Global energy spectra of bands and density of states in a class of two-tile systems

Electronic properties of a general class of one-dimensional two-tile systems are calculated exactly. The systems containing periodic crystals, generalized Fibonacci quasicrystals, generalized Thue-Morse aperiodic lattices and even other two-tile aperiodic lattices, can be divided into two different families which are constructed by the inflation rules: {A, B}{A ^m11 B ^m12,A ^m21 B ^m22} and {A, B}{A ⁿ¹¹ B ⁿ¹²,B ⁿ²¹ A ⁿ²²}, respectively. As typical examples, global spectra of bands and density of states in some two-tile aperiodic systems are numerically calculated. Some interesting properties are obtained.     

电磁场边值关系中的独立方程

文献[1]曾指出、在麦克斯韦微分方程组中,只有二个旋度方程是独立的。文献[2]曾就定态波的特殊情况,指出电磁场边值关系中,也只有二个方程是独立的。本文进一步在随时间任意变化场情况下,从电磁场的二切向分量边值关系推导出另外二个法向分量的边值关系,从而普遍的证明了时变电     

SO_2和NO_2在γ-Al_2O_3(110)表面吸附的第一性原理计算

采用基于平面波基组的Vienna Ab-initio Simulations Package (VASP)程序研究了SO_2和NO_2在γ-Al_2O_3(110)表面和羟基化γ-Al_2O_3(110)表面的吸附,获得了SO_2和NO_2吸附的不同构型和结构参数.对吸附能,电荷转移,差分电荷密度和投影态密度等进行分析和讨论.对比发现,在γ-Al_2O_3(110)表面SO_2的吸附能力强于NO_2.SO_2或NO_2在非羟基化γ-Al_2O_3(110)表面吸附时O原子的2p轨道和Al原子的3s3p轨道作用形成O-Al键,且SO_2吸附时键结强度高于NO_2.NO_2吸附时费米能级以下有部分反键态,削弱了与γ-Al_2O_3(110)表面相互作用.在羟基化γ-Al_2O_3(110)表面SO_2或NO_2的吸附能力会低于非羟基化表面,但是SO_2的吸附能力依旧强于NO_2.计算结果说明SO_2与γ-Al_2O_3(110)表面的相互作用强于NO_2.以上研究,将有助于理解SO_2和NO_2在γ-Al_2O_3的反应性,为进一步研究它们的非均相转化和在灰霾形成中的促进作用奠定基础.     

COF-42:一种理想的锂硫电池锚定材料

寻找理想的锚定材料抑制穿梭效应是锂硫电池面临的重要问题之一.本文采用密度泛函方法,研究了四种共价有机框架COFs材料(COF-1,CTF-1,COF-LZU1和COF-42)和硫锂化合物(Li_2S_n)的作用机理.通过分析吸附构型、吸附能、电子密度差分以及态密度等性质,发现COFs材料与硫锂化合物的化学吸附作用主要源于COFs表面极性N和O原子与Li之间的静电作用力.在COF-42/Li_2S_n吸附构型中,N和O原子与Li之间形成双重类离子键;电子密度差分和Bader电荷差分表明,与其他COFs材料相比,Li_2S_n和COF-42之间电荷转量最多,因此,COF-42具有最强的锚定作用.比较Li_2S_n和COF-42以及常用电解质分子1,3-二氧戊环(DOL)和二甲氧基乙烷(DME)的吸附能,证明COF-42可以抑制电解质分子的溶剂化作用; COF-42与COF-1,CTF-1和COF-LZU1相比较,具有良好导电性.因此,COF-42可能是一种理想的锂硫电池锚定材料.     

硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料,是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一,有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布,纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

剪切形变下掺杂及缺陷对MoS2电子结构的影响

本文利用密度泛函理论,研究剪切形变下掺杂改性及不同类型缺陷对MoS2电子结构的影响。发现：剪切形变下,MoS2+P体系为相对最稳定的结构,掺杂改性相较于缺陷对模型稳定性影响更小;模型MoS2+P+Se中P-Mo键易形成共价键,而其中的Se-Mo键和MoS2+P-Mo-S模型中的P-Mo键,易形成离子键;掺杂使MoS2模型能隙变大,而缺陷使能隙减小,且S和Mo原子共缺陷的模型带隙为0;缺陷相较于掺杂改性模型,更能使Mo原子周围增加电荷聚集度,带隙值更低,更能影响或调控模型的电子结构。     

A posteriori error estimates for optimal control problems governed by parabolic equations

Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem. Received July 7, 2000 / Revised version received January 22, 2001 / Published online January 30, 2002 RID="*" ID="*" Supported by EPSRC research grant GR/R31980     

Lp (?m × ?n) boundedness for the Marcinkiewicz integral on product spaces

L^p(R^m × Rⁿ) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the L^p(R^m × Rⁿ) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained.     

平面动力问题的理论求解

通过对平面动力问题控制方程的分析,研究了相应的应力函数，得出了关于应力函数的基本方程。     

Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam

In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control actiondecays exponentially or in negative power of time t as t→∞.