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.

Optimization of alloy design and hot rolling conditions for shape memory in Fe–Mn–Si-based alloys

The effect of composition and hot rolling conditions on the shape memory effect (SME) in the Fe–Mn–Si-based system has been studied to obtain improved shape memory without the need to rely on “training”. It has been found that the texture is not markedly affected by rolling conditions, and texture is therefore not a major factor in explaining variations in SME with processing conditions. Decreasing the pre-deformation temperature to below the Ms was found to have a beneficial effect on shape memory. It was found that the best SME was achieved in an alloy that had Ms just above room temperature, and had been processed by hot rolling followed by recovery annealing. Alloys of different compositions exhibited different optimum rolling temperatures for maximum shape memory performance.

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.

Identification of cashmere and superfine merino wool with wavelet texture analysis

This paper presents the use of the wavelet transform to extract fibre surface texture features for classifying cashmere and superfine merino wool fibres. To extract features from brightness variations caused by the cuticular scale height, shape and interval provides an effective way for characterising different animal fibres and subsequently classifying them. This may enable the development of a completely automated and objective system for animal fibre
identification.

Identification of animal fibers with wavelet texture analysis

This paper presents the use of the wavelet transform to extract fiber surface texture features for classifying cashmere and superfine merino wool fibers. Extracting features from brightness variations caused by the cuticular scale height, shape and interval provides an effective way for characterizing different animal fibers and subsequently classifying them. This may enable the development of a completely automated and objective system for animal fiber identification.

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.

Crystal structures and textures in the hot-forged Ni-Mn-Ga shape memory alloys

Three ferromagnetic shape-memory alloys with the chemical compositions of Ni₅₃Mn₂₅Ga₂₂, Ni₄₈Mn₃₀Ga₂₂, and Ni₄₈Mn₂₅Ga₂₂Co₅ were prepared by the induction-melting and hot-forging process. The crystal structures were investigated by the neutron powder diffraction technique, showing that Ni₅₃Mn₂₅Ga₂₂ and Ni₄₈Mn₂₅Ga₂₂Co₅ have a tetragonal, 14/mmm martensitic structure at room temperature, while Ni₄₈Mn₃₀Ga₂₂ has a cubic, L2₁ austenitic structure at room temperature. The development of textures in the hot-forged samples shows the in-plane plastic flow anisotropy from the measured pole figures by means of the neutron diffraction technique. Significant texture changes were observed for the Ni₄₈Mn₂₅Ga₂₂Co₅ alloy after room temperature deformation, which is due to the deformation-induced rearrangements of martensitic variants. An excellent shape-memory effect (SME) with a recovery ratio of 74 pct was reported in this Ni₄₈Mn₂₅Ga₂₂Co₅ polycrystalline alloy after annealing above the martensitic transformation temperature, and the “shape-memory” influence also occurs in the distributions of grain orientations.

Orientation relationship, texture and microstructure in electromagnetic processed materials (EPM)

In this work, some of our recent results in microstructure, texture and orientation relationship resulting from the application of an external high magnetic field during diffusional and non-diffusional phase transformation in both steel and functional metallic materials have been summarized. A 12-T magnetic field was applied to the diffusional decomposition of austenite in 0.81C-Fe alloy and martensitic transformation of a Ni-Mn-Ga magnetic shape memory alloy. For the 0.81C-Fe alloy, it was found that the magnetic field induces the formation of proeutectoid ferrite and slightly enhances the <001> fiber component in ferrite in the transverse field direction. The magnetic dipolar interaction between Fe atoms in the transverse field direction accounts for this phenomenon. The magnetic field favors the formation of pearlite with Pitsch-Petch 2 (P-P 2) and Isaichev (IS) orientation relationships (OR) between the lamellar ferrite and cementite. For the Ni-Mn-Ga magnetic shape memory alloy, the magnetic field makes the martensite lamellas to grow in some specific directions with their c-axes [001] orientated to the field direction and transverse field direction.

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

Sparse representation with multi-manifold analysis for texture classification from few training images

Texture classification is one of the most important tasks in computer vision field and it has been extensively investigated in the last several decades. Previous texture classification methods mainly used the template matching based methods such as Support Vector Machine and k-Nearest-Neighbour for classification. Given enough training images the state-of-the-art texture classification methods could achieve very high classification accuracies on some benchmark databases. However, when the number of training images is limited, which usually happens in real-world applications because of the high cost of obtaining labelled data, the classification accuracies of those state-of-the-art methods would deteriorate due to the overfitting effect. In this paper we aim to develop a novel framework that could correctly classify textural images with only a small number of training images. By taking into account the repetition and sparsity property of textures we propose a sparse representation based multi-manifold analysis framework for texture classification from few training images. A set of new training samples are generated from each training image by a scale and spatial pyramid, and then the training samples belonging to each class are modelled by a manifold based on sparse representation. We learn a dictionary of sparse representation and a projection matrix for each class and classify the test images based on the projected reconstruction errors. The framework provides a more compact model than the template matching based texture classification methods, and mitigates the overfitting effect. Experimental results show that the proposed method could achieve reasonably high generalization capability even with as few as 3 training images, and significantly outperforms the state-of-the-art texture classification approaches on three benchmark datasets. © 2014 Elsevier B.V. All rights reserved.

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.