Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

铝灰的回收处理及资源化利用研究现状

铝灰是铝工业生产过程中产生的有害固体废物,每年的产生量达到上百万吨。铝灰的大量堆积会引起严重的环境与公共安全问题。铝灰中含有较多的金属铝及其氧化物、氮化物,综合回收利用铝灰对减少环境压力、提升铝行业的经济效益具有重要意义。阐述了铝灰的火法和湿法处理工艺,通过比较得出无盐火法工艺和湿法工艺是值得开发的工艺。介绍了铝灰在耐火材料、陶瓷产品、氢气制备以及工程材料等领域的综合利用现状及研究进展。指出在进一步巩固和发展铝灰原有的高附加值资源化利用的同时,应加强对铝灰处理过程中产生的气体的利用。建议根据铝灰的特性进一步开发新的资源化利用方向。     

Effect of an abrupt change in pulling rate on microstructures of directionally solidified Al2O3-Er3Al5O12 eutectic and off-eutectic composite ceramics

Directionally solidified microstructures of Al₂O₃-Er₃Al₅O₁₂ eutectic and off-eutectic in situ composite ceramics were explored under abrupt-change pulling rate conditions. Corresponding temperature distributions and interface locations were studied. In eutectic composition, fluctuation of eutectic spacing occurred when the pulling rate increased abruptly. A gradually increase or abrupt increase in eutectic spacing was observed when the pulling rate decreased abruptly. In hypoeutectic and hypereutectic compositions, formation of the primary phases were suppressed when the pulling rate increased abruptly from 10?µm/s to 100?µm/s, while primary phases precipitated when the pulling rate decreased abruptly from 100?µm/s to 10?µm/s. The interface altitude decreased after the pulling rate increased abruptly, but increased after the pulling rate decreased abruptly. The liquid composition restriction (around the eutectic composition) at the eutectic interface plays an important role in the suppression of the primary dendrite and coupled eutectic oxides can be obtained in off-eutectic compositions even under higher solidification rate conditions.     

Visual Detection of Adenosine Triphosphate by Taylor Rising: A Simple Point-of-Care Testing Method Based on Rolling Circle Amplification

Rapid and sensitive point-of-care testing (POCT) is an extremely critical mission in practical applications, especially for rigorous military medicine, home health care, and in the third world. Here, we report a visual POCT method for adenosine triphosphate (ATP) detection based on Taylor rising in the corner of quadratic geometries between two rod surfaces. We discuss the principle of Taylor rising, demonstrating that it is significantly influenced by contact angle, surface tension, and density of the sample, which are controlled by ATP-dependent rolling circle amplification (RCA). In the presence of ATP, RCA reaction effectively suppresses Taylor-rising behavior, due to the increased contact angle, density, and decreased surface tension. Without addition of ATP, untriggered RCA reaction is favorable for Taylor rising, resulting in a significant height. With this proposed method, visual sensitive detection of ATP without the aid of other instruments is realized with only a 5 μL droplet, which has good selectivity and a low detection limit (17 nM). Importantly, this visual method provides a promising POCT tool for user-friendly molecular diagnostics.     

Microstructure and damage evolution of SiCf/PyC/SiC and SiCf/BN/SiC mini-composites: A synchrotron X-ray computed microtomography study

SiC_f/PyC/SiC and SiC_f/BN/SiC mini-composites comprising single tow SiC fibre-reinforced SiC with chemical vapor deposited PyC or BN interface layers are fabricated. The microstructure evolutions of the mini-composite samples as the oxidation temperature increases (oxidation at 1000, 1200, 1400, and 1600?°C in air for 2?h) are observed by scanning electron microscopy, energy dispersive spectrometry, and X-ray diffraction characterization methods. The damage evolution for each component of the as-fabricated SiC_f/SiC composites (SiC fibre, PyC/BN interface, SiC matrix, and mesophase) is mapped as a three-dimensional (3D) image and quantified with X-ray computed tomography. The mechanical performance of the composites is investigated via tensile tests.The results reveal that tensile failure occurs after the delamination and fibre pull-out in the SiC_f/PyC/SiC composites due to the volatilization of the PyC interface at high temperatures in the air environment. Meanwhile, the gaps between the fibres and matrix lead to rapid oxidation and crack propagation from the SiC matrix to SiC fibre, resulting in the failure of the SiC_f/PyC/SiC composites as the oxidation temperature increases to 1600?°C. On the other hand, the oxidation products of B₂O₃ molten compounds (reacted from the BN interface) fill up the fracture, cracks, and voids in the SiC matrix, providing excellent strength retention at elevated oxidation temperatures. Moreover, under the protection of B₂O₃, the SiC_f/BN/SiC mini-composites show a nearly intact microstructure of the SiC fibre, a low void growth rate from the matrix to fibre, and inhibition of new void formation and the SiO₂ grain growth from room to high temperatures. This work provides guidance for predicting the service life of SiC_f/PyC/SiC and SiC_f/BN/SiC composite materials, and is fundamental for establishing multiscale damage models on a local scale.     

Microstructures and mechanical properties of B4C-TiB2-SiC composites fabricated by ball milling and hot pressing

B₄C-TiB₂-SiC composites were fabricated via hot pressing using ball milled B₄C, TiB₂, and SiC powder mixtures as the starting materials. The impact of ball milling on the densification behaviors, mechanical properties, and microstructures of the ceramic composites were investigated. The results showed that the refinement of the powder mixtures and the removal of the oxide impurities played an important role in the improvement of densification and properties. Moreover, the formation of the liquid phases during the sintering was deemed beneficial for densification. The typical values of relative density, hardness, bending strength, and fracture toughness of the composites reached 99.20%, 32.84?GPa, 858?MPa and 8.21?MPa?m^1/2, respectively. Crack deflection, crack bridging, crack branching, and microcracking were considered to be the potential toughening mechanisms in the composites. Furthermore, numerous nano-sized intergranular/intragranular phases and twin structures were observed in the B₄C-TiB₂-SiC composite.