电磁波在周期介质中的传播及二维光子晶体的光子带结构

光子晶体是光学与凝聚态物理交叉的新领域,也是近年来应用物理学的一个重要研究领域,它是一种由介电常数高的(低的)介质在另一种介电常数低的(高的)背景介质中周期排列所组成的人造多维周期结构材料,能够产生光子带隙。频率落在带隙内的光在晶体里沿任何方向都不能传播,因而具有能够抑制原子、分子的自发辐射等诱人的光电子学特性,在基础研究和实际应用上都有着巨大的潜力。本文在这一领域里进行了富有成效的研究,获得了很好的结果。主要有:(1)利用平面波展开方法来计算二维光子晶体的带隙结构。首先,我们设计正方晶胞的二维光子晶体模型。设x₃方向为介质柱的轴方向,二维周期结构在x₁-x₂平面上。晶胞的晶格常数为a,半径为r,介质柱和空气柱的介电常数分别为ε_a=17和ε_b=1,a>2r。设计的核心思想是通过降低光子晶体结构的对称性,消除光子能带在晶体的布里渊区高对称点上的本征简并。(2)对于二维光子晶体的电磁波理论及周期介质中的Bloch波解做了详细的推导,给出了光子晶体中禁带存在的理论依据。同时以正方格子晶格的二维光子晶体为例,验证了电介质在空气圆孔中的排列存在E偏振和H偏振的光子带隙重叠区,称为绝对光子带隙。对于二维的光子晶体,两种本征偏振模式的光子能带结构可以独立地调节,以实现两者的光子带隙的最优重叠, 从而大大提高了二维光子晶体的完全带隙宽度。     

Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations

We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adiabatic Euler system. This result is a generalization of the well-known result on 2-d steady potential flow and a recent similar result on the pressure gradient system.Research partially supported by NSF of China with No. 10301022, NSF from Beijing Municipality, Fok Ying Tong Educational Foundation, and the Key Program from Beijing Educational Commission with no. KZ200510028018.Research partially supported by NSF-DMS-0305497, 0305114.     

超快二维红外光谱用于研究单体水分子中的直接振动能量传递

Vibrational relaxation dynamics of monomeric water molecule dissolved in d-chloroform solution were revisited using the two dimensional Infrared (2D IR) spectroscopy. The vibrational lifetime of OH bending in monomeric water shows a bi-exponential decay. The fast component (T₁=(1.2±0.1) ps) is caused by the rapid population equilibration between the vibrational modes of the monomeric water molecule. The slow component (T₂=(26.4±0.2) ps) is mainly caused by the vibrational population decay of OH bending mode. The reorientation of the OH bending in monomeric water is determined with a time constant of τ=(1.2±0.1) ps which is much faster than the rotational dynamics of water molecules in the bulk solution. Furthermore, we are able to reveal the direct vibrational energy transfer from OH stretching to OH bending in monomeric water dissolved in d-chloroform for the first time. The vibrational coupling and relative orientation of transition dipole moment between OH bending and stretching that effect their intra-molecular vibrational energy transfer rates are discussed in detail.     

激光激发水中产生超声波的实验研究

采用压电陶瓷水听器研究了Nd：YAG脉冲激光激发水中产生瞬态超声波的特性,给出了声压信号随距离的变化关系。研究结果表明：用激光产生水下声波是完全可行的。当观测点与光击穿区的距离r远大于柱体长度时,垂直于光传播方向的激光瞬态超声波幅值与r成反比;当观测点与光击穿区的距离r很小时,垂直于光传播方向的声压幅值与产成反比。此外,当激光入射角度发生变化,超声脉冲的幅值也随之发生变化,其幅值在激光束垂直入射的时候最大。     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [DSZ2,DSZ3] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of \({\mathcal {O}(N) \to \mathbb {CP}^m}\) and, in an asymptotic sense, for those of line bundles over general Kähler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.     

三维荧光光谱结合二阶校正方法同时测定水中两种酚类

水是生命之源,人们日常生产生活离不开水。近年来水体污染日趋严重,已经危害到人类的健康。酚类化合物(Phenolic Compound)是一种广泛存在且很难降解的有机污染物,指的是芳香烃中苯环上的氢原子被羟基取代所生成的含羟基衍生物,毒性很强,对动植物及人类的生命活动有严重危害。实验研究对象选取间苯二酚(resorcinol,RES)和对苯二酚(hydroquinone,HYD)来配制待测样本,并且在其中3组预测样本中加入苯酚(phenol,PHE)作为干扰物,待测样本和空白溶剂分别用FS920稳态荧光光谱仪(edinburgh instruments,EI)扫描得到荧光光谱数据。对所得到的数据通过扣除空白溶剂法来消除拉曼散射的影响,得到的数据在消除干扰的同时最大程度保留下来原光谱所包含的重要信息。校正后光谱变得更加圆滑,荧光强度显著增强,因此,校正处理后的光谱信息更为准确。利用三维荧光光谱(EEM)结合平行因子分析(PARAFAC)和交替惩罚三线性分解(APTLD)两种二阶校正方法,分别完成在不含干扰物和含有干扰物、同时激发-发射光谱严重重叠时对间苯二酚、对苯二酚的快速、直接、准确测量,并给出定性、定量分析结果。PARAFAC算法对混合体系的组分数(即化学秩)较敏感,组分数选取过大易使其陷入计算"沼泽",迭代次数增多,计算耗时变长。故本文利用核一致诊断法(CORCONDIA)预估计出准确的组分数,保证PARAFAC算法更加快速准确。从定性分析结果知,当不含有干扰物时,PARAFAC能够准确分辨出间苯二酚和对苯二酚,二者荧光峰位置极为接近,很难用传统方法分辨,体现出将三维荧光光谱技术与化学计量学二阶校正方法相结合所具有的"二阶优势";定量分析结果给出,在有干扰物共存时,分别应用两种二阶校正法解析光谱数据结果显示:PARAFAC的浓度预测回收率为93.4%±0.5%~97.1%±1.0%,预测均方根误差小于0.190 mg·L^-1;APTLD的浓度预测回收率为95.9%±1.6%~97.2%±0.8%,预测均方根误差小于0.116 mg·L^-1,通过比较两种方法性能得:PARAFAC对待测物组分数敏感,对待分解的光谱数据严格线性要求高;而APTLD对混合物组分数不敏感,计算速度快,抗噪声能力较强,结果稳定,具有较明显的优势。     

Geometric Quantization and Two Dimensional QCD

In this article, we will discuss geometric quantization of two dimensional Quantum Chromodynamics with fermionic or bosonic matter fields. We identify the respective large-N _c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In [33], it was shown that the linearization of the equations of motion for the Grassmannian gave the 't Hooft equation. We will see that the linearization in the bosonic case leads to the scalar analog of the 't Hooft equation found in [36]. Received: 13 August 1996 / Accepted: 20 May 1997     

Two Dimensional NMR Study of Aspidospermine

Two dimensional COSY, HETCOR and inverse HMBC experiments were performed on a natural alkaloid, Aspidospermine, which allowed complete ¹H and ¹³C spectral assignments to be made. These results suggest that the reversal of certain ¹³C literature assignments of related compounds is required.     

二维不稳定流形的计算

提出了动力系统中稳定流形和不稳定流形的一种实用的快速算法,可以求得稳定流形和不稳定流形的直观图像,从而从几何角度研究动力系统的动态行为和稳定性区域的边界特征.算法由两步构成:①在不稳定流形上求得一些分布均匀的点,以精确反映流形的每个细节;②借助三角形剖分或二维单纯形剖分利用①的算法将这些点画出直观流形图像.     

Two Dimensional Array of Antenna-Coupled Microbolometers

Antenna-coupled microbolometers are known for having short time constants and high responsivity, but their small dimensions make them unsuitable for imaging applications where a typical pixel area is generally greater than 20 × 20 m². In this paper a two dimensional array of antenna-coupled microbolometers is demonstrated as an area receiver. Using the response of microbolometers to visible frequencies a two-dimensional diagnostic scan in the visible was performed on these arrays which allowed measurement of their homogeneity. Frequency response measurements gave time constants around 130 nsec, similar to the ones obtained for single element microbolometers which indicates that a detector of virtually any size can be fabricated without sacrificing time response. Response and noise measurements show lower noise and higher responsivity compared to single element microbolometers. These results make two-dimensional arrays of antenna-coupled microbolometers a promising option for development of pixels in infrared focal plane arrays.     

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as \((\ln t)^{2/3}\) with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.     

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories and cosmology, many models contain more than just one scalar field (e.g., inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form, and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g., dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g., spherically reduced scalar-tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.     

Discrete Charges on a Two Dimensional Conductor

We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for “singular” domains. For smooth conductors, the locations of the charges can be determined, to within $O\left( {\sqrt {\log {N \mathord{\left/ {\vphantom {N {N^2 }}} \right. \kern-0em} {N^2 }}} } \right)$ by an integral equation due to Pommerenke [ Math. Ann., 179: 212–218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.     

Superdiffusivity of Two Dimensional Lattice Gas Models

It was proved [Navier–Stokes Equations for Stochastic Particle System on the Lattice. Comm. Math. Phys. (1996) 182, 395; Lattice gases, large deviations, and the incompressible Navier–Stokes equations. Ann. Math. (1998) 148, 51] that stochastic lattice gas dynamics converge to the Navier–Stokes equations in dimension d=3 in the incompressible limits. In particular, the viscosity is finite. We proved that, on the other hand, the viscosity for a two dimensional lattice gas model diverges faster than (log t)^1/2. Our argument indicates that the correct divergence rate is (log t)^1/2. This problem is closely related to the logarithmic correction of the time decay rate for the velocity auto-correlation function of a tagged particle.     

艾比湖流域地表水二维荧光峰值与水质指标关系初探

随着技术的进步与发展,国内外学者早已利用不同的技术手段对水质指标的评价与估算开展了大量研究,但是利用二维荧光峰值估算水质指标的方法尚不多见。以艾比湖流域地表水为研究对象,利用多元统计分析和逐步回归分析方法,对二维荧光峰值和水质指标建立估算模型以初步探究二者的相互关系。结果表明：(1)艾比湖流域不同河流的水质状况不同,博尔塔拉河(简称博河)的TN含量最高,水库及水渠的TP含量最高。(2)同一水样点有三个荧光峰(Peak1,Peak2和Peak3)且强度逐渐减弱,不同河流的荧光峰强度不同,其中博河、水库及水渠的荧光峰强度变幅最大。(3)经过荧光峰值与水质指标的相关分析发现Peak1与BOD₅,Peak2与BOD₅,Peak2与COD,Peak2与DO具有较好的相关性,相关系数分别为：0.479,0.371,0.655和0.618。将单荧光峰值和水质指标建立估算模型,经验证四组估算模型的精度较差,单峰值建模无法达到监测要求。因此,在单荧光峰值建模的基础上,将每个水样的三组荧光峰值和水质指标进行综合建模,建立多元回归方程,经模型验证得出三组荧光峰值与DO的综合模型效果最好,R=0.756, RMSE=1.001。因此二维荧光峰值与水质指标DO的综合估算模型是可行的,对干旱区水质指标监测具有一定的参考意义,为艾比湖流域水资源的开发、利用及保护提供科学依据。     

Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts—instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.     

On Symmetric Water Waves with Constant Vorticity

We prove that a solution to the gravity water wave problem with constant vorticity, whose wave profile as well as its horizontal velocity component at the free surface are symmetric at any instant of time, is given by a traveling wave. The proof is based on maximum principles and structural properties of the governing equations.