Testing monotonicity over graph products

We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G₁, G₂, to test monotonicity over their product G₁ × G₂. Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n]^d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n]^d which significantly improves its query complexity analysis in the low‐dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log ²n/ε) to O(log n/ε). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure

Mother-of-pearl, also known as nacre, is the iridescent material which forms the inner layer of seashells from gastropods and bivalves. It is mostly made of microscopic ceramic tablets densely packed and bonded together by a thin layer of biopolymer. The hierarchical microstructure of this biological material is the result of millions of years of evolution, and it is so well organized that its strength and toughness are far superior to the ceramic it is made of. In this work the structure of nacre is described over several length scales. The tablets were found to have wavy surfaces, which were observed and quantified using various experimental techniques. Tensile and shear tests performed on small samples revealed that nacre can withstand relatively large inelastic strains and exhibits strain hardening. In this article we argue that the inelastic mechanism responsible for this behavior is sliding of the tablets on one another accompanied by transverse expansion in the direction perpendicular to the tablet planes. Three dimensional representative volume elements, based on the identified nacre microstructure and incorporating cohesive elements with a constitutive response consistent with the interface material and nanoscale features were numerically analyzed. The simulations revealed that even in the absence of nanoscale hardening mechanism at the interfaces, the microscale waviness of the tablets could generate strain hardening, thereby spreading the inelastic deformation and suppressing damage localization leading to material instability. The formation of large regions of inelastic deformations around cracks and defects in nacre are believed to be an important contribution to its toughness. In addition, it was shown that the tablet junctions (vertical junctions between tablets) strengthen the microstructure but do not contribute to the overall material hardening. Statistical variations within the microstructure were found to be beneficial to hardening and to the overall mechanical stability of nacre. These results provide new insights into the microstructural features that make nacre tough and damage tolerant. Based on these findings, some design guidelines for composites mimicking nacre are proposed.     

磁粉法检测表面裂纹概率曲线的测定

本文介绍了利用实物零件测定裂纹检出概率的方法，并作出了用磁粉法检测表面裂纹的检测概率曲线，为大型构件检测周期的确定提供了可靠数据，为结构损伤容限设计，可靠性设计提供了重要的依据。     

A rigorous assessment of the benefits of miniaturization in the Kolsky bar system

A rigorous experimental and numerical assessment is made of the benefits and limits of miniaturization in the Kolsky bar system. The primary issues that arise in very high strain rate testing (stress equilibration, inertial effects, wave dispersion, friction, and controllability of deformations) are addressed through experiments coupled with explicit finite element analyses. A miniaturized Kolsky bar system that includes the input bar is developed, together with the use of the laser occlusive radius detector to obtain local measurements of specimen strain during the very high rate deformations. It is demonstrated that this miniaturized Kolsky bar system can be used to provide fully validated results, including the explicit determination of equilibration, over a very wide range of strain rates (1×10³ to 5×10⁴ s⁻¹). The desired high strain rate can be achieved even at low accumulated strains, and the total strain developed can be controlled very effectively. Specific conditions are developed for determining the range of utility of the technique for a given material. The technique is applied to the characterization of 6061-T651 aluminum, and the results are compared with the results obtained using a conventional Kolsky bar.     

破碎岩石渗透性的试验测定方法

传统的试验仪器和方法仅能测试岩石破坏前的渗透系数，文中介绍了一种自行设计并已获国家专利的破碎岩石压实渗透仪，依靠其与MTS815.02岩石力学伺服系统连接匹配。利用MTS的两套闭环系统施加轴压和孔压，可测试压力作用下岩石破碎后的渗透系数，对破碎砂岩进行高压下的渗透测试进一步说明该方法的可行性。利用该方法得出的测试结果。对破碎岩体中渗流问题研究及灾害防治具有参考价值。     

An engineering approach to blade designs for low to medium pressure rise rotor-only axial fans

Low to medium pressure rise axial fan equipment of the arbitrary vortex flow rotor-only type is widely used in industrial and commercial applications, with many of the installations and rotor designs being far from optimum. Complex computational methods exist for analyzing flows in, for example, high-speed axial flow compressors with multistage blade rows; however, the designers and manufacturers of low-speed, general-purpose axial flow fan equipment have been reluctant to embrace this technology. A simpler yet reliable design technique is presented that allows this category of ducted axial fan rotors, in the presence of swirl-free inlet flow, to be designed to achieve a specified duty with sufficient accuracy for engineering purposes. Practical blade design recommendations and limits, similar to those that exist for free vortex flow axial rotors, have been established for the arbitrary vortex flow rotor-only case.

The technique employs a straightforward engineering approach to arbitrary vortex flow axial fan rotor design, and the equation set can be solved by using relatively simple numerical methods. Estimates of pressure rise and shaft power characteristics for a proposed fan/rotor design can be computed and the design loop iterated until an acceptable set of blade parameters is identified. It is also possible to analyze the performance of an existing axial fan installation as a prelude to the design of a more efficient and effective replacement rotor.

Experimental data used in validating the design and analysis techniques are also presented. These data include comprehensive Cobra pressure probe surveys of local flow parameters downstream of three different low boss ratio, low solidity, arbitrary vortex flow rotors (all with circular arc camber line type blades) as well as fan performance characteristics for one of the experimental rotors configured as a direct-exhaust fan unit. Installation-dependent factors such as direct-exhaust losses and tip clearance effects are also examined. The analytical technique is shown to provide acceptable estimates of fan/rotor pressure rise performance and shaft power characteristics over a moderately wide range of blade angles and operating conditions.     

用地面模拟试验识别卫星太阳电池翼伸展运动的各种阻尼参数

本文利用Lagnrange方程建立了卫星太阳电池翼伸展运动的数学模型.这是一个包含摩擦阻尼、结构阻尼和空气阻尼参数的非线性微分方程组.在用气垫消除了重力影响但存在空气阻尼的地面环境中,对实尺太阳电池翼模型进行了伸展运动的模拟试验并用频闪摄影技术记录了运动的时间历程.再利用最小p乘优化方法识别出该系统的各个阻尼参数.通过对系统运动方程进行数值积分求得的太阳电池翼的伸展运动历程与实测值相当吻合.取空气阻尼等于零,得出了太阳电池翼在无空气阻尼的太空中的伸展运动规律.     

Improvement of UV stability and mechanical properties of biopolyesters through the addition of β-carotene

β-carotene, the most abundant carotenoid in nature and a natural antioxidant, has been added at a concentration of 2 × 10⁻⁴ g per mL of polymer film forming solution to three biopolyester matrices, poly(lactic acid) (PLA), polycaprolactone (PCL) and polyhydroxybutyrate-co-valerate (PHBV). The dispersion and stability of the antioxidant within the films was studied using confocal Raman imaging spectroscopy, colorimetry and UV/visible spectrophotometry. The films were characterized in terms of thermal and mechanical properties in comparison with control films without β-carotene. Addition of β-carotene to the three biopolyesters studied resulted in significant increases in the deformation at break and lower Young modulus. This antioxidant is thought to act as a plasticizer in the biopolyesters, thus increasing their free volume and causing a change in their thermal properties. Moreover, when exposed to UV light the mechanical properties of the films with β-carotene were less affected displaying, in general, higher modulus and similar ultimate tensile strength while keeping the films more ductile than the pure films. Therefore, β-carotene can be potentially used as a natural additive to increase the UV stability of the biopolyesters.     

Mechanical behavior under nanoindentation of a new Ni-based glassy alloy produced by melt-spinning and copper mold casting

An investigation was made into the thermal stability and mechanical behavior under nanoindentation of a new glassy alloy with composition Ni₅₀Nb₂₈Zr₂₂, produced in the form of melt-spun ribbons and copper mold-cast wedges. The alloy composition was designed based on the lambda criterion combined with the electronegativity difference among the elements. X-ray diffraction and scanning electron microscopy confirmed that the ribbons and wedges (up to 200 μm in thickness) are amorphous. The thermal properties of these samples were evaluated by differential scanning calorimetry (DSC). Nanoindentation revealed that the hardness of this alloy, around 10 GPa, is among the highest reported for metallic glasses. Remarkably, the cast wedge exhibits greater hardness and higher elastic modulus than the ribbon. This correlates with the larger amount of frozen-in free volume in the ribbons than in the cast wedges, as evidenced by DSC. In addition, finite element simulations of nanoindentation curves were performed. The Mohr-Coulomb yield criterion allows for better adjustment of the experimental data than the pressure-independent Tresca yield criterion. The simulations also reveal that the cohesive stress in the ribbons is lower than in the wedges, which explains the difference in hardness and Young's modulus between the two samples.