Interacting electrons on a two-dimensional surface: planar vs. spherical geometries

The center-of-mass excitations are identified in the spectrum of electrons on a two-dimensional surface in the lowest Landau level. The correspondence between the quantum numbers labeling electron states on a sphere and on a plane is drawn. The excitation spectrum on a sphere with increasing radius is shown to converge to that on a plane. In particular, in the presence of a lateral confinement (i.e. for the case of quantum dots), identical series of magic states appear in both cases. Also, a class of interaction potentials which lead to the fractional quantum Hall effect in an extended system are identified.     

Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation

This paper continues a systematic theoretical analysis of electromagnetic scattering by a group of arbitrarily sized, shaped, and oriented particles embedded in an absorbing, homogeneous, isotropic, and unbounded medium. The previously developed microphysical approach is used to derive the generalized form of the radiative transfer equation (RTE) applicable to a large group of sparsely, randomly, and uniformly distributed particles. The derivation of the RTE directly from the macroscopic Maxwell equations yields unambiguous and definitive analytical expressions for the participating quantities and thereby fully resolves the lasting controversy caused by the conflicting outcomes of several phenomenological approaches.     

Wave-obstacle interaction in a lossy medium: energy perturbations and negative extinction

The concept of a generalized extinction cross-section introduced in a previous paper is given in detail and exemplified by the problem of scattering by an elastic cylinder embedded in a viscoelastic matrix. It is shown that under certain conditions the presence of inclusion may have a supporting effect on wave propagation (negative extinction). The derived low-frequency expansions indicate that the Rayleigh law may not hold in the case of a lossy medium. Numerical results as well as discussions concerning separation between scattering and intrinsic viscoelastic losses are also given.     

Collective excitations in low-density 2D electron systems

We report the observation of sharp plasmon and magnetoplasmon modes in ultra-low-density 2D electron systems. Well defined dispersions for the modes are observed at densities as low as 1.1×10⁹ cm⁻² and with excitation wave vectors as large as 1.2×10⁵ cm⁻¹. Interestingly, both modes are found to be more easily measured in low-density systems than in high-density systems. The strength of the light scattering cross-sections at low density suggests potential applications to the study of quantum phase transitions at large r_s.     

Light scattering by a spherical particle with multiple densely packed inclusions

This paper calculates light scattering by a spherical water particle containing densely packed inclusions at a visible wavelength 0.55 \mum by a combination of ray-tracing and Monte Carlo techniques. While the individual reflection and refraction events at the outer boundary of a sphere particle are considered by a ray-tracing program, the Monte Carlo routine simulates internal scattering processes. The main advantage of this method is that the shape of the particle can be arbitrary, and multiple scattering can be considered in the internal scattering processes. A dense-medium light-scattering theory based on the introduction of the static structure factor is used to calculate the phase function and asymmetry parameters for densely packed inclusions. Numerical results of the single scattering characteristics for a sphere containing multiple densely packed inclusions are given.     

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

The surface integral formulation is a flexible, multiscale and accurate tool to simulate light scattering on nanostructures. Its generalization to periodic arrays is introduced in this paper. The general electromagnetic scattering problem is reduced to a discretizated model using the Method of Moments on the surface of the scatterers in the unit cell. The study of the resonances of an array of bowtie antennas illustrates the main features of the method. When placed into an array, the bowtie antennas show additional resonances compared to those of an individual antenna. Using the surface integral formulation, we are able to investigate both near-field and far-field properties of these resonances, with a high level of accuracy.     

表面上方微粒及微粗糙度偏振光散射特性

为了区分由表面上方微粒和表面微粗糙度两种散射机理引起的散射光,利用偏振双向反射分布函数,并借助于由,■,■组成的正交右手基组表示了入射电场和散射电场。从理论上给出了两种不同散射机理在不同偏振状态下的双向反射分布函数与入射面外方位角之间的变化关系,并通过对这两种散射机理下的偏振双向反射分布函数的比较发现,利用p偏振入射产生的p偏振散射光(BRDFpp)可以将表面上方微粒和表面微粗糙度两种散射机理区分开来。     

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

极化合成孔径雷达海面成像模拟及分析

海浪极化SAR成像模拟对海面散射的研究有重要的意义.基于海浪谱理论,在考虑大、小尺度海浪影响的基础上,构建了双尺度的随机粗糙海面.根据该海面模型,利用Bragg散射模型,小扰动模型与速度聚束理论,模拟了不同状况下海浪的极化SAR图像.并针对海浪参数对极化图像的影响进行了分析,结果符合成像统计特性,得出了一些有益于海浪信...     

Molecular motion in restricted geometries

Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations. An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.      

Wannier-Stark states of a quantum particle in 2D lattices

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a nonseparable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.     

基于压缩感知的一维海面与二维舰船复合后向电磁散射快速算法研究

矩量法作为数值方法中积分方程方法的代表, 具有计算精度高、所用格林函数自动满足辐射条件、无须额外设置边界条件等优点. 但是在舰船目标与海面复合后向电磁散射仿真中, 传统矩量法需针对每个入射角反复求解矩阵方程组, 导致其在处理后向散射问题时计算量大, 耗时长, 仿真效率低下. 为解决上述问题, 本文提出了一种基于压缩感知技术的矩量法的改进算法. 该算法在求解复合后向散射问题时, 首先利用观测矩阵与传统矩量法中的电压矩阵相乘, 得到一组新的低维度的电压矩阵; 其次通过求解新电压矩阵下的矩阵方程组, 获得电流矩阵的观测值; 最后利用恢复算法(本文采用正交匹配追踪算法)重构出所需的原始入射源照射下的电流系数. 通过与传统矩量法的计算结果对比, 表明本文所提算法能够在保证计算精度的前提下, 明显减少计算时间, 提高计算效率.     

具有二维fBm特征的分层介质粗糙面电磁散射的特性研究

运用微扰法研究了平面波入射分层介质粗糙面的电磁散射,推出了不同极化状态下的双站散射系数公式.采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合二维fBm分形粗糙面的功率谱导出了平面波入射二维fBm分形分层介质粗糙面的散射系数计算公式.通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线,讨论了分维、底层介质介电常数、中间介质介电常数和厚度及入射波频率对双站散射系数的影响,得到了二维fBm分形分层介质粗糙面散射系数的分维特征、基本特征、分区特征和随频率变化的特征. 关键词： 电磁散射 二维fBm分形粗糙面 分层介质 微扰法     

On the sensitivity of the 2D electromagnetic invisibility cloak

A computational study of the sensitivity of the two dimensional (2D) electromagnetic invisibility cloaks is performed with the finite element method. A circular metallic object is covered with the cloak and the effects of absorption, gain and disorder are examined. Also the effect of covering the cloak with a thin dielectric layer is studied.     

Coulomb drag experiments in low density 2D hole bilayers

We performed experiments studying the Coulomb drag in low density 2D hole bilayers, with r_s ranging from roughly 10 to 20. As the carrier density is lowered into the dilute regime, we observe a significant enhancement of the drag resistivity, such that the interlayer carrier–carrier scattering rate constitutes a major component of the single layer resistivity. In addition, anomalies to the expected temperature and in-plane magnetic field dependences are observed, and are found to correlate with similar anomalies in the single layer resistivity. These results suggests that the origin of the 2D metal–insulator transition phenomena affects both transport properties in a very similar fashion.     

A hybrid model for the acoustic response of a two-dimensional rough surface to an impulse incident from a refracting medium

A numerical model to calculate the impulse response of a two-dimensional, impenetrable, rough surface directly in the time domain has been recently introduced [J. Acoust. Soc. Am. (2000) 107, 27]. This model is based on wedge diffraction theory and assumes that the half-space containing the source and receiver is homogeneous. In this work, the model is extended to handle media where the index of refraction varies with the distance to the surface by merging the scattering model with a ray-based propagation model. The resulting hybrid model is tested against a Finite-Difference Time-Domain (FDTD) method for the problem of backscattering from a corrugated surface in the presence of a refractive layer. This new model can be applied, for example, to calculate acoustic reverberation from the sea surface in cases where the water mass is inhomogeneous and in the presence of a subsurface bubble layer at low frequencies where dispersion is negligible. It can also be used for atmospheric propagation problems where there is a sound speed gradient overlying rough terrain.     

Two-dimensional magnetic ordering in a multilayer structure

The effect of confinement from one, two or from all three directions on magnetic ordering has remained an active field of research for almost 100 years. The role of dipolar interactions and anistropy are important to obtain, the otherwise forbidden, ferromagnetic ordering at finite temperature for ions arranged in two-dimensional (2D) arrays (monlayers). We have demonstrated that conventional low-temperature magnetometry and polarized neutron scattering measurements can be performed to study short-range ferromagnetic ordering of in-plane spins in 2D systems using a multilayer stack of non-interacting monolayers of gadolinium ions formed by Langmuir-Blodgett (LB) technique. The spontaneous magnetization could not be detected in the heterogeneous magnetic phase observed here and the saturation value of the net magnetization was found to depend on the sample temperature and applied magnetic field. The net magnetization rises exponentially with lowering temperature and then reaches saturation following a T ln(βT) dependence. The T ln (βT) dependence of magnetization has been predicted from spinwave theory of 2D in-plane spin system with ferromagnetic interaction. The experimental findings reported here could be explained by extending this theory to a temperature domain of βT<1.