二维正方格子磁性光子晶体的带隙结构

采用平面波展开的方法计算了正方格子二维磁性光子晶体(MPC)的光子带隙结构.散射子的形状分别为：长方形，正方形，六角形和圆形.通过调节磁导率，填充率和散射子的旋转角度，找到了MPC各种结构的最大的绝对带隙宽高比ω_R.研究发现：随着磁导率的增加，MPC绝对带隙中心频率ω_g单调减小，绝对带隙宽度Δω和其宽高比ω_R可能不同时达到最大值.而随着填充率或者散射子旋转角的增加，基本不改变ω_g的大小，各种结构的Δω和ω_R同时达到最大值. 关键词： 磁性光子晶体 光子带隙结构     

Suzuki晶格光子晶体的光子带结构

系统地研究了Suzuki晶格光子晶体能带结构,包括介质中周期排列的空气孔光子晶体和空气中周期排列的介质柱光子晶体。采用平面波展开法计算了空气孔和介质柱半径及折射率对光子带隙的影响。结果发现介质中周期排列的空气孔光子晶体主要形成TM模光子禁带,空气中周期排列的介质柱光子晶体主要形成TE模光子禁带,只有介质折射率较大时两类光子晶体才能够形成完全带隙。介质中周期排列的空气孔光子晶体能带结构中沿Г-X1和X1-M方向出现了群速度接近于零的色散曲线,而在另一类光子晶体中并未出现这种情况,在其它晶格类型的光子晶体中也未发现这种情况。     

The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

Synthesis of highly‐ordered hierarchical ZnO nanostructures and their application in dye‐sensitized solar cells

In order to improve the performance of ZnO‐based solar cells, highly‐ordered hierarchical ZnO nanostructures were design and fabricated. The hierarchical nanostructures were grown on FTO (fluorine doped tin oxide, SnO₂:F) glass substrates via a facile, low‐temperature, and low‐cost chemical route. The morphology and structure of the obtained products has been confirmed by field‐emission scanning electron microscopy and X‐ray diffraction measurements. The performance investigation of the prepared dye‐sensitized solar cells (DSSCs) demonstrates that the hierarchical ZnO nanostructure‐based solar cell shows a higher short‐circuit current density compared with the ZnO nanowire counterpart. The enhanced current density may be due to the fact that the surface area of the hierarchical nanostructures is increased. These results indicate that hierarchical ZnO nanostructures are more suitable for the application as photoelectrode of DSSCs. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

自掺杂TiO2纳米管：液相制备及光催化性能

采用水合肼（N₂H₄·H₂O）作为还原剂,在液相环境中制备了自掺杂TiO₂纳米管阵列（NTs）。利用FE-SEM、EDS、XPS、XRD、Raman、UV-Vis/NIR分光光度法以及半导体特性分析系统（Keithley 4200 SCS）分别对样品的形貌,晶体结构,光学特性以及电学性能进行了表征。结果表明：通过这种方法制备的自掺杂TiO₂NTs在带隙中引入了大量的氧空位,创造了氧空位能级,从而提高了样品的电导率,有效提高光生电子-空穴对的产生、分离和传输。此外,由于氧空位的作用,使得TiO₂NTs的带隙变窄,增强了可见光吸收能力,致使样品具有较高的光催化活性,并通过降解甲基橙溶液对样品的光催化活性进行评估。结果显示当光照150min后,自掺杂TiO₂NTs对甲基橙溶液的降解率达73%,并且这种催化剂便于回收和重复使用。     

Characteristics of electron beam evaporated nanocrystalline SnO2 thin films annealed in air

Tin oxide (SnO₂) thin films (about 200 nm thick) have been deposited by electron beam evaporation followed by annealing in air at 350-550 °C for two hours. Optical, electrical and structural properties were studied as a function of annealing temperature. The as-deposited film is amorphous, while all other annealed films are crystalline (having tetragonal structure). XRD suggest that the films are composed of nanoparticles of 5-10 nm. Raman analysis and optical measurements suggest quantum confinement effects that are enhanced with annealing temperature. For instance, Raman peaks of the as-deposited films are blue-shifted as compared to those for bulk SnO₂. Blue shift becomes more pronounced with annealing temperature. Optical band gap energy of amorphous SnO₂ film is 3.61 eV, which increases to about 4.22 eV after crystallization. Two orders of magnitude decrease in resistivity is observed after annealing at 350-400 °C due to structural ordering and crystallization. The resistivity, however, increases slightly with annealing temperature above 400 °C, possibly due to improvement in stoichiometry and associated decrease in charge carrier density.     

Photocurrent measurements on GaAs1−xNx epilayers grown by metalorganic chemical vapor deposition

GaAs_1−xN_x epilayers were grown on a GaAs(0 0 1) substrate by metalorganic chemical vapor deposition. Composition was determined by high resolution X-ray diffraction. Band gap was measured from 77 to 400 K by using photocurrent measurements. The photocurrent spectra show clear near-band-edge peak and their peak energies drastically decrease with increasing nitrogen composition due to band gap bowing in the GaAs_1−xN_x epilayers. Those red shifts were particularly notable for low nitrogen compositions. However, the shifts tended to saturate when the nitrogen composition become higher than 0.98%. When the nitrogen composition is in the range 1.68–3.11%, the measured temperature dependence of the energy band gap was nicely fitted. However, the properties for the nitrogen composition range 0.31–0.98% could not be fitted with a single fitting model. This result indicates that the bowing parameter reaches 25.39 eV for low nitrogen incorporation (x=0.31%), and decreases with increasing nitrogen composition.     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

Integrality gaps for colorful matchings

We study the integrality gap of the natural linear programming relaxation for the Bounded Color Matching (BCM) problem. We provide several families of instances and establish lower bounds on their integrality gaps and we study how the Sherali–Adams “lift-and-project” technique behaves on these instances. We complement these results by showing that if we exclude certain simple sub-structures from our input graphs, then the integrality gap of the natural linear formulation strictly improves. To prove this, we adapt for our purposes the results of Füredi (1981). We further leverage this to show upper bounds on the performance of the Sherali–Adams hierarchy when applied to the natural LP relaxation of the BCM problem.