First-principles study of the relaxor ferroelectricity of Ba(Zr,Ti)O_3

Ba(Zr, Ti)O3is a lead-free relaxor ferroelectric. Using the first-principles method, the ferroelectric dipole moments for pure Ba Ti O3 and Ba(Zr, Ti)O3supercells are studied. All possible ion configurations of Ba Zr0.5Ti0.5O3 and Ba Zr0.25Ti0.75O3 are constructed in a 2 × 2 × 2 supercell. For the half-substituted case, divergence of ferroelectric properties is found from these structures, which greatly depends on the arrangements of Ti and Zr ions. Thus our results provide a reasonable explanation to the relaxor behavior of Ba(Zr, Ti)O3. In addition, a model based on the thermal statistics gives the averaged polarization for Ba(Zr, Ti)O3, which depends on the temperature of synthesis. Our result is helpful to understand and tune the relaxor ferroelectricity of lead-free Ba(Zr, Ti)O3.     

原子核单粒子共振态的研究进展

共振是自然界普遍存在的有趣现象。在核物理领域,存在许多奇特现象,共振在其中扮演着重要角色。介绍了近期发展的RMF-CSM、RMF-CGF和RMF-CMR方法及其对原子核单粒子共振态的研究。给出了120Sn,31Ne等核的单粒子共振态的能量和宽度及其随质量数、形变的变化规律,分析了19C,31Ne和39Mg等核的晕形成的物理机制和在N=20附近能级反转的原因。特别是新发展的RMF-CMR方法,在描述稳定核和奇特核方面都取得了成功,支持Zr同位素存在巨晕的预言。Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.     

First-principles study of structural,elastic, and thermodynamic properties of ZrHf alloy

Structural parameters, elastic constants, and thermodynamic properties of ordered and disordered solid solutions of Zr Hf alloys are investigated through first-principles calculations based on density-functional theory(DFT). The special quasi-random structure(SQS) method is used to model the disordered phase as a single unit cell, and two lamella structures are generated to model the ordered alloys. Small strains are applied to the unit cells to measure the elastic behavior and mechanical stability of Zr Hf alloys and to obtain the independent elastic constants by the stress–strain relationship. Phonon dispersions and phonon density of states are presented to verify the thermodynamic stability of the considered phases. Our results show that both the ordered and disordered phases of Zr Hf alloys are structurally stable. Based on the obtained phonon frequencies, thermodynamic properties, including Gibbs free energy, entropy, and heat capacity, are predicted within the quasi-harmonic approximation. It is verified that there are no obvious differences in energy between ordered and disordered phases over a wide temperature range.     

Effects of Zr substitution on structural,morphological, and magnetic properties of bismuth iron oxide phases

The present study involves co-precipitation method to grow un-doped and Zr-doped bismuth iron oxide with x_(Zr)=0.10–0.30. The molar solutions of ferric chloride(FeCl_3), zirconyle chloride(ZrOCl_2), and bismuth chloride(BiCl_3) are prepared in distilled water, and are allowed to react with sodium hydroxide(Na OH). The synthesized powders are then converted into pellets, which are sintered at 500℃ for two hours in a muffle furnace. X-ray diffraction(XRD) shows multi-phase formation in un-doped and Zr doped samples. Scanning electron microscope(SEM) depicts layered structure at low Zr concentration x_(Zr)= 0.10, while uniform surface with smaller grains and voids is observed at x_(Zr)= 0.20, but at x_(Zr)= 0.30, cracks and voids become prominent. The ferromagnetic nature of the un-doped sample is observed by vibrating sample magnetometer(VSM), while paramagnetic behavior appears due to Zr doping. The ferromagnetism in un-doped sample is lost by Zr doping, which is due to the formation of additional Fe–O–Zr bonds that induce paramagnetic behavior.     

Single-particle resonance states of 122Zr in relativistic mean-field theory combined with real stabilization method

Single-particle resonance states of ¹²²Zr are studied in the real stabilization method within the framework of relativistic mean field theory. Two efficient methods are adopted to extract the resonance energy and width of ¹²²Zr. The results are compared with those obtained from the analytic continuation in the coupling approach and scattering phase-shift methods.     

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

The dynamic coupling effects on fusion cross sections for reactions~(32)S + ~(94,96)Zr and ~(40)Ca + ~(94,96)Zr are studied with the universal fusion function formalism and an empirical coupled channel(ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in ~(32)S +~(94)Zr(~(40)Ca +~(94)Zr) is almost the same as that in ~(32)S +~(96)Zr(~(40)Ca +~(96)Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with94 Zr as target should be similar as that in the reactions with ~(96) Zr as target. This implies that the quadrupole deformation parameters β_2of ~(94)Zr and~(96) Zr should be similar to each other.However, β_2 's predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on~(48) Ca +~(94)Zr or~(36) S +~(94)Zr are suggested to solve the puzzling issue concerning β_2for~(94)Zr.     

用长气体靶研究22Na+α共振散射

在日本东京大学CRIB 次级束装置上,用长气体靶开展了22Na+ α共振散射的厚靶实验研究。针对长气体靶实验中的两体运动学重构问题,提出了一套包括构建空间复杂几何关系、计算能量损失以及反应运动学的逐事件分析方法;对22Na+α共振散射的实验数据进行了重构分析,得到了E_c.m. = 4.2 ~ 5.4 MeV 区间22Na( α,α ) 的激发函数,从实验的激发函数中观测到了复合核26Al 5 个较为明显的共振峰。鉴于26Al 共振态的衰变模式比较复杂,本工作发现的26Al新共振态的能级性质有待进一步的理论分析。The 22Na+α resonant scattering is studied via a conventional thick target inverse kinematic method with an extended gas target. A data analysis method is proposed for the two-body reaction kinematic reconstruction, in which the spatial geometry, the reaction kinematics and the energy losses are considered. The experimental data of 22Na+ αresonant scattering have been thus reconstructed, and the excitation function is obtained in the energy interval of Ec.m. =4.2~5.4 MeV. Five resonant states in 26Al are observed in the experimental excitation function. Since several decay modes coexist for the observed 26Al resonant states, multi-channel theoretical analysis is thus needed to reveal their structure and decay features.     

逆运动学弹性共振散射方法在非束缚核结构研究中的应用

简要介绍了近几年发展起来的厚靶逆运动学弹性共振散射方法在非稳定核结构测量中的应用。它是研究非束缚态核结构的实验方法之一。通过测量反冲轻核的激发函数，提取共振态的能量、自旋宇称和衰变宽度等。主要用于研究非稳定核素的结构、核天体物理中相关核的阈能共振态的能级参数测量等。The method of elastic resonance scattering in inverse kinematics, which was progressed in recent years, is briefly introduced. It is a novel experimental technique to perform meaningful experiments under conditions of the very short-lived nuclides and the beam intensities only 1 000 atoms/s. The excitation function of recoil proton has been measured in experiment; the shape of proton energy spectrum can be also used to uniquely deter- mine the energy of resonant states, spin-parity, partial decay width and spectroscopic factors of the states. This method is mainly used in the investigation of unstable nuclei and the level parameters measurement of near threshold resonant state of the nuclear astrophysics related nuclei.     

Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Density functional study on the bimetallic Ti_mZr_n(n+m ≤ 5) clusters and their interactions with H_2

Equilibrium geometries, stabilities, and electronic properties of small Ti_mZr_n(n + m ≤ 5) clusters were investigated using the density functional method. The ground states were determined, and it was found that the larger clusters and those consisting of more Zr atoms are more stable. The electronic properties of the clusters were discussed based on HOMO-LUMO gaps, vertical ionization potentials(VIP), and vertical electron affinities(VEA). Furthermore, we studied the interactions between those clusters and molecular hydrogen, and found that in all the cases dissociative chemisorptions occurred. According to the chemisorption energies, the pure Zr clusters are relatively more active towards H_2 when compared with the others except Ti_3Zr, which shows the highest activity. The magnetic moments of Ti_mZr_n and Ti_mZr_nH_2 were also compared, and the results show that the hydrogenated clusters have the same or decreased total magnetic moments with respect to the bare clusters except for Ti_3Zr_2.     

蒸气压缩式制冷装置仿真的基本理论和热点问题

针对蒸气压缩式制冷装置仿真的基本理论进行了总结。将稳态仿真方法归纳为四种 :连续替代 (SS)方法、牛顿 -辛普生 (NR)方法、顺序模块 (SM)方法以及联立方程解 (SES)方法。动态仿真研究在总量上还较少 ,从中难以归纳出普遍适用的方法。模型的数值健壮性、模型的通用性以及大型机组的仿真是目前的热点问题。     

Consistent Burgers equation expansion method and its applications to high- dimensional Burgers-type equations

In this paper, a novel method, named the consistent Burgers equation expansion (CBEE) method, is proposed to solve nonlinear evolution equations (NLEEs) by the celebrated Burgers equation. NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method. In order to verify the effectiveness of the CBEE method, we take (2+1)-dimensional Burgers equation as an example. From the (1+1)-dimensional Burgers equation, many new explicit solutions of the (2+1)-dimensional Burgers equation are derived. The obtained results illustrate that this method can be effectively extended to other NLEEs.     

二维多介质可压缩流的RKDG有限元方法

应用RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法、Level Set方法和Ghost Fluid方法数值模拟二维多介质可压缩流,其中Euler方程组、Level Set方程和重新初始化方程的空间离散采用DG(Discontinuous Galerkin)有限元方法,时间离散采用Runge-Kutta方法.对二维的气-气和气-液两相流进行了数值计算,得到了分辨率较高的计算结果.     

基于SNGR方法的后缘噪声数值模拟

采用随机噪声产生和传播(SNGR)方法对后缘噪声进行数值模拟.SNGR方法结合随机方法和计算流体力学,耗费较少的计算资源就可以预测噪声水平.数值模拟时采用有限体积法求解雷诺平均Navier-Stokes(RANS)方程;采用有限差分法求解声学扰动方程,数值格式采用色散关系保持(DRP)格式,远场边界条件采用无反射边界条件.以二维平板和NACA0012翼型为例,编制程序,与参考结果对比表明,程序可以预测后缘噪声.     

An interpolating boundary element-free method (IBEFM) for elasticity problems

The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.     

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

In this paper, we analyze the generalized Camassa and Holm （CH） equation by the improved element-free Galerkin （IEFG） method. By employing the improved moving least-square （IMLS） approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.     

An improved boundary element-free method （IBEFM） for two-dimensional potential problems

The interpolating moving least-squares (IMLS) method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method (BEFM), combining the boundary integral equation (BIE) method with the IMLS method, the improved boundary element-free method (IBEFM) for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker δ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker δ function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.     

A standard and direct method to obtain multiple soliton solutions of the nonlinear partial differential equation

In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative equations are investigated by this method and multiple soliton solutions are found.     

Solving unsteady Schr?dinger equation using the improved element-free Galerkin method

By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrödinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.     

Efficient Analysis of Millimeter Wave Ferrite Circulators by the GMRES Iterative Algorithm

The finite element method (FEM) combined with the perfectly matched layers (PML) is given for simulation of waveguide ferrite circulators. The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. The formulation of FEM and the algorithm of GMRES method are described in detail. The reflection and insertion losses of millimeter wave waveguide circulator are analyzed and the results are compared with those obtained from literature.