弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

外加直流电场作用下高阶弱非线性复合介质的电势分布

利用同伦分析方法, 研究了一类由柱形杂质随机嵌入基质所形成的、电场和电流密度满足J = σ E + χ |E|²E + η|E|⁴E 形式本构关系的高阶弱非线性复合介质在外加直流电场作用下的电势分布问题. 首先利用模函数展开法, 将本构方程及边界条件化成了一系列非线性常微分方程的边值问题; 再利用同伦分析方法进行求解, 给出了电势在基质和杂质区域的渐近解析解. 关键词： 高阶弱非线性复合介质 模函数展开法 同伦分析方法 电势分布     

关於展开子

本文讨论展开子的一些性质。将展开子A_nrst变换至ξ表示,定义为〈ξ|〉=∑ξ₀^-n-1ξ₁^rξ₂^sξ₃^tA_nrst,立即可以看出〈ξ|〉在洛伦兹变换中的变换,正如标准表示中的变换。由此可以立即证明,在标志洛伦兹群的各种不可约表示的两个量J=-1/2I_klI^kl,I=1/2ε^klmnI_klI_mn中,对於展开子而言,I一定等於零。我们也证明了如果我们要求J的本徵函数〈ξ|〉在各处行为正常,便获得J<0,亦即展开子表示为么正的条件。对於在展开子空间(J,0)及其他空间(I′,J′)中作用的矢量算符,我们作出了计算。选择定则为(i)I′=0,J′=1+J±2(1+J)^1/2;(ii)I′=±(1+J)^1/2i,J′=1+J。我们又证明了ξ^vξ_v?/(?ξ^μ)/(ξ^μ)-(1±(1+J)^1/2)ξ_μ将(J,0)空间变为(1+J±2(1+J)^1/2,0)空间。利用上式中取“-”符号的算符,我们可以构成一个像(-ir_μp^μ+k)ψ=0的波动方程,其中ψ只在两个展开子空间中。     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

Reduced s-d model with antiferromagnetically coupled impurity spins

An antiferromagnetic equivalent-neighbour Heisenberg interaction H_i between impurity spins is added to the reduced s-d Hamiltonian H_r previously introduced by simplifying the Kondo s-d exchange Hamiltonian H_K. Asymptotic mean-field theory is developed for H_r + H_i, in the presence and absence of external magnetic field, and applied to (La_1−xCe_x)Al₂ alloys. Specific heat c_i(T) and zero-field susceptibility χ_i(0,T) curves for (La_1−xCe_x)Al₂ are depicted. The coupling constants of H_r + H_i and conduction bandwidth are adjusted so that T_c temperatures for x = 0.2, 0.1 are equal to the experimental values. c_i(T) exhibits a jump at T_c and is decreasing for T < T_c. χ_i(0,T) has a first order pole at T_c which corresponds to the maximum of experimental susceptibility and χ_i(0,0) > 0. These results improve those obtained earlier on the grounds of H_r theory.     

稠苯芳杂环及其烷基质子化学位移的计算

本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。 将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σ_mi,ci为各苯环的环流效应。σ_1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ_1,He=(1/2)^d-1δ_x=y(或σ_z)+σ_c-c·σ_m,H. σ_x-y与σ_z为杂原子或其基团的屏蔽效应,σ_c=c为存在于芳杂环中的乙烯基的效应,σ_m,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σ_p,CH3+ασ_c,CH3+βσ_t,CH3+σ_l,G σ_l,G为稠苯芳杂环基的某级效应。     

Interrelations of discrete Painlevé equations through limiting procedures

We study the discrete Painlevé equations associated to the affine Weyl group which can be obtained by the implementation of a special limits of -associated equations. This study is motivated by the existence of two -associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a -associated discrete Painlevé equation. Applying the same limiting procedures to other -associated equations we obtained several -related equations most of which have not been previously derived.     

Structural phase transitions at clean and metal-covered Si(111) surfaces investigated by RHEED spot analysis

Structural phase transitions between various kinds of superlattice structures formed on a Si(111) surface have been investigated by spot analysis of reflection high-energy electron diffraction (RHEED). Reversible transitions induced by temperature changes and irreversible ones induced by metal depositions were observed. Detailed discussions on the dynamics of the phase transitions are made by quantitative analyses of integrated spot intensity and profile. For a phase transition of 7′7  1′1 structures on a clean Si(111) surface, a hysteresis with temperature difference of 5°C. between in heating and cooling processes was found in the spot intensity change, indicating a first-order transition. Hysteresis was hardly recognized, on the other hand, for transitions of Au-induced superstructures (5×2-Au or ×-Au)  1×1-Au. The spot profiles were found to be broadened during the transition of Si(111)-×-Au  1×1-Au, which was a signature of a continuous transition, while the profiles remained unchanged during the transitions of the 7×7  1×1 and 5×2-Au  1×1-Au phases. Structural conversions induced by In adsorption on the Si(111) surface kept at constant temperatures were also analyzed. The conversions at room temperature were totally dependent on the initial substrate surface structures; the 7×7 surface did not show any structural conversion with In adsorption, while the ×-In surface successively converted to a 2×2 and a × phase with coverage increase. The structural transitions at elevated temperatures were sensitively dependent on the temperatures. Sequences of transitions among the 7×7, 4×1, ×, 1×, and ×4 were quantitatively revealed as changes in RHEED spot intensity.     

ErP5O14非晶玻璃的红外量子剪裁

研究了Er_1.0P₅O₁₄铒非晶玻璃的红外量子剪裁现象. 从吸收谱和激发光谱的计算比较中肯定了Er_1.0P₅O₁₄非晶 玻璃的1537.0 nm红外荧光为多光子量子剪裁荧光. 从Er_1.0P₅O₁₄非晶玻璃的可见和红外荧光发射光谱中发现激发²H_11/2, ⁴G_11/2和⁴G_9/2能级所导致的⁴I_13/2→⁴I_15/2量子剪裁红外荧光很强;基于自发辐射速率、无辐射弛豫速率和能量传递速率等参数的计算,对其量子剪裁机理进行了分析.发现起源于基态的强下转换能量传递{²H_11/2→⁴I_9/2,⁴I_15/2→⁴I_13/2},{⁴G_11/2→⁴I_13/2, ⁴I_15/2→²H_11/2},{⁴G_9/2→⁴F_7/2,⁴I_15/2→⁴I_13/2}和{⁴G_9/2→⁴I_13/2, ⁴I_15/2→²H_11/2}是导致Er_1.0P₅O₁₄非晶玻璃具有强的三光子和四光子量子剪裁红外荧光的原因.研究结果对改善太阳能电池效率有一定意义.