Two magnetic impurities with arbitrary spins in open boundary t-J model

From the open boundary t-J model an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in detail. We discuss also the string solutions of the Bethe ansatz equations, which describe the bound states of the charges and spins. By minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz equations. The finite size correction of the free energy contributed by the magnetic impurities is obtained explicitly. The properties of the system at some special limits are discussed and the boundary bound states are obtained.     

Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section

We extend the design of radially symmetric invisibility cloaks through transformation optics as proposed by Pendry et al. [Science 312, 1780 (2006)] to coated cylinders of an arbitrary cross section. The validity of our Fourier-based approach is confirmed by both analytical and numerical results for a cloak displaying a non-convex cross section of varying thickness. In the former case, we evaluate the Green's function of a line source in the transformed coordinates. In the latter case, we implement a full-wave finite-element model for a cylindrical antenna radiating a p-polarized electric field in the presence of a F-shaped lossy object surrounded by the cloak.     

任意多面体隐身罩材料参数的推导及验证

基于坐标变换理论推导了任意多面体隐身罩的隐身条件,并得到了相应隐身罩材料参数的张量表达式.根据导出的材料参数的张量表达式,通过全波仿真分别对正四面体和十四面体隐身罩进行仿真验证,仿真结果证实了所得材料参数张量表达式的正确性,研究结果为三维复杂形状隐身罩的设计奠定了理论研究基础. 关键词： 坐标变换 多面体隐身罩 张量表达式 全波仿真     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Analytic method of arbitrary cross section open groove guide

Groove guide is one of the waveguides that have been used at millimeter and submillimeter waveband. This paper analyzes arbitrary groove guides by means of the eigen-weighted boundary integral equation method that uses the eigenfunctions of a fictitious regular boundary as weighting functions. In comparison with the theoretical and experimental results published, the numerical results for rectangular, circular and V-groove guides using this method are exact enough with fast convergence and less calculation.The Project Supported by National Natural Science Foundation of P.R. China     

Single particle model calculations with potentials of arbitrary shapes

A technique of expanding arbitrary functions of two variables in separable terms is applied to nuclear single-particle potentials, and a method for high-speed calculation of the eigenstates of the Hamiltonian has been developed. The applicability of the scheme, for spherical as well as highly eccentric shapes. is demonstrated for a sequence of two-centered potentials.     

Numerical visualization of free surface oscillation predicted with arbitrary Lagrangian-Eulerian method

A numerical prediction method has been proposed to predict non-linear free surface oscillation in a three-dimensional container. The fluid motions are numerically predicted with Navier-Stokes equations discretized in a Lagrangian scheme with sufficient numerical accuracy. The profile of a free surface is precisely represented with three-dimensional body-fitted coordinates (BFC), which are regenerated in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) formulation. The computational method was applied to non-linear sloshings and transitions from sloshing to swirling motions. The predicted free surface motions were visualized as sequential image files and animations to understand their dynamic futures     

The boundary-residual method for three-dimensional homogeneous field problems with boundaries of arbitrary geometry

Boundary-residual methods are extended to include three-dimensional homogeneous field problems applicable to millimeter-wave problems. Their connection to pointmatching methods is shown, and the reason why pointmatching fails and boundary residual methods do not is explained. A numerical example is used to demonstrate the validity of these methods. A discussion of the limitations of these methods is also included.     

折射率渐变透镜的数值设计

传统折射率渐变透镜的设计要求初级馈源天线具有稳定的相位中心,这就限制了透镜的应用范围。为拓宽透镜的应用范围,提出了一种折射率渐变透镜的数值设计方法,通过对馈源天线的极化电场离散采样获得相位信息,并据此设计透镜,随后用金属短线结构的新型人工电磁材料来实现这种透镜。这种设计方法简单灵活,对馈源天线没有限制。以经典矩形贴片天线为例,比较了贴片天线和透镜天线的回波损耗和远场方向图,结果表明运用这种方法设计的透镜使贴片天线的增益提高了2 dB,口径效率从62%提高到了99%。     

折射率渐变透镜的数值设计

传统折射率渐变透镜的设计要求初级馈源天线具有稳定的相位中心,这就限制了透镜的应用范围。为拓宽透镜的应用范围,提出了一种折射率渐变透镜的数值设计方法,通过对馈源天线的极化电场离散采样获得相位信息,并据此设计透镜,随后用金属短线结构的新型人工电磁材料来实现这种透镜。这种设计方法简单灵活,对馈源天线没有限制。以经典矩形贴片天线为例,比较了贴片天线和透镜天线的回波损耗和远场方向图,结果表明运用这种方法设计的透镜使贴片天线的增益提高了2 dB,口径效率从62%提高到了99%。     

Numerical treatment of acoustic problems with boundary singularities by the singular boundary method

The singular boundary method (SBM) is a novel boundary-type meshless method based on the fundamental solution of the given governing equation. The SBM employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions. In this paper, we investigate the acoustic problems with boundary singularities using the SBM. This is achieved by combining the SBM with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution. The singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities. Then the regular solution is obtained by the SBM. Numerical examples show the excellent performance of the proposed technique.     

X波段六腔渡越管振荡器的高频特性研究

 从麦克斯韦方程出发，采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法，通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布，计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率，验证了TEM波吸收边界条件，并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

X波段六腔渡越管振荡器的高频特性研究

从麦克斯韦方程出发,采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法,通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布,计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率,验证了TEM波吸收边界条件,并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

核磁共振测井仪探头设计中的数值方法

核磁共振测井仪探头的优化设计能够增强仪器的探测特性,提高仪器的信噪比, 而探头设计中的数值方法对设计结果至关重要.本文利用电磁场有限元方法对贴井壁型核磁共振测井仪探头静磁场和射频场进行了2D和3D的数值模拟,深入分析了数值模型形状、模型尺寸、 单元形状对数值模拟结果的影响,并将有限元数值模拟结果与实测数据做了对比. 结果显示:数值模拟结果与实测数据符合.在设计核磁共振测井仪探头结构时, 选取与井眼形状一致的圆形模型,模型尺寸范围在10—15倍探头外径, 并采用三角形单元可以有效提高数值模拟方法精度,增强优化设计结果的可靠性.     

Screening in three-dimensional QED with arbitrary fermion mass

We compute the quark–antiquark potential in three-dimensional massive quantum electrodynamics for an arbitrary fermion mass. The result indicates that screening prevails for any quark masses, contrary to the classical expectations, generalizing our previous result obtained for large masses. We also test the validity of several approximation schemes using a detailed numerical analysis. The classical result is still reproduced for a small separation of the quarks. Received: 16 May 2000 / Published online: 25 September 2000     

The novel boundary integral equation method for solving arbitrary cross-section waveguides

A novel method for solving arbitrary cross-sectionn waveguides is presented. The novel method is a modification of the eigen-weighted boundary integral equation method; the EWBIEM is modified by using the eigenfunction of a fictitious regular boundary as weighting function, whose eigenvalue may be the known value, and meanwhile using the domain-bases. To confirm the validity of the novel method, numerical analysis are presented for circular groove guide as an example.The Project Supported by National Natural Science Foundation of P.R. China     

A feasible approach to field concentrators of arbitrary shapes

We propose a simple method to design field concentrators of arbitrary shapes based on Fabry–Pérot resonances. The material parameters are feasible in terms of metallic layered structures and gradient index dielectrics. The functionalities are well confirmed by numerical simulations.