A periodic isoperimetric problem related to the unique games conjecture

We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the unique games conjecture, less a small error. Let n ≥ 2. Suppose a subset Ω of n‐dimensional Euclidean space satisfies ?Ω = Ω^c and Ω + v = Ω^c (up to measure zero sets) for every standard basis vector . For any and for any q ≥ 1, let and let . For any x ∈ ?Ω, let N(x) denote the exterior normal vector at x such that ‖N(x)‖₂ = 1. Let . Our main result shows that B has the smallest Gaussian surface area among all such subsets Ω, less a small error: In particular, Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor 6 × 10^?9 would prove the endpoint case of the Khot‐Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the unique games conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the unique games conjecture. Nevertheless, this paper does not prove any case of the unique games conjecture.     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.     

Influence of substrate temperature and N2/Ar flow ratio on the stoichiometry,structure and hardness of TaNx coatings deposited by DC reactive sputtering

The effect of substrate temperature and N2/Ar flow ratio on the stoichiometry, structure and hardness of TaN_x coatings prepared on (111) Si substrates by DC reactive sputtering was investigated. For the structural, chemical and morphological analysis, X‐ray diffraction (XRD), Auger electron scanning and atomic force microscopy were respectively used. Hardness values of thin films were determined using the work of indentation model from nanoindentation measurements. TaN stoichiometric coatings were obtained for samples deposited at room temperature. The stoichiometric TaN phase was not obtained by increasing the temperature up to 773 K, even when increasing the N₂/Ar flow ratio. Even when a saturation in nitrogen content was achieved, nitrogen vacancies are still present in those samples. For coatings prepared at 773 K and low N₂/Ar flow ratio, a phase mixture between TaN_x and cubic α‐Ta was observed, while a cubic structure δ‐TaN was formed by increasing the N₂/Ar flow ratio. A maximum in hardness and (38 GPa) was obtained for the sample deposited at 773 K and a N₂/Ar flow ratio of 0.2, which presented a δ‐TaN cubic crystalline structure and a roughness value of 1.6 nm. Copyright © 2015 John Wiley & Sons, Ltd.     

Micromechanical properties of one-step and sequentially crosslinked UHMWPEs for total joint replacements

Microindentation hardness testing was applied to five types of highly-crosslinked ultrahigh molecular weight polyethylenes (UHMWPEs) for total joint replacements. UHMWPE's were crosslinked using the same total radiation dose (75 kGy; γ-radiation) either by the standard, single-step irradiation (one-step crosslinking) or by the newer, several-step irradiation (sequential crosslinking). Each irradiation step was followed by thermal treatment (annealing at 110 °C or remelting at 150 °C) in an inert atmosphere. We showed that: (i) the micromechanical properties were determined by the last thermal treatment step, while the number of irradiation cycles was insignificant and (ii) the values of microhardness, microcreep and microplasticity from the microindentation experiments were in excellent agreement with the changes of UHMWPE structure, characterized by IR and DSC. Statistical evaluation of the results, the agreement with theoretical predictions and the comparison with previous studies on similar systems demonstrated that microindentation was a reliable and sensitive method of UHMWPE characterization.     

摩托车传动用滚子链磨损特性的研究

道路行驶磨损试验结果表明，摩托车传动用滚子链套筒和销轴零件的主要磨损形式是磨粒磨损，并伴随有疲劳磨损的特征．由微观分析和链条的磨损伸长量可知：套筒和销轴的初始表面硬度较高，有利于改善其磨损表面形貌状态和耐磨性；在磨粒磨损机制下，套筒和销轴零件的表面硬度较低，容易产生“犁切”，表面层的循环硬化现象比较明显，磨损严重；在油池润滑条件下，套筒和销轴零件的表面硬度较高，裂纹的扩展速率较快，循环软化现象也较明显，当表面硬度较低时发生循环硬化．循环软化与循环硬化是导致磨损严重的原因之一．     

硬度及冲击韧性对高钒高速钢磨损稳定性的影响

通过改变热处理工艺获得不同硬度及冲击韧性、含钒10%的高钒高速钢试样,提出了磨损稳定性的概念及采用磨损稳定性因子(K)量化磨损稳定性的方法,研究了硬度和冲击韧性对高钒高速钢的磨损稳定性影响.结果表明:随着硬度增加,磨损稳定性及其耐磨性提高;随着冲击韧性提高,虽然耐磨性降低,但磨损稳定性有所提高.在本文试验条件下,随着残余奥氏体变化量(△A)增加,高钒高速钢的磨损稳定性下降.     

纳米压痕过程的三维有限元数值试验研究

采用有限元方法模拟了纳米压痕仪的加、卸载过程，三维有限元模型考虑了纳米压痕仪的标准Berkovich压头．介绍了有限元模型的几何参数、边界条件、材料特性与加载方式，讨论了摩擦、滑动机制、试件模型的大小对计算结果的影响，进行了计算结果与标准试样实验结果的比较，证实了模拟的可靠性．在此基础上，重点研究了压头尖端曲率半径对纳米压痕实验数据的影响．对比分析了尖端曲率半径r＝0与r＝100nm两种压头的材料压痕载荷—位移曲线．结果表明，当压头尖端曲率半径r≠0时，基于经典的均匀连续介质力学本构理论、传统的实验手段与数据处理方法，压痕硬度值会随着压痕深度的减小而升高．     

Shear Band Formation in Fe–Cr–Mo–V–B–Si Amorphous Alloy under Nanoindentation

The formation of shear bands in Fe–Cr–Mo–V–B–Si amorphous alloy under nanoindentation Is studied. The indentation process is considered against the background of shear band formation in the amorphous material.     

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

The Orion Water-Hardness Electrode: An Unexpected Response to Magnesium Ion

Abstract

The Orion water-hardness electrode, while being used to measure magnesium ion activity in a series of calcium-free solutions, displayed some unanticipated changes in potential. As the overall potential change observed for one solution was 183 mV (equivalent to more than six orders of magnitude changes in magnesium-ion activity), several precautions are suggested which should be observed when using this electrode for specific purposes. In particular, it is recommended that the exchanger be pre-equilibrated with an appropriate solution if the electrode is to be used in restricted systems of known chemical composition.