Critical Configurations for 1-View in Projections from ℙ<Superscript>k</Superscript> → ℙ<Superscript>2</Superscript>

In this paper we describe, from a theoretical point of view, critical configurations for the projective reconstruction of a set of points, for a single view, i.e. for calibration of a camera, in the case of projections from ℙ^k to ℙ² for k ≥ 4. We give first a general result describing these critical loci in ℙ^k, which, if irreducible, are algebraic varieties of dimension k−2 and degree 3. If k=4 they can be either a smooth ruled surface or a cone and if k = 5 they can be a smooth three dimensional variety, ruled in planes, or a cone. If k≥ 6, the variety is always a cone, the vertex of which has dimension at least k − 6. The reducible cases are studied in Appendix A. These results are then applied to determine explicitly the critical loci for the projections from ℙ^k which arise from the dynamic scenes in ℙ³ considered in [13]. Marina Bertolini is currently Associate Professor of Geometry at the Department of Mathematics at the Università degli Studi di Milano, Italy. Her main field of research is Complex Projective Algebraic Geometry, with particular interest for the classification of projective varieties and for the geometry of Grassmann varieties. On these topics M. Bertolini has published more than twenty reviewed papers on national and international journals. She has been for some years now interested also in applications of Algebraic Geometry to Computer Vision problems. Cristina Turrini is Associate Professor of Geometry at the Department of Mathematics of Università degli Studi di Milano, Italy. Her main research interest is Complex Projective Algebraic Geometry: subvarieties of Grassmannians, special varieties, automorphisms, classification. In the last two years she has started to work on applications of Algebraic Geometry to problems of Computer Vision. She is author or co-author of about thirty reviewed papers. She is also involved in popularization of Mathematics, and on this subject she is co-editor of some books.     

Phase equilibria of the ternary Al-Cu-Ni system and interfacial reactions of related systems at 800 °C

A series of Al-Cu-Ni alloys of various compositions were made and annealed at 800 °C. The equilibrium phases were studied by metallography, X-ray diffraction (XRD) analysis, and electron probe microanalysis. The isothermal section of the ternary Al-Cu-Ni system at 800 °C was then determined based on these experimental results and the available phase relationship knowledge of the three constituent binary systems. No ternary compound was found. All three phases, AlNi₃, AlNi, and Al₃Ni₂, have very high ternary solubility, especially the AlNi phase, which almost reaches the binary Al-Cu side. However, no continuous solid solution was formed between the AlNi phase and any of the binary Al-Cu phases. Interfacial reactions of Al/Ni, Al/Cu, Al-Cu/Ni, and Al-Ni/Cu at 800 °C were investigated by using reaction couple techniques. The results showed that Al₃Ni and Al₃Ni₂ phases were formed in the Al/Ni couples; β-AlCu₄, γ ₁-Al₄Cu₉, and ɛ ₂-Al₂Cu₃ phases were formed in the Al/Cu couples. As for the results in the Al-2 at. pct Ni/Cu, Al-5 at. pct Ni/Cu, and Al-2 at. pct Cu/Ni, Al-4.5 at. pct Cu/Ni, and Al-6 at. pct Cu/Ni were similar to those in the binary Al/Cu and Al/Ni couples, respectively. A different reaction path was found in the Al-7.5 at. pct Cu/Ni couples, and an AlNi solid solution layer was formed instead of the Al₃Ni and Al₃Ni₂ phases.     

The hot blow forming of AZ31 Mg sheet: Formability assessment and application development

The hot blow forming of magnesium sheet offers significant opportunity for forming complex, lightweight parts for automotive applications. This paper characterizes the elevated-temperature formability of AZ31 magnesium sheet materials and the effect of processing conditions on the performance of these materials. In addition, magnesium sheet application development at General Motors Corporation is reviewed.     

Simulation of Strength Distribution in Ground Ceramics by Incorporating Residual Stress Effect

Strength of ground ceramics may be affected by residual stress as well as surface flaws induced by grinding. Strength prediction for ground ceramics is convenient for mechanical design of ceramic components. In this article, a numerical procedure based on fracture mechanics was proposed to estimate strength distribution of ground ceramics by considering grinding-induced residual stress. Bending strength and residual stress of ground ceramics were measured for three grinding-conditions. By comparison of simulated results with experimental ones, it was revealed that strength characteristics in experiments were well simulated by using the proposed procedure.     

Fracture toughness evaluation of adjacent flow weld line in polystyrene by the SENB method

Fracture toughness of adjacent flow weld lines, defined as weld lines that occur when two flow fronts meet and continue to flow together in the same direction (meld line or hot weld line), was evaluated by the single‐edge notched‐bend (SENB) method using three differently‐shaped obstructive pins. Although the fracture toughness varied depending upon the shapes of the pin, the values could be standardized as the distance from the meeting point of the two flow fronts flowing around the pin. The fracture toughness decreased drastically from the meeting point along the weld line and then slightly increased. These characteristic features could be explained by flow‐induced molecular orientation at the weld line interface. The molecules around the meeting point that were initially oriented parallel to the weld line due to fountain flow were able to relax, and then entanglement across the weld line interface developed because the flow stopped in the middle of the filling process, resulting in high fracture toughness. In contrast, the material at the downstream side of the weld line continued flowing during the filling process, being stretched along the flow direction. So, the molecular orientation at this area could not relax. In addition, the V‐notch shape, i.e., the depth and length at the surface of the weld line, which also varied depending on the shape of the obstacles, was considered to be identical when the meeting point was allowed to be a datum point. Thus, the meeting point was found to be a significant factor when the properties of weld lines are investigated. POLYM. ENG. SCI., 45:1059–1066, 2005. © 2005 Society of Plastics Engineers     

Synthesis,characterization and ion exchange properties of zirconium(IV) tungstoiodophosphate,a new cation exchanger

Zirconium(IV) tungstoiodophosphate has been synthesized under a variety of conditions. The most chemically and thermally stable sample is prepared by adding a mixture of aqueous solutions of 0·5 mol L⁻¹ sodium tungstate, potassium iodate and 1 mol L⁻¹ orthophosphoric acid to aqueous solution of 0·1 mol L⁻¹ zirconium(IV) oxychloride. Its ion exchange capacity for Na⁺ and K⁺ was found to be 2·20 and 2·35 meq g⁻¹ dry exchanger, respectively. The material has been characterized on the basis of chemical composition, pH titration, Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis. The effect on the exchange capacity of drying the exchanger at different temperatures has been studied. The analytical importance of the material has been established by quantitative separation of Pb²⁺ from other metal ions.     

A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.     

Effects of contact shape on biological wet adhesion

Wet adhesion is widely adopted in biological adhesion systems in nature. Wet adhesion is studied in this paper with the focus on the effect of different contact shapes (flat, concave, convex, and ring-like) on the adhesion force. The evolution of the liquid bridge between a fiber tip and substrate during the detaching process shows two transition points. The first transition from the radius-controlled to the contact-angle controlled process is critical to influence the strength and robustness of adhesion. We show that a concave shape is more effective than a flat one, while a convex shape has no advantage. A ring-like contact shape has advantages in a hydrophobic environment and on a rough surface.     

Dye-sensitized solar cell based on nanocrystalline TiO<Subscript>2</Subscript> with 3–10 nm in diameter

Nanocrystalline TiO₂ with 3–10 nm in diameter was prepared with a surfactant-template method. Dye-sensitized solar cells were assembled using the prepared nanocrystalline TiO₂ with large surface area and high crystallinity, which achieved significant higher Jsc when compared to cells fabricated with bigger particles of 25 nm in diameter. In the cells with nanocrystalline TiO₂, the sintering temperature drastically affected the conversion performance of the cells.