Closed Unstretchable Knotless Ribbons and the Wunderlich Functional

In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible shapes of the band. By using the developability of the band, Wunderlich reduced the bending energy from a surface integral to a line integral without assuming that the width of the band is small. Although Wunderlich did not completely succeed in determining the equilibrium shape of the Möbius band, his dimensionally reduced energy integral is arguably one of the most important developments in the field. In this work, we provide a rigorous justification of the validity of the Wunderlich integral and fully formulate the energy minimization problem associated with finding the equilibrium shapes of closed bands, including both orientable and nonorientable bands with arbitrary number of twists. This includes characterizing the function space of the energy functional, dealing with the isometry and local injectivity constraints, and deriving the Euler–Lagrange equations. Special attention is given to connecting edge conditions, regularity properties of the deformed bands, determination of the parameter space needed to ensure that the deformation is surjective, reduction in isometry constraints, and deriving matching conditions and jump conditions associated with the Euler–Lagrange equations.

     

探测器偏置重建算法在工业CT检测中的应用

工业CT检测对象的大小是不固定的,最大限度地利用已有探测器的成像面积非常重要。采用探测器偏置来获得更大的扫描视野,并推导相应的重建算法。该算法首先使用Parker类型函数对采集到的投影数据中的冗余部分进行加权,然后采用扇束滤波反投影重建算法重建得到断层图像。在实验中使用实际工业CT系统分别采集钢制线对块与铝合金变速器外壳的投影数据进行重建算法的验证,重建结果证明了使用的探测器偏置重建算法的正确性与有效性,且空间分辨率和标准扫描的重建结果保持一致,这个方法可以在工业CT成像上有效使用。     

Investigation on Properties of Polypropylene/Multi-walled Carbon Nanotubes Nanocomposites Prepared by a Novel Eccentric Rotor Extruder Based on Elongational Rheology

The properties of polymer matrix composites are related not only to the chemical composition of the materials but also to the processing equipment used for their preparation which has a direct influence on the microstructure of the composites. In this paper polypropylene (PP)/multi-walled carbon nanotubes (MWCNTs) nanocomposites were prepared by melt blending through a self-developed, eccentric rotor extruder (ERE). The structure and elongational deformation mechanism of an ERE were described in detail. The morphological, rheological, thermal and mechanical properties of the resulting PP/MWCNTs nanocomposites were investigated. Scanning electron microscopy (SEM) and rheological analysis showed that the MWCNTs were well dispersed in the PP matrix. The thermal stability was investigated by thermogravimetric analysis (TGA) and indicated that the addition of MWCNTs could effectively improve the thermal stability of pure PP. The percentage of crystallinity and tensile strength of the composites were improved as a result of the heterogeneous nucleation effect of the MWCNTs in the PP matrix. The research results revealed that the enhancement of the properties of PP/MWCNTs composites could be attributed to a better dispersion of the MWCNTs in the matrix as compared to samples prepared by conventional extrusion.     

Morphology and elemental behaviour in the alteration layer of borosilicate glass in simulated groundwater

To understand the behaviour of nuclear waste glass in groundwater, borosilicate glasses were placed in simulated groundwater for more than 200 days. The composition of the simulated groundwater was similar to that of the groundwater in Beishan (a potential nuclear waste site). The pH value of groundwater was adjusted to 7.5, and the ratio of the surface area of glass to the volume of the solution (SA/V) was set to 10?m^?1. Solutions and bulk glasses were characterised to obtain the elemental behaviour and surface morphology of the glass/solution interface, which was named the alteration layer. The mean thicknesses of the alteration layer were 5.16?±?0.11?µm and 11.67?±?0.28?µm at 70°C and 90°C, respectively. A thicker alteration layer was attributed to the lower surface activation energy of the glass and a high ion exchange between K⁺ and Na⁺ in the interface between the glass surface and the solution. For the elemental behaviour, mobile species B and Na were depleted, while K and Ca from the solution were enriched in the alteration layer due to ion exchange. Network species Si decreased in the layer, leading to the corrosion of the backbone of the glass; however, species Al increased, which implied that some [SiO₄] units were partially replaced by [AlO₄] units. In this work, glass in groundwater suffered much more intense corrosion than that in de-ionised water.     

Electronic band structure of a type-II ’W’ quantum well calculated by an eight-band k·p model

In this paper, we present an investigation of type-II 'W' quantum wells for the InAs/Ga_1-xIn_xSb/AlSb family, where 'W' denotes the conduction profile of the material. We focus our attention on using the eight-band k?p model to calculate the band structures within the framework of finite element method. For the sake of clarity, the simulation in this paper is simplified and based on only one period---AlSb/InAs/Ga_1-xIn_xSb/InAs/AlSb. The obtained numerical results include the energy levels and wavefunctions of carriers. We discuss the variations of the electronic properties by changing several important parameters, such as the thickness of either InAs or Ga_1-xIn_xSb layer and the alloy composition in Ga_1-xIn_xSb separately. In the last part, in order to compare the eight-band k?p model, we recalculate the conduction bands of the 'W' structure using the one-band k?p model and then discuss the difference between the two results, showing that conduction bands are strongly coupled with valence bands in the narrow band gap structure. The in-plane energy dispersions, which illustrate the suppression of the Auger recombination process, are also obtained.     

Current and strain-induced spin polarization in InGaN/GaN superlattices

The lateral current-induced spin polarization in InGaN/GaN superlattices (SLs) without an applied magnetic field is reported. The fact that the sign of the nonequilibrium spin changes as the current reverses and is opposite for the two edges provides a clear signature for the spin Hall effect. In addition, it is discovered that the spin Hall effect can be strongly manipulated by the internal strains. A theoretical work has also been developed to understand the observed strain-induced spin polarization. Our result paves an alternative way for the generation of spin polarized current.     

Numerical study of InGaN tandem solar cells with intermediate bands

Theoretical investigations of InGaN tandem solar cells with intermediate bands (IBs) have been conducted through calculating the diode equation taking into account the radiative and nonradiative recombination currents. The calculated maximum ef?ciencies of the double‐junction cell with one IB in each subcell are 57.85% and 68.37% under AM1.5G one‐sun and 46000‐sun illuminations, respectively. It has also been observed that the combined device with the top‐cell bandgaps of 2.9–3.4 eV (2.6–3.4 eV for full concentration) may have an opportunity to realize the application of over 50% efficiency. We suggest that the optimized width of the IB layer be designed in the range of 1–6 μm if its absorption coefficient is 10⁴–10⁵ cm^–1 in the IB region.     

Burst synchronization transitions in a neuronal network of subnetworks

In this paper, the transitions of burst synchronization are explored in a neuronal network consisting of subnetworks. The studied network is composed of electrically coupled bursting Hindmarsh-Rose neurons. Numerical results show that two types of burst synchronization transitions can be induced not only by the variations of intra- and intercoupling strengths but also by changing the probability of random links between different subnetworks and the number of subnetworks. Furthermore, we find that the underlying mechanisms for these two bursting synchronization transitions are different: one is due to the change of spike numbers per burst, while the other is caused by the change of the bursting type. Considering that changes in the coupling strengths and neuronal connections are closely interlaced with brain plasticity, the presented results could have important implications for the role of the brain plasticity in some functional behavior that are associated with synchronization.     

欧洲FAIR中超导二极磁体样机的初步设计与分析

介绍了欧洲FAIR超导二极磁体样机设计的背景及设计要求,以及磁体样机的几个大部件及其作用。用有限元分析软件ANSYS进行了线圈电磁性能分析,得到其磁场、电感、储能随电流的变化曲线,并对其中的一个部件线圈盒进行了结构分析,为下一步的设计提供参考。