is discussed as well as the less traditional grating coupling technique. A brief discussion of some recent developments using twisted gratings is also presented. Finally a short summary of the potential device applications is given.

Long-range surface modes supported by thin films

Abstract: A detailed analysis of the surface modes of a thin slab of material of dielectric constant ${\mathrm{\ensuremath{\epsilon}}}_{2}$ (=${\mathrm{\ensuremath{\epsilon}}}_{\mathit{r}2}$-i${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}2}$) surrounded symmetrically by dielectric media is presented. Results show that in the thin-film limit, as well as the well-known long-range surface plasmon for a thin metal layer and the TM guided mode for a thin dielectric, a long-range surface mode exists for almost any value of ${\mathrm{\ensuremath{\epsilon}}}_{2}$. This is even true if the imaginary part of ${\mathrm{\ensuremath{\epsilon}}}_{2}$, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}2}$, is much larger than the real part ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{r}2}$. We also find that a long-range surface mode may arise from the coupling between two surfaces which individually cannot support a surface mode. These are a pair of special coupled-surface modes which may exist below a certain critical film thickness and which have two separate propagation vectors each with the same field symmetry. It is also found that the inverse situation may pertain, that is for certain relative values of dielectric constants even though ordinary surface modes may exist, below a critical thickness the resulting coupled long-range mode no longer exists. The analysis has also been extended to practical situations with weakly absorbing surrounding media and to circumstances where the dielectric constants of the surrounding media are slightly different. Both of these effects modify the dispersion relations obtained for the simple case and introduce further limit thicknesses into the problem. Analytic formulas in the thin-film limit are presented for all the above situations and field distributions and energy flow (Poynting vector) profiles presented to illustrate as necessary the nature of the modes supported by these systems. Finally experimental results are presented which illustrate the rather sweeping conclusion that a long-range surface mode may exist on a thin film for almost all values of ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{r}2}$ and ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}2}$. This result paves the way for a range of optics experiments on absorbing structures.

Use of 137Cs measurements to investigate soil erosion on arable fields in the UK: potential applications and limitations

Abstract: SUMMARY Recent awareness of the potential hazard of soil erosion on arable land in the UK has highlighted the lack of reliable data concerning actual rates of soil loss. This lack of information reflects both a low level of interest, and the lack of a simple and generally applicable method of documenting long-term rates of soil loss. Existing methods involving the use of hazard classification procedures and direct measurement techniques, including erosion plots and field surveys, all possess significant limitations. The use of 137Cs measurements to provide information on rates of soil loss and deposition averaged over the past 30 years would appear to offer considerable potential. The results of applying this approach to three arable fields on contrasting soil types in Britain are reported. These results confirm the viability of the technique and its potential for providing information on patterns and rates of erosion and deposition within individual fields and their overall sediment budgets. Limitations include the restricted size of the areas that can be investigated and the need to take account of additional inputs of 137Cs derived from the Chernobyl accident.

Biographical Precursors of Musical Excellence: An Interview Study:

Abstract: Forty-two students (aged 10-18) from a special school for musically gifted children were interviewed. Twenty of their parents were also interviewed. The interviews provided exhaustive information a...

The mechanisms of indentation creep

Abstract: A physically-based theoretical model is developed for describing the phenomenon of indentation creep over the whole temperature range, from 300 K to melting. In agreement with experimental data col ...

The linear inviscid secondary instability of longitudinal vortex structures in boundary layers

Abstract: The inviscid instability of a longitudinal vortex structure within a steady boundary layer is investigated. The instability has wavelength comparable with the boundary-layer thickness so that a quasi-parallel approach to the instability problem can be justified. The generalisation of the Rayleigh equation to such a flow is obtained and solved for the case when the vortex structure is induced by curvature. Two distinct modes of instability are found; these modes correspond with experimental observations on the breakdown process for Gortler vortices.

Epithelial-myoepithelial carcinoma of salivary glands.

Abstract: Four cases of epithelial-myoepithelial carcinoma of the salivary glands arose as painless masses in patients over 60 years old, three in the parotid and one in the submandibular gland. Histologically, all the tumours were composed of small ducts with a double cell lining surrounded by a basement membrane. The inner cells were epithelial and the outer cells myoepithelial, the latter usually possessing clear cytoplasm. There was a variable degree of intervening hyalinised stroma. All the tumours were partly encapsulated, but also displayed local invasiveness. One of the tumours also showed areas of dedifferentiation when it later recurred and metastasised. The other three were apparently cured by initial excision, with adjuvant radiotherapy in one instance. In the past this tumour has been described as clear cell adenoma, and it was only recently that its true malignant nature, albeit low grade, was recognised. Reports of epithelial-myoepithelial carcinoma are still relatively few, with only one case described from Britain. It is recommended that this histologically distinct neoplasm deserves wider recognition.

Campanian–Maastrichtian (Cretaceous) stratigraphy of the James Ross Island area, Antarctica

Abstract: One of the most important outcrops of uppermost Cretaceous (Campanian–Maastrichtian) sedimentary rocks in the southern high latitudes occurs within the James Ross Island group, northeastern Antarctic Peninsula. These rocks comprise a 1500–2000 m thick sequence of predominantly shallow marine clastic sediments that were deposited within a retro-arc basin. They are virtually undeformed and have yielded prolific invertebrate and vertebrate faunas, and a wide range of plant taxa. Campanian–Maastrichtian strata are contained within two component formations of the Upper Cretaceous-lower Tertiary Marambio Group. The lower Santa Marta Formation is approximately 1100m thick and has three constituent members. Ammonites within the Santa Marta Formation indicate an early to late Campanian age assignment. Dinoflagellates suggest that the lower levels of the formation may range into the Santonian Stage. In the northern James Ross Island to Vega Island region there is a conformable transition into the overlying Lopez de Bertodano Formation. Here the basal Cape Lamb Member is unconformably overlain by the Sandwich Bluff Member. Although there are some lithological and fauna1 discrepancies, which are attributed to marked lateral facies changes across the basin, it is believed that the Cape Lamb Member can be correlated with the lower to middle regions of the 1200 m thick sequence of undifferentiated Lopez de Bertodano Formation lithologies exposed on Seymour Island. Molluscan data indicate a late Campanian–Palaeocene age range for this upper formation. Dinoflagellates again suggest that the lowest beds may be slightly older. The correlation presented provides the basis for a formal subdivision of the Campanian and Maastrichtian stages in the southern high latitudes. It has also revealed two major basin shallowing events (in the late Campanian–early Maastrichtian and latest Maastrichtian, respectively) and the existence of a major fault/fault zone across southeastern James Ross Island. The improved temporal framework will aid late Cretaceous palaeoclimatic and palaeobiological studies in Antarctica.

Screening for treatable diabetic retinopathy: a comparison of different methods.

Abstract: The results of the screening of 3318 diabetic patients for sight-threatening diabetic retinopathy in three UK centres are reported. The aims of the study were to determine the extent of diabetic retinopathy in the screened population and to assess the relative effectiveness of different screening methods in appropriately referring cases from a diabetic population, in a context very close to a routine clinical service. Patients were assessed by ophthalmoscopic examination by an ophthalmological clinical assistant. The clinical assistants' referral grades formed the reference standard against which to assess the effectiveness of other screening methods including ophthalmoscopy by primary screeners who were general practitioners (GPs), ophthalmic opticians and hospital physicians, and the assessment by consultant ophthalmologists of non-mydriatic Polaroid fundus photography. The performance of primary screeners based on ophthalmoscopy ranged from a sensitivity of 0.41, with a specificity of 0.89, for one of the GP groups, to a sensitivity of 0.67, with a specificity of 0.96, for the hospital physician group. The performance of the non-mydriatic camera ranged from a sensitivity of 0.35, with a specificity of 0.95, to a sensitivity of 0.67, with a specificity of 0.98.

The peak oxygen uptake of British children with reference to age, sex and sexual maturity.

Abstract: The purposes of this study were to provide baseline data on the peak oxygen consumption (VO2) of British children, aged 11–16 years and to examine the peakVO2 of children in relation to their pubertal stage of development. The peakVO2 of 226 boys and 194 girls was determined during either treadmill running or cycle ergometry. The sexual maturity of 320 of the children was estimated using Tanner's indices. PeakVO2 increased with chronological age in both sexes and from about the age of 12 years boys exhibited significantly higher (P<0.05) values than girls. Boys' peakVO2 in relation to body mass was consistent over the age range studied and was superior (P<0.05) to girls' values at all ages. It appears that mass-related peakVO2 is independent of sexual maturity in both sexes. The more mature boys demonstrated a significantly higher (P<0.05) peakVO2 (l·min−1) than the less mature boys on both ergometers. The more mature girls demonstrated significantly higher (P<0.05) peakVO2 (l·min−1) than the less mature girls only on the cycle ergometer. On both ergometers the differences between the peakVO2 of the girls and boys were more pronounced in the mature children whether expressed in relation to body mass or not. Comparison of the results with earlier data drawn from smaller samples failed to provide evidence to suggest that British children's peakVO2 has declined in recent years. No study with which to compare our maturity peakVO2 data appears to be available.

On the receptivity problem for Goertler vortices: Vortex motions induced by wall roughness

Abstract: The receptivity problem for Goertler vortices induced by wall roughness is investigated. The roughness is modelled by small amplitude perturbations to the curved wall over which the flow takes place. The amplitude of these perturbations is taken to be sufficiently small for the induced Goertler vortices to be described by linear theory. The roughness is assumed to vary in the spanwise direction on the boundary layer lengthscale, while in the flow direction the corresponding variation is on the lengthscale over which the wall curvature varies. In fact the latter condition can be relaxed to allow for a faster streamwise roughness variation so long as the variation does not become as fast as that in the spanwise direction. The function which describes the roughness is assumed to be such that its spanwise and streamwise dependences can be separated; this enables progress by taking Fourier or Laplace transforms where appropriate. The cases of isolated and distributed roughness elements are investigated and the coupling coefficient which relates the amplitude of the forcing and the induced vortex amplitude is found asymptotically in the small wavelength limit. It is shown that this coefficient is exponentially small in the latter limit so that it is unlikely that this mode can be stimulated directly by wall roughness. The situation at 0(1) wavelengths is quite different and this is investigated numerically for different forcing functions. It is found that an isolated roughness element induces a vortex field which grows within a wedge at a finite distance downstream of the element. However, immediately downstream of the obstacle the disturbed flow produced by the element decays in amplitude. The receptivity problem at larger Goertler numbers appropriate to relatively large wall curvature is discussed in detail.

Psychobiology of the near-miss in fruit machine gambling

Abstract: Explanations involving the etiology of pathological gambling have tended to emphasize psychosocial factors. However, the possibility that psychobiological factors may be important in the development of pathological gambling behavior should not be ruled out. Psychobiological approaches are becoming ever more prominent with the three main lines of research being (a) a search for a physiological disposition and/or underlying biological substrate in pathological gamblers, (b) an examination of the role of arousal in gambling, and (c) speculation about endorphin-related explanations. The data from questionnaires and interviews with fruit machine gamblers suggest that both physiological and cognitive factors (e.g., the psychology of the near-miss) may be important in the explanation of excessive fruit machine gambling. Thus, if a gambler becomes physiologically aroused when he or she wins or nearly wins, it will stimulate further play, here termed the psychobiology of the near-miss.

Physical activity patterns defined by continuous heart rate monitoring.

Abstract: To investigate the physical activity patterns of British primary schoolchildren (mean (SD) 10.7 (0.3) years) the minute by minute heart rates of 67 boys and 65 girls were monitored continuously for three 12 hour periods during normal schooldays. In addition 39 children had their heart rates monitored during a 12 hour period on a Saturday. Few children experienced the volume (frequency, intensity, and duration) of physical activity associated with an improvement in cardiopulmonary fitness. Shorter (five minute) periods of the required intensity were, however, quite common. No difference between moderate amounts of activity was detected between boys and girls, but the boys had more five minute sessions of intense activity than the girls. These findings suggest that more research into the effects of short periods of intense physical activity on the cardiopulmonary systems of young children is required and that the determinants of habitual physical activity require further investigation especially in the context of sex differences at such an early age.

Polarization conversion from diffraction gratings

Abstract: If a surface-modulated diffraction grating is arranged so that the scattering vector does not lie in the plane of incidence of the illuminating radiation, then polarization conversion can occur. This conversion can be strongly enhanced if a surface mode, such as a surface-plasmon-polariton or guided mode, is excited at the grating surface. In this paper we develop a mathematical description of the polarization conversion process, using a method that transforms the grating surface into a planar system. The predicted polarization conversion is compared very favorably with data for surface-mode-enhanced conversion.

Uptake, accumulation and translocation of arsenate in arsenate-tolerant and non-tolerant Holcus lanatus L.

Abstract: summary Uptake, translocation and accumulation of arsenate was determined in arsenate-tolerant and non-tolerant genotypes of Holcus lanatus L. Over a 6 h period of growth in 005 mol m−3arsenate, non-tolerant genotypes accumulated arsenate to a much greater extent than tolerant plants. Tolerant plants transported a much greater proportion of As to their shoots compared with non-tolerant plants. Phosphate at a concentration of either 0.05 or 0.5 mol m−3decreased arsenate uptake in both tolerant and non-tolerant genotypes. When arsenate uptake was determined over 3 d at the same arsenate concentration, non-tolerant plants grown in the presence of 0 and 0.05 mol m−3phosphate died, while those growing in 0.5 mol m−3phosphate survived and continued to take up arsenate. At all three phosphate levels tolerant plants survived. Over the 3 d period transport of arsenate to the shoots decreased. With increasing phosphate levels in solution transport of arsenate to the shoots increased in tolerant plants. The results from these experiments are discussed in terms of strategies for metal tolerance in this species.

Adolescent health behaviour and similarity-attraction: friends share smoking habits (really), but much else besides.

Abstract: Smoking habits and related attitudes were assessed in a sample of 4059 11- to 16-year-olds who also identified their best friends from among their fellow respondents. Subjects' responses were directly collated with those of their friends and indicated a clear covariation of smoking status (controlling for sex and age) as anticipated from previous research in which adolescents have been asked to report on the smoking habits of their friends. Such covariation, however, was not specific to smoking habits, but generalized to related measures of attitude and normative beliefs, alcohol use, health locus of control, school performance, spending habits and socio-economic status. Similarities on these other attributes were much the same, whether or not friends shared each others' smoking habits. It is concluded that these data argue against a simplistic view of unidirectional ‘peer group influence’ and invite an interpretation of friendship choice based on multiple dimensions of similarity.

Why the evolution of resistance to anthropogenic toxins normally involves major gene changes: the limits to natural selection

Abstract: Standard population genetic theory suggests that adaptation should normally be achieved by the spread of many genes each of small effect (polygenes), and that adaptation by major genes should be unusual. Such models depend on consideration of the rates of acquisition of adaptation. In practice, adaptation to pollutants and anthropogenic toxins has most frequently been achieved by the spread of major genes. A simple model is developed to explain this discrepancy, in which the determining factor is not the rate of spread, but the maximum response achievable under the two contrasting models of polygenic or major gene inheritance. In the short term, for a given mean and genetic variance, characters in which the additive genetic variance is produced by the segregation of many genes of small effect at intermediate gene frequencies are unable to produce as large a response to directional selection as characters in which the variance is caused by genes of large effect at low frequency. If the ‘target’ for selection is a long way from the mean prior to selection (as it may well be for adaptation to novel anthropogenic stresses) then adaptation can only be achieved by species possessing major genes. The model is discussed with reference to the example of heavy metal tolerance in plants.

Evidence for a role for the cell membrane in copper tolerance of Mimulus guttatus Fischer ex DC.

Abstract: SUMMARY The effect of copper on root growth, K"*^ efflux and short-term copper uptake by three isogenic genotypes of Mimulus guttatus Fischer ex DC. differing only in their copper tolerance gene is studied. The tolerant homozygotes do not differ in any way from the heterozygotes. The non-tolerant homozygotes show greater rooi inhibition, greater K^ efHux, and greater short-term Cu^" uptake. The difference in the uptake parameters is best described by a greater linear diffusion term in the non-tolerant genotypes. These results suggest that copper damages the cell membrane, and that this damage leads to an increase m the leakiness of the membrane, leading to both greater K' efflux and Cu^"^ influx via diffusion. This suggests that the primary copper tolerance mechanism probably resides in the cell membrane. The rapidity with which the differences between the genotypes is established suggests that the differences are constitutive. It is argued that these results provide further evidence against the involvement of phytochelatin s in the primary tolerance mechanism.