Quantum topology phase diagrams for molecules,clusters, and solids

The need to make more quantitative use of the total electronic charge density distribution is demonstrated in this short perspective. This is framed in the perspective of the ground breaking early work of Bader and coworkers, along with mathematicians who captured the essential nature of a molecule in a suitably compact form in real space. We see that this simple form is the Poincaré–Hopf relation for molecules and clusters and the Euler–Hopf relation in solids. Thom's theory of elementary catastrophes combined with the Poincaré–Hopf relation provides the inspiration for the new quantum topology. An alternative use of the Poincaré–Hopf relation, molecular recognition, is discussed. Quantum topology is then used to create a topology phase diagram for both molecules and solids. The author adds their perspectives of the huge potential of the quantum topology approach by demonstrating the ease with which new theoretical ideas can be generated. © 2013 Wiley Periodicals, Inc.     

Synthesis and comparative study of the heterocyclic rings on liquid crystalline properties of 2,5-aryl-1,3,4-oxa(thia)diazole derivatives containing furan and thiophene units

A series of heterocyclic liquid crystalline compounds containing 1,3,4-oxadiazole/thiadiazole, furan and thiophene units were synthesised and characterised by means of electrospray ionisation-mass spectrometry (ESI-MS), high-resolution mass spectroscopy (HRMS), ¹H nuclear magnetic resonance (NMR) and ¹³C NMR. The thermal behaviours were investigated by differential scanning calorimetry (DSC) and polarised optical microscopy (POM). The effect of the 1,3,4-oxadiazole, 1,3,4-thiadiazole, furan, thiophene and benzene rings on the liquid crystalline properties was discussed briefly in context with the geometrical and electronic factors. The results showed that the tendency to form mesophases follows the sequence: 1,4-disustituted benzene >2,5-disubstituted thiophene >2,5-disustituted furan and 1,3,4-thiadiazole >1,3,4-oxadiazole.     

Gap formulas for closed linear relations

A classical formula for the gap between two densely defined closed operators in a Hilbert space is extended to the case of linear relations. Copyright © 2014 John Wiley & Sons, Ltd.     

4类图完美匹配数目的递推求法

本文研究了4类特殊图完美匹配数目的显式表达式.利用划分,求和,再递推的方法分别给出了图3-n Z4,2-n(2-C6),2-n(2-K4)和3-n(C4-C6)的完美匹配数目的计算公式.     

Circumventing the OCl versus OOH scaling relation in the chlorine evolution reaction: Beyond dimensionally stable anodes

The development of selective electrocatalysts for the chlorine evolution reaction (CER) is majorly restrained by a scaling relation between the OCl and OOH adsorbates, rendering that active CER catalysts are also reasonably active in the competing oxygen evolution reaction (OER). While theory predicts that the OCl versus OOH scaling relation can be circumvented as soon as the elementary reaction steps in the CER comprise the Cl rather than the OCl adsorbate, it was demonstrated recently that PtN₄ sites embedded in a carbon nanotube follow this theoretical prediction. Advanced experimental analyses illustrate that the PtN₄ sites also reveal a different reaction kinetics compared to the industrial benchmark of dimensionally stable anodes (DSA). A reverse Volmer–Heyrovsky mechanism was identified, in which the rate-determining Volmer step for small overpotentials is followed by the kinetically limiting Heyrovsky step for larger overpotentials. Since the PtN₄ sites excel DSA in terms of activity and chlorine selectivity, we suggest the Cl intermediate as well as the reverse Volmer–Heyrovsky mechanism as the design criteria for the development of next-generation electrode materials beyond DSA.     

Grey relational analysis for optimization of wear parameters and surface roughness on nano composite coating

The higher wear resistance of Ni based nano composite coatings makes them potential replacement in protecting the substrate materials. The role of surface roughness of the coating along with wear parameters on the specific wear rate, pin temperature, and COF are addressed in the present study. The use of hard nano Al₂O₃ particles found significant role in increasing the resistance to wear for Ni matrix coatings on Al6061 material. The resistance to dislocation offered by these nano Al₂O₃ particles and smear out of debris with plastic deformation indicated abrasive and adhesive nature of wear mechanism in combination. The optimization of wear parameters are carried out by surface response method based grey relation analysis. The normal load applied onto the pin has significant influence on the specific wear rate and temperature rise in the pin. The surface roughness of the coating has also found instrumental in the higher pin temperature and friction coefficient.     

A new high frequency dynamic mechanical analysis system: An approach to direct high frequency testing of tire tread rubber

Dynamic Mechanical Analysis (DMA) systems are measurement devices for obtaining master curves and complex modules of viscoelastic materials, such as rubbers. The conventional DMAs measurement systems in market have several limitations, which restrict their ability for operating at high frequencies. Thus, Williams, Landel and Ferry (WLF) relation is used to produce master curves and predict the material properties at high frequencies. In conventional DMAs, experiments are done in a range of temperatures, and then a master curve is made for a chosen reference temperature by shifting the measurements data to high frequencies. Therefore, the obtained results, which are not based on direct measurements, can be inaccurate. In order to overcome this problem a new simple shear high-frequency DMA (HFDMA) system is designed and built to directly measure the dynamic mechanical properties of viscoelastic material at high frequencies and the strain levels sufficient for tire manufacturers. The new HFDMA can be used to test any viscoelastic materials which have glass transmission temperature (Tg) lower than room temperature (about 23 °C) such as the Styrene-butadiene rubber (SBR). The SBR is the base material for tire tread. The designing process of this new HFDMA is presented in this paper. The rubber specimen shape is chosen by taking into account the shear elastic wave effect, bending, buckling effect and heat generation in the specimen. The repeatability test is accomplished to ensure that the results obtained from the new HFDMA are repeatable and the repeatability uncertainty is about 0.04%. The new HFDMA is validated by comparing to the direct test results of conventional DMA at 100 Hz. The direct high frequency (5 kHz) complex shear modulus and damping factor are compared with the master curve of the conventional DMA developed by the use of WLF relation for SBR. This comparison revealed that the complex shear modulus and damping factor of the SBR obtained from the HFDMA at 5 kHz and 0.05% strain amplitude are about 7% and 6.5% higher than those obtained from the conventional DMA, respectively.     

钽的层裂实验数值模拟

 采用连续介质力学基唯象模型模拟分析了钽的平板撞击层裂行为。该模型包括了材料的非线性弹性（状态方程）、率相关塑性和孔洞的形核及生长等多种效应,并且采用一种对角隐式Runge-Kutta方法来求解本构率方程组,提高了热粘塑性本构关系计算的稳定性及精度。将数值模拟结果和相关实验数据进行了对比分析,结果表明,对于样品中的拉应力峰值明显高于材料层裂强度的实验（中、高速平板撞击实验）,理论模型具有较好的预估能力,但对于临界层裂问题（低速平板撞击实验）,该模型对材料损伤与失效过程的描述可能不够准确,需要进一步改进。     

基于物理中面FGM板屈曲的有限元分析

基于物理中面的概念,根据最小势能原理推导了功能梯度材料FGM薄板屈曲的有限元控制方程,求得临界荷载的有限元解。利用FGM板的屈曲方程与参考均匀板的屈曲方程之间的相似性,建立了FGM板的临界荷载与参考均匀板的临界荷载之间的相似转换关系式,从而将FGM板临界荷载的计算转变为参考均匀板的临界荷载和材料不均匀系数的计算,极大地提高了计算效率,为FGM的推广起积极的推动作用。通过数值算例,将由有限元法和转换关系式得到的临界荷载进行了比较,并讨论了边界条件、荷载工况、材料组成和几何尺寸等对FGM板临界荷载的影响。     

Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit-qubit and qutrit-qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.