Radiation from a Line Source Placed in Two-dimensional Photonic Crystals

A novel formulation of radiation from a localized line source placed in two-dimensional photonic crystals consisting of layered periodic arrays of parallel circular cylinders is presented. The method employs the spectral domain approach. The spectral response of the photonic crystals to the line source excitation is calculated using the lattice sums, the T-matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The far-zone radiated field is obtained using the conventional asymptotic method to the spectral response. The radiation patterns of the localized line source sandwiched by two photonic crystals are numerically studied.     

Subextensive Singularity in the 2D ± <Emphasis Type="Italic">J</Emphasis> Ising Spin Glass

The statistics of low energy states of the 2D Ising spin glass with +1 and −1 bonds are studied for L × L square lattices with L≤ 48, and p = 0.5, where p is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of L, in order to obtain the low temperature behavior of the model. For large finite L there is a range of T in which the heat capacity is proportional to T ^{5.33 ± 0.12}. The range of T in which this behavior occurs scales slowly to T = 0 as L increases. Similar results are found for p = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation d ν = 2 − α, even though T _c = 0. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented. PACS numbers: 75.10.Nr, 75.40.Mg, 75.60.Ch, 05.50.+q     

几种高分子材料的域结构、分子动力学和相互作用的固体NMR研究

聚3-羟基丁酸酯(PHB)是微生物细胞在其生长的特定时期在胞内合成的具有相应生物功能的聚羟基烷酸酯类物质, 是一种具有潜在的广泛应用前景的生物可降解的高分子材料. 由于天然的PHB其较高的结晶度和较窄的温度处理范围,它在应用过程中受到较大的局限性. 人们将结构相似的单体3-羟基戊酸(HV)与3-羟基丁酸(HB)共聚形成共聚物(PHBV)以后, 显著改善了PHB的物理机械性能,譬如:冲击强度和韧性有所增加，而硬度脆性有一定程度的下降. 人们虽然在这些降解高分子材料的开发、制备和物理机械性能以及这些材料的应用等方面有很多研究，但是有关分子水平的问题并未得到系统的探索. 因此，针对这些分子基础问题(结构域特征和分子动力学等)做了一些初步的研究.  全氟磺酸树脂(Nafion)是杜邦公司生产的一种燃料电池电极薄膜材料，其较低的使用温度(<100℃)严重地限制了它的应用范围. 人们发现，当把层状硅酸盐(蒙脱土)和Nafion合成为有机无机纳米复合材料之后，在一定程度上提高了它的使用温度. 虽然这种复合材料很容易合成出来并且已经运用到了实际工业应用之中，但是这种热稳定性提高的原因却不甚清楚. 通过固体NMR等分析方法从微观相互作用方面来认识这种宏观性能改善的原因.  使用固体¹³C CP MAS、¹³C SPE MAS NMR以及XRD方法测定了PHB和两种PHBV的结晶度(X_c)，发现随着HV的引入它们的X_c 逐渐减小. 研究同时发现在测量X_c 的这几种方法中¹³C SPE MAS NMR误差较小. 实验中我们利用质子弛豫诱导谱编辑(PRISE)、质子自旋扩散(Spin-diffusion)等固体NMR技术研究了PHB以及不同含量HV的PHBV的结构域特征和相应结构域的运动性. 实验结果表明随着HV含量的增加，它们的非晶相结构域尺寸增大，晶相结构域尺寸减小，可以看出HV的引入导致PHB的结构域特征的变化是其宏观性能改善的原因.  进一步通过低分辨固体NMR测量了PHB和PHBV的变温质子弛豫时间(T₁, T_1ρ, T₂), 然后通过理论拟合获得了它们不同运动状态的分子运动相关频率(τ_c)和分子活化能(E_a)等动力学信息，研究发现随着HV含量的增加，分子运动加快，活化能减小，在分子水平上认识了HV的引入使得PHB宏观性能改善的微观原因.  通过溶胶凝胶法合成了燃料电池电极薄膜(Nafion)和层状硅酸盐(蒙脱土)纳米复合材料来提高Nafion的使用温度，FT-IR和²⁹Si MAS NMR实验结果表明在杂化材料中虽然质子化的十二烷基胺修饰的蒙脱土(MMT)的引入没有导致MMT的骨架结构发生明显变化，而且Nafion也没有插入到MMT的层间，但是TGA分析表明杂化材料中的Nafion的热稳定性比纯的Nafion高. 通过一系列固体NMR技术包括¹⁹F MAS、¹H-¹³C CP MAS NMR和¹H-¹³C HETCOR 2D NMR实验初步证实了这种材料的热稳定性的提高可能是由于MMT表面吸附的NH⁺₃与Nafion侧链上的SO^-₃之间存在较强的静电相互作用，初步可以认为这种相互作用是导致电极材料性能改善的原因.     

复合六边形空气孔格点光子晶体光纤的色散特性分析

提出了一种复合六边形空气孔格点光子晶体光纤,其包层是由两种不同大小的空气孔组合而构成的。利用带有良匹配层(APML)吸收边界的全矢量频域有限差分法(FDFD)对其色散特性进行了数值分析。结果表明,通过调节包层中两种不同尺寸的空气孔的大小以及孔间距这三个参量,可以得到不同水平的平坦色散曲线,甚至超低超平坦的色散曲线。在孔间距Λ取2.1μm,小尺寸空气孔直径取0.5μm,大尺寸空气孔直径取0.8μm的条件下,在1.48~1.78μm的波长范围内得到了0±0.545 ps/(km.nm)的色散。     

波动方程角度域偏移成像

在共炮集数据的波动方程深度偏移成像中,利用常规的波场传播算子进行检波点波场和震源波场的向下传播,在各个深度层借助波场的窗口Fourier框架展开,得到局部角度域的检波点波场和震源波场,然后应用偏移成像原理,提出了共炮集数据的波动方程角度域偏移成像方法.通过角度域偏移成像,可以得到地下成像点处的角度域成像矩阵以及共地层倾角偏移成像剖面和共反射角偏移成像剖面.也可为基于偏移成像的后续处理方法技术,如振幅随角度变化分析处理、角度域共成像道集提取和角度域速度分析,提供基础资料.以陡倾角模型和国际标准的Marmousi模型为数值试验例子,验证了波动方程角度域偏移成像方法的正确性和有效性.     

复合外场中磁光薄膜(BiTm)3(FeGa)5O12缺陷周围磁畴壁的形貌特征

用自组装系记录了外场分别为均速率增加的直流磁场，低频交变磁场和它们同时存在时，磁光薄膜（BiTm)3(FeGa)5O12一种缺陷周围磁畴壁的形貌特征。分析表明：三种不同取向磁畴壁的交界处往往是磁光薄膜的缺陷所在处；在低频交变场下，该缺陷区域出现无畴条块或区域，在直流场中无此现象。在低频交变场以及复合外场下该缺陷周围磁畴壁形成椭圆形图案。     

Effect of induced shielding current transmission in longitudinal direction on levitation force of melt grown single-domain YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript> cylindrical superconductor

A novel layer deletion method is used to experimentally investigate the effect of induced shielding current transmission (ISCT) in the longitudinal direction on the levitation force of a single-domain YBa₂Cu₃O_7−x (YBCO) cylindrical superconductor (ϕ30×7 mm). In the experiment the sample was gradually sliced into two equal sheets, at the middle height along a diameter with 5 mm every step. The experimental results show that the levitation force is closely related with the ISCT in the longitudinal direction. Any layer deletion, even a small piece of layer deletion can reduce the levitation force of the sample. After the whole layer was deleted the levitation force can diminish about 50%. It is also found that the levitation force is directly proportional to the effective factor of surface area, which is equal to the top surface area divided by the total surface area parallel to the top surface of the sample.     

Improved Uncertainty of Optical Frequency Domain Reflectometry Based Length Measurement by Linearizing the Frequency Chirping of a Laser Diode

Length resolution of optical-frequency-domain-reflectometry (OFDR) is improved by reducing the chirping fluctuation of a laser diode. The fluctuation is detected as the frequency deviation of a beat signal from a reference interferometer, which is used as the control signal for servo-control of the laser diode (LD) drive current. As a result of the effective chirping stabilization, chirping span limited-resolution is achieved. In addition, use of a block gauge as the path difference of the reference interferometer enables the OFDR system to improve accuracy of the length as well as the resolution.     

Exact Algorithm for Concave Knapsack Problems: Linear Underestimation and Partition Method

Integer programming problems with a concave cost function are often encountered in optimization models involving economics of scale. In this paper, we propose an efficient exact algorithm for solving concave knapsack problems. The algorithm consists of an iterative process between finding lower and upper bounds by linearly underestimating the objective function and performing domain cut and partition by exploring the special structure of the problem. The lower bound is improved iteratively via cutting and partitioning the domain. This iteration process converges to the optimality in a finite number of steps. Promising computational results are reported for large-scale concave knapsack problems with up to 1200 integer variables. Comparison results with other existing methods in the literature are also presented. *Research supported by the National Natural Science Foundation of China under Grants 79970107 and 10271073,and the Research Grants Council of Hong Kong under Grant CUHK 4214/01E.     

Multiplicity Results for an Eigenvalue Problem for Hemivariational Inequalities in Strip-Like Domains

In this paper we study the multiplicity of solutions for a class of eigenvalue problems for hemivariational inequalities in strip-like domains. The first result is based on a recent abstract theorem of Marano and Motreanu, obtaining at least three distinct, axially symmetric solutions for certain eigenvalues. In the second result, a version of the fountain theorem of Bartsch which involves the nonsmooth Cerami compactness condition, provides not only infinitely many axially symmetric solutions but also axially nonsymmetric solutions in certain dimensions. In both cases the principle of symmetric criticality for locally Lipschitz functions plays a crucial role.Mathematics Subject Classifications (2000) 35A15, 35P30, 35J65.Supported by the EU Research Training Network HPRN-CT-1999-00118.