Isometries and additive mapping on the unit spheres of normed spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.     

Inclined Substrate Deposition of Nanostructured TiO2 Thin Films for DSSC Application

Nanostructured TiO₂ films were deposited onto Indium Tin Oxide (ITO) and glass substrates by dc reactive magnetron sputtering at different substrate inclination angles. The structural and optical properties of the deposited films were studied by X-ray diffraction, scanning electron microscopy and UV–Vis spectrophotometer, respectively. Dye-sensitized solar cells (DSSC) were assembled using these TiO₂ films as photoelectrodes and the effect of the substrate inclination angle in the preparing process of TiO₂ films on the DSSC conversion efficiency was studied.     

甲醇在M@CNTs表面吸附和初步裂解机理的DFT研究

基于密度泛函理论(DFT)研究了CH_3OH在M@CNTs(M=Fe、Co、Ni、Cu、Fe_2、Co_2、FeCo)表面吸附和初步裂解机理.在M@CNTs表面CH_3OH裂解存在C-H、C-O、O-H 3条可能路径.我们计算了CH_3OH及中间体在CNTs和M@CNTs表面的吸附能,并计算了3条可能路径下的相关反应热和活化能.计算结果表明,CH_3OH在CNTs和M@CNTs表面是物理吸附,O-H键断裂是最有利的路径,其在不同催化剂表面的活化能顺序是CNTs(1.60 eV)、Cu@CNTs(1.57 eV)、Ni@CNTs(1.38 eV)、Co@CNTs(1.11 eV)、Fe@CNTs(1.10 eV)、Fe_2@CNTs(1.06 eV)、Co_2@CNTs(1.00 eV)、Fe Co@CNTs(0.76 eV),即Fe Co@CNTs可作为CH_3OH初步裂解的有效催化剂.     

Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows. We prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large oscillations and the initial density may allowed to contain the interior and far field vacuum states. Furthermore, the large time behavior of the solution is obtained as well.     

Manipulating Nonlinear Photocurrent from Interlayer Coupling in Bilayer Metamaterials for Polarized Terahertz Generation

Polarized terahertz (THz) wave generation is of great significance for chiral and anisotropic sensing applications. However, how to manipulate amplitude, polarization, and ellipticity of the THz generation is still a fundamental challenge. Herein, polarized THz wave generation is achieved from a bilayer metamaterial consisting of T-shaped structure (TSS) and split resonator rings (SRRs) by combining Maxwell and hydrodynamic equations. The elliptically polarized THz wave can be synthetized directly from horizontally and vertically polarized THz components due to the orthogonal nonlinear photocurrents along the arm-directions of TSS and SRRs, respectively. Besides, the ellipticity and the orientation angle of the THz polarization ellipse can be modulated by the twist angle between the SRRs and TSS layers. The maximum ellipticity can reach 0.34 while the orientation angle is tunable from −0.45 to 0.48π by tuning the twist angle. This work proposes an interlayer coupling method for the polarized THz sources based on metamaterials in potential circular dichroism and chiral sensing applications.     

Flexibly Enhanced Photonic Spin Hall Effect via Selective Brewster Angle

The manipulating of photonic spin Hall effect (SHE) plays a crucial role for development of spin-dependent nanodevices and systems. Since the photonic SHE is generally enhanced near the Brewster angle, the choice of incident angle usually has low flexibility with natural materials due to their dielectric constants. Herein, an efficient method to flexibly enhance the photonic SHE by utilizing selective Brewster angle in an anisotropic metamaterial is proposed. Through adjusting the thickness ratio of two media in metamaterial, the Brewster angle can be flexibly adjusted in a broad range (nearly 0–90°). With the selective Brewster angle, the spin-dependent transverse shift can be enhanced at nearly arbitrary incident angles. Furthermore, based on this structure, a binary encoding system is demonstrated, realizing information conversion around incident angles. This research work provides more possibilities for applications in manipulating photonic SHE.     

Improving Data Quality in Traditional Low-Dose Scanning Transmission Electron Microscopy Imaging

It has become very important to study and find optimal conditions for imaging electron-beam (e-beam) sensitive materials in scanning transmission electron microscopy under low electron-dose with high signal-to-noise ratio (SNR). Convergence and collection angles and electron-probe current are essential parameters. However, these parameters have rarely been discussed in a systematic way. In this paper, the illumination and collection conditions are optimized according to the resolution requirement of different materials by adjusting the condenser and intermediate lenses in a commercial transmission electron microscope. To demonstrate the significance of optimizing these parameters, two examples, zeolite MFI and metal–organic framework (MOF) MIL-101, are taken among the sensitive materials, with the most important electron incidences along the [010] and <110> directions, respectively. High SNR atomic resolution images of MFI are obtained with e-beam current as low as 0.50 pA, reaching information transfer for reflection up to 18 0 2 corresponding to d-spacing of 0.11 nm, close to the resolution limit of 0.098 nm from resolvable diffraction limit. MOF MIL-101 is characterized under an even lower e-beam 0.2 pA to avoid severe beam damage. High-quality annular dark and bright field images are obtained, which proves the wide applicability of this method on more e-beam sensitive materials.     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

Three-Dimensional Dynamic Contact Problem for an Elliptic Crack Interacting with a Normally Incident Harmonic Compression–Expansion Wave

The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented     

A DECAGONAL QUASICRYSTAL WITH AN ARC-SHAPED CRACK

A decagonal quasicrystal,which is weakened by an arc-shaped crack penetratingthrough the solid in the period direction,and which is subjected to remote uniform phonon stresses,is investigated by applying the complex variable method which is just developed by the authors.It is found that the phonon and phason stresses near the crack tips exhibit inverse square rootsingularities.The four complex stress functions characterizing the phonon and phason fields arederived.Explicit expressions for the phonon and phason stress intensity factors,crack openingdisplacements and energy release rate are also presented.