Microworlds and mathematics: what shape is that?

The author provides ways to explore and use MicroWorlds to enhance mathematics teaching and learning. The procedures given randomly choose a shape from the specified list, draw the shape and require the user to type the name of the shape.

Plato's legacy : How to do philosophy

Although it has its origins earlier, philosophy as we know it in the West took its shape from the Socrates of Plato's Dialogues. It is not implausible to regard the Dialogues as heuristic devices designed for engaging in philosophical inquiry. As such, they would model the process of philosophical inquiry as well as illustrate the common pitfalls or errors to avoid when engaging in such inquiry. So it will not be surprising to see Socrates, the character of the Dialogues, modeling questionable, even poor, inquiry techniques as well as good; admonishing other characters for poor technique and reminding them of lessons they should have learned earlier in their tuition. Plato presumably would expect students reading and role-playing a Dialogue to recognise when and where such instances occur. It is instructive then to take a close look at one of the longer dialogues featuring Socrates engaging in such inquiry, not with an untutored interlocutor, but with a professional, the sophist Protagoras, in order to identify the features of the inquiry itself. For this will reveal something of what Plato conceived to be the activity of philosophy to which we are the heirs. The Protagoras can be read as an illustration (not a definition) of how to do philosophy. And to aid this reading, I propose to focus on the logical form of the inquiry, the moves made by the characters and the techniques displayed, rather than the adequacy of the substantive arguments they mount.

An experimental investigation of yarn tension in simulated ring spinning

Yarn tension is a key factor that affects the efficiency of a ring spinning system. In this paper, a specially constructed rig, which can rotate a yarn at a high speed without inserting any real twist into the yarn, was used to simulate a ring spinning process. Yarn tension was measured at the guide-eye during the simulated spinning of different yarns at various balloon heights and with varying yarn length in the balloon. The effect of balloon shape, yarn hairiness and thickness, and yarn rotating speed, on the measured yarn tension, was examined. The results indicate that the collapse of balloon shape from single loop to double loop, or from double loop to triple etc, lead to sudden reduction in yarn tension. Under otherwise identical conditions, a longer length of yarn in the balloon gives a lower yarn tension at the guide-eye. In addition, thicker yarns and/or more hairy yarns generate a higher tension in the yarn, due to the increased air drag acting on the thicker or more hairy yarns.

Numerical investigation of ramp and constant pressurization system during tube crushing process

The requirement for the automotive industry at present and even more so in the future is to simultaneously develop materials, economic forming processes and techniques for weight reduction of the component. To fulfil this need steel manufacturers have developed Advanced High Strength Steels which have high strength and good formability. Due to high strength, material thickness can be reduced without compromising the function of the component. High pressure hydro forming is one process that can be used to produce complex components from these materials. However, reduction in material thickness of these steels does not result in a large decrease of internal fluid pressure and die closing force during tube hydro forming and hence the higher strengths of these steels will require higher pressures. Tube crushing is a process in which the component can be formed with low pressures. In this paper numerical comparison of ramp and constant pressurization system during tube crushing for a TRIP steel is studied. It is proposed that ramp pressure is the best option to obtain a part with accurate geometrical shape from tube crushing with less die closing force. The stress and thickness distribution of the part during tube crushing were critically analysed.

Thin film drainage : hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.

Face Recognition from Video Using the Generic Shape-Illumination Manifold

In spite of over two decades of intense research, illumination and pose invariance remain prohibitively challenging aspects of face recognition for most practical applications. The objective of this work is to recognize faces using video sequences both for training and recognition input, in a realistic, unconstrained setup in which lighting, pose and user motion pattern have a wide variability and face images are of low resolution. In particular there are three areas of novelty: (i) we show how a photometric model of image formation can be combined with a statistical model of generic face appearance variation, learnt offline, to generalize in the presence of extreme illumination changes; (ii) we use the smoothness of geodesically local appearance manifold structure and a robust same-identity likelihood to achieve invariance to unseen head poses; and (iii) we introduce an accurate video sequence “reillumination” algorithm to achieve robustness to face motion patterns in video. We describe a fully automatic recognition system based on the proposed method and an extensive evaluation on 171 individuals and over 1300 video sequences with extreme illumination, pose and head motion variation. On this challenging data set our system consistently demonstrated a nearly perfect recognition rate (over 99.7%), significantly outperforming state-of-the-art commercial software and methods from the literature

Using geometric shape variations to create an inverse model for a sheet metal process

The output of the sheet metal forming process is subject to much variation. This paper develops a method to measure shape variation in channel forming and relate this back to the corresponding process parameter levels of the manufacturing set-up to create an inverse model. The shape variation in the channels is measured using a modified form of the point distribution model (also known as the active shape model). This means that channels can be represented by a weighting vector of minimal linear dimension that contains all the shape variation information from the average formed channel.

The inverse models were created using classifiers that related the weighting vectors to the process parameter levels for the blank holder force (BHF), die radii (DR) and tool gap (TG) of the parameters. Several classifiers were tested: linear, quadratic Gaussian and artificial neural networks. The quadratic Gaussian classifiers were the most accurate and the most consistent type of classifier over all the parameters.

Observations of loxocythere (loxocythere) ouyenensis (chapman, 1914) (ostracoda) from the cenozoic of S.E. Australia with comments on species attributed to microcytherura müller, 1894 and hemiparvocythere hartmann, 1982 from Australian and New Zealand ma

The type material of Loxocythere (Loxocythere) ouyenensis (Chapman, 1914) from mid Cenozoic strata of the Mallee Bore No. 11 in the Murray Basin, S.E. Australia is partially redescribed and refigured. This species belongs to a discrete group of large elongate Cenozoic fossil and living Loxocythere species, the carapaces of which possess sub-rectangular inner margin outlines, and broadly rounded posterior extremities. Some much smaller but otherwise very similarly shaped species, that have previously been placed under the genus Microcytherura (i.e. Microcytherura? peterroyi Yassini and Jones, 1995) or the genus Hemiparvocythere Hartmann, 1982 (i.e. Hemiparvocythere Iagunicola Hartmann, 1982), are also known from marine Cenozoic strata and modern seas of the Australasian region. There is a marked difference in the shape of the inner margin between this group of small Australasian forms and European species of Microcytherura s.s .. The former have broadly rounded posterior inner margins, whilst the latter have acutely rounded posterior inner margins. The latter also usually present posterior extremities located well below mid carapace height. It is here argued that this difference in inner margin shape between smaller Australasian species such as Microcytherura? peterroyi, and European species of Microcytherura s.s ., suggests that there is not a direct phylogenetic relationship between these two species groups.

Description of loxocythere (novoloxocythere) pelius subgen. sp. nov. (ostracoda) from the cenozoic of S.E. Australia with comments on species of antarctiloxoconcha hartmann, 1986 and loxoreticulatum benson, 1964 from Australian and Antarctic marine waters

Loxocythere (Novoloxocythere) pelius subgen. et sp. nov. is described from Upper Miocene strata of the Port Phillip and Western Port Basins. Victoria. It has its acme in shallow open marine facies of latest Miocene (Cheltenhamian) age. This species, along with Loxocythere (Novoloxocythere) kerryswansoni Yassini and Jones, 1995, forms a discrete group of rotund Australian Loxocythere species that possess posterior extremities in both valves that are positioned well above mid carapace height (i.e. adjacent to dorsal margin). This feature along with a sub-triangular inner margin outline, defines a carapace shape that is distinct from that of rotund species of Loxocythere (loxocythere) Hornibrook, 1952 and Antarctiloxoconcha Hartmann, 1986. The type species of Antarctiloxoconcha – A.frigida (Neale. 1967), possesses internal carapace features that are very similar to the type species of Loxocythere - L. crassa Hornibrook, 1952. Both have relatively short carapaces and sub-quadrate inner margin outlines with posterior extremities in both valves positioned below mid carapace height. Species of Loxocythere (Novoloxocythere), in particular L. (N.) kerryswansoni, have a carapace shape that is transitional between Loxocythere and Loxoreticulatum Benson, 1964. Species of Loxoreticulatum generally possess a sub-parallelogram shaped carapace/inner margin and arched median hinge element. The latter feature is distinct from the mostly straight median hinge elements of Loxocythere (Loxocythere) and Loxocythere (Novoloxocythere) species. Species of Loxocythere (Novoloxocythere) are also readily distinguishable from relatively elongate species of Loxocythere, such as L. (L.) hornibrooki McKenzie, 1967, as the latter possess long (for genus), sub-rectangular shaped carapaces/inner margin outlines and posterior extremities below mid height.

Spherical indentation hardness of shape memory alloys

Using dimensional analysis and the finite element method, the spherical indentation hardness of shape memory alloys (SMAs) is investigated. The scaling relationship between the hardness and the mechanical properties of a SMA, such as the forward transformation stress, the maximum transformation strain magnitude, has been derived. Numerical results demonstrated that the hardness increases with the indentation depth but there is no three-fold relationship between the hardness and the forward transformation stress. Increasing the maximum transformation strain magnitude would reduce the hardness of the material. These research results enhance our understanding of the hardness from the spherical indentation of SMAs.

Geometric shape errors in forging: developing a metric and an inverse model

The complexity of the forging process ensures that there is inherent variability in the geometric shape of a forged part. While knowledge of shape error, comparing the desired versus the measured shape, is significant in measuring part quality the question of more interest is what can this error suggest about the forging process set-up? The first contribution of this paper is to develop a shape error metric which identifies geometric shape differences that occur from a desired forged part. This metric is based on the point distribution deformable model developed in pattern recognition research. The second contribution of this paper is to propose an inverse model that identifies changes in process set-up parameter values by analysing the proposed shape error metric. The metric and inverse models are developed using two sets of simulated hot-forged parts created using two different die pairs (simple and 'M'-shaped die pairs). A neural network is used to classify the shape data into three arbitrarily chosen levels for each parameter and it is accurate to at least 77 per cent in the worst case for the simple die pair data and has an average accuracy of approximately 80 per cent when classifying the more complex 'M'-shaped die pair data.

Microscopic nature and elemental composition of brown coal fly ash particles from a large coal fired power station

In this study, Australian brown coal fly ash particles have been collected from power station and analysed by scanning electron microscopy to obtain morphological information and elemental composition of individual particles. The most common particles found to be the irregular shape particle aggregates. Other shapes include ball shape with smooth surface and with some attachments; and crystal shape fine particles. The X-ray spectra of each fly ash particle revealed five groups of elemental composition, they are Si-rich particles; Ca-rich particles; Fe-rich particles; particles with Mg-Ca Matrix and particles with Si-Ca matrix. A particle sire distribution analysis has been conducted using particle size analyser and found to have a mean particle size of 21fim. The sample then was separated into fine and coarse fractions using aerodynamic classifier, and the elemental composition of both fractions were determined by ICP-AES. Borate fusion and acid dissolution method was used for sample preparation. It is found that some environmental sensitive elements such as Zn, Pb, Ni, K and Cu are enriched in fine fly ash particles. Ca has much higher contents in fine particles as well. Si and Mg have higher concentrations in coarse particles.

Spherical indentation of superelastic shape memory alloys

Spherical indentation of superelastic shape memory alloys (SMAs) has been theoretically analyzed. Two characteristic points on the superelastic indentation curve have been discovered. The bifurcation force corresponding to the bifurcation point relies on the forward transformation stress and the return force corresponding to the return point relies on the reverse transformation stress.
Based on these theoretical relationships, an approach to determine the transformation stresses of superelastic SMAs has been proposed. To improve the accuracy of the measurement, a slope method to locate the two characteristic points from the slope curves is further suggested. Additionally, the spherical indentation hardness was also analyzed.