Retardation effects in damping of nuclear collective excitations

We expand the nonmarkovian collision integral in terms of multipolarities of the distortion of the Fermi surface. It is shown that damping of zero-sound is determined by all multipolarities of the Fermi-surface deformation. For large zero-sound velocity with respect to the Fermi velocity the relaxation time is related to the quadrupole deformation of the Fermi surface. The contributions of collisions to the total widths of the giant multipole resonances are calculated in a semiclassical macroscopic nuclear model.     

An adiabatic formulation of the quadrupolar charge deformation in the study of lattice dynamics of covalent solids

An adiabatic formulation of the dipolar charge deformation has been found to be quite important in solids. The present formulation is quite general and may be applied to cases where in addition to the dipole deformation the quadrupole is also important. However, as a preliminary application of the formulation we consider homopolar crystals where the symmetry indicates that the dominant multipole deformation of the charge cloud is quadrupolar, dipolar deformation being totally absent. The results obtained give us an idea about the order of magnitude of this effect.     

钠原子团簇相变的多极形变特征

运用距离相关紧密结合的分子动力学模型,通过无量纲的形变参数S1对简单金属原子团簇Na4、Na8、Na14和Na20相变时的多极形变特征进行了分析,发现S1可以用作表征团簇形变的灵敏探针.     

Spectrum of relativistic radiation from electric charges and dipoles as they fall freely into a black hole

The motion of electric charges and dipoles falling radially and freely into a Schwarzschild black hole is considered. The inverse effect of the electromagnetic fields on the black hole is neglected. Since the dipole is assumed to be a point particle, the deformation due to the action of tidal forces on it is neglected. According to the theorem stating that “black holes have no hair”, the multipole electromagnetic fields should be completely radiated as a multipole falls into a black hole. The electromagnetic radiation power spectrum for these multipoles (a monopole and a dipole) has been found. Differences have been found in the spectra for different orientations of the falling dipole. A general method has been developed to find the radiated multipole electromagnetic fields for multipoles (including higher-order multipoles—quadrupoles, etc.) falling freely into a black hole. The calculated electromagnetic spectra can be compared with observational data from stellar-mass and smaller black holes.     

Cardiac magnetic source imaging based on current multipole model

It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares (MNLS) method, the optimal weighted pseudoinverse method (OWPIM), and the optimal constrained linear inverse method (OCLIM) are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared.     

The series solution to the metric of stationary vacuum with axisymmetry

The multipole moment method not only conduces to the understanding of the deformation of the space--time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.     

边界元奇异与近奇异数值积分方法及其应用于大规模声学问题

提出了综合处理Burton-Miller方法所导致的奇异积分与近奇异积分问题的数值求积方法,以此改进了基于常量元素的常规边界元和低频快速多极边界元方法。对于奇异积分问题,利用Hadamard有限积分方法进行解决;对于近奇异积分问题,则采用极坐标变换法和PART方法(Projection and Angular&;Radial Transformation)进行克服。与解析解和LMS Virtual.Lab商业软件的结果比较验证了方法的正确性,并对比分析了奇异积分与近奇异积分对计算精度的影响。采用低频快速多极子方法以加速常规边界元法的计算效率,计算分析了计算复杂度,并成功实现了34万自由度大规模问题的计算。结果表明,近奇异积分问题主要由超奇异核函数引起,对计算精度的影响不容忽略;快速多极边界元法的精度与常规边界元法一致,但计算复杂度要远低于后者。      

Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed,by which the conventional and fast multipole BEMs(boundary element methods) for 3D acoustic problems based on constant elements are improved.To solve the problem of singular integrals,a Hadamard finite-part integral method is presented,which is a simplified combination of the methods proposed by Kirkup and Wolf.The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART(Projection and Angular Radial Transformation).The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab.In addition,the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution.The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations.A large-scale acoustic scattering problem,whose degree of freedoms is about 340,000,is implemented successfully.The results show that,the near singularity is primarily introduced by the hyper-singular kernel,and has great influences on the precision of the solution.The precision of fast multipole BEM is the same as conventional BEM,but the computational complexities are much lower.     

On the simplest equivalent currents of an ellipsoidal body

The solution is obtained to the Frenkel problem of determining the surface current on the boundary of an ellipsoidal region of space, equivalent (i.e., producing the same external magnetic field) to the simplest steady-state current specified in the bulk of this region. Simultaneously, multipole representations of pseudoscalar magnetic potentials of the volume and surface currents are determined in the framework of this particular problem. It is shown that these representations are completely analogous to the corresponding multipole representations of the scalar potentials of the ellipsoid associated with the volume or surface distributions of scalar sources (charges or masses).     

快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

On the stability of ferromagnetism in intermediate valence systems

It is known that the deformations of the electronic charge density induced by lattice displacements play an important role in lattice dynamics. The multipole expansion of these deformations around the positions of both the cation and the anion leads to a rather general type of deformable shell model. This cluster deformation model can be applied not only to ionic crystals but also to a large variety of other materials like mixed-valence compounds. Taking TiN as an example, it is shown that the model is able to describe the very pronounced phonon anomalies in superconducting transitionmetal compounds and to reproduce the measured phonon dispersion curves within the experimental errors.     

Solution of the Vlasov equation for collective modes in nuclei

A semiclassical theory of giant resonances based on the Vlasov equation is developed. The linearized Vlasov equation is solved for the bound motion of particles in a central potential with an external time-dependent multipole field. The solution obeys an RPA-type integral equation. If the time-dependent part of the self-consistent field is neglected, the solution of the Vlasov equation has a simple analytical form. The strength function for each multipole can be expressed in terms of the natural frequencies of classical orbits and of radial integrals over the classical motion. The method is illustrated by studying the isoscalar monopole, quadrupole and octupole response in medium-heavy nuclei without residual interaction. There are remarkable similarities between the solutions of the semiclassical problem and the corresponding quantum problem. For a central potential with Saxon-Woods shape there is an interesting shift and concentration of strength in the quadrupole and octupole response functions.     

非局域非线性介质中多极表面光孤子的解析解及其稳定性分析

本文主要对非局域非线性介质中存在的多极表面亮孤子进行了研究. 理论研究表明多极表面孤子也可以被看做是具有反对称振幅分布的体孤子的一半, 由此我们可以给出多极表面孤子的解析解. 其次, 用数值计算的方法给出了它的数值解, 比较结果表明数值解与解析解基本符合. 最后, 研究了本模型下的多极表面孤子的稳定性, 发现二极表面孤子的不稳定区间比四极体孤子的不稳定区间小, 另外, 二极以上的表面孤子皆不稳定.     

Self-consistent calculation of the ground state properties of some rare-earth nuclei

Ground state intrinsic deformation properties of some rare earth nuclei are calculated within the Hartree-Fock approximation using a Skyrme effective interaction. After a careful optimization of basis parameters, calculations have been performed with a basis corresponding to 13 spherical oscillator shells. In order to obtain the multipole moments, good numerical convergence is necessary. Calculated quadrupole and hexadecapole moments are in agreement with available experimental data. Ground state binding energies are also well reproduced.     

General solution for flat-space longitudinal momentum

The momentum constraint of the initial-value problem of general relativity is addressed. The undressed extrinsic curvature of a general compact momentum source is presented in terms of multipole moment integrals.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景.     

On the extinction multipole plasmons in gold nanorods

On the basis of the T-matrix formalism and numerical simulations, we derive an explicit rule for partial multipole contributions to the plasmon resonances of gold nanorods at a fixed or random orientation. The parity of a given spectral resonance number n coincides with the parity of their multipole contributions l, where l is equal to or greater than n, and the total resonance magnitude is determined by the lowest multipole contribution. We also investigate the dependence of multipole plasmons on the size, shape, and orientation of nanorods with respect to the polarized incident light. It is shown that the multipole resonance wavelengths as a function of the aspect ratio divided by the resonance number collapse onto one linear scaling curve. This scaling is explained by using the plasmon standing wave concept introduced by Schider et al. [Plasmon dispersion relation of Au and Ag nanowires. Phys Rev B 2003;68:155427].