Corrigendum:Stochastic resonance in a parallel array of linear elements

In this paper, we point out the errors occurring in the paper （Dong X J 2009 Chin. Phys. B 18 70） and present a correct conclusion.

A MULTI-GRID ALGORITHM FOR MIXED PROBLEMS WITH PENALTY BY C°-PIECEWISE LINEAR ELEMENT APPROXIMATION

In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.

OPTIMAL INTERIOR AND LOCAL ERROR ESTIMATES OF A RECOVERED GRADIENT OF LINEAR ELEMENTS ON NONUNIFORM TRIANGULATIONS

We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.

Simple experimental scheme of teleporting a two-qubit state via linear optical elements

We propose a simple experimental scheme in which an unknown two-qubit state is faithfully and deterministically teleported from Alice to Bob. The scheme is constructed with four photons from parametric down conversion, linear optical elements, and conventional photon detectors, all of which are available in current technology. It is shown that the probability of successful teleportation ideally reaches 100% based on single-photon two-qubit-assisted Bell-state measurement, which can distinguish all four Bell-states simultaneously via conventional photon detectors. By generalizing the scheme, the teleportation of an unknown multi-qubit system can also be realized.

Scheme for Concentration of Unknown Photonic GHZ Entangled States via Linear Optical Elements

We propose two schemes to concentrate unknown nonmaximally tripartite GHZ entangled states via linear optical elements. The finial maximally entangled states obtained from our schemes are shared by two or three parties. Our schemes only need polarizing beam splitters and single-photon detectors. In addition, the schemes can be demonstrated within current experimental technology.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reffect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.

Finite element analysis of the effect of micro-pore defect on linear friction welding of medium carbon steel

Micro-pore is a very common material defect. In the present paper, the temperature fields of medium carbon steel joints with and without micro-pore defect during linear friction welding （LFW） were investigated by using finite element method. The effect of micro-pore defect on the axial shortening of joints during LFW was examined. The x- and y-direction displacements of micro-pore during the LFW process were also studied. In addition, the shape of micro-pore after LFW was observed. The heat conducted from the weld inteace to the specimen interior. The fluctuation range of the temperature curves for the joint with micro-pore is larger than that without micro-pore. Position of micro-pore changes with the change of the friction time. The circular shape of micro-pore becomes oval after welding.

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.

Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods

This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Predicting urbanization level by main element analysis and multiple linear regression---taking Xiantao district in Hubei Province as an example

In this paper we firstly select main factors relating to urbanization level of Xiantao District in Hubei Province by main element, then, make model of urbanization level by analysis of multiple liner regression, and lastly predict its urbanization level

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

Finite Element Methods Applied to the Tubular Linear Stepping Motor

In this paper proposes a Finite Element Methods analyzing applied to the linear tubular stepping actuator. The linear displacement is modeled by means of a layer of finite elements placed in the air gap. The design of the linear stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. The magnetic field of the actuator has been analyzed using the finite element method over a current-displacement variation. The magneto static field and electromagnetic force was introduced in order to predict before construction, the inductance values according to the displacement and the currents into the coils. The results were obtained for the magnetic flux density distribution and the electromagnetic force for different positions and current.

Analysis of the Influence of Parafunctional Loads on the Bone-Prosthesis System: A Non-Linear Finite Element Analysis

The present study evaluates the effects of occlusal loading on an implant-supported dental implant with external hexagon dental implant-abutment systems, using the finite element method analysis. Tensile analyses were performed to simulate different axial and obliquous masticatory loads. The influence of the variations in the contouring conditions of the interfaces was analyzed to weigh the osseointegration with linear and non-linear cases, by means of a parametric design. The geometry selected to place the prostheses was a jaw section, considering the properties of the set of cortical and trabecular bones. The results show that for non-linear contour conditions, the stress presents smaller value distributions and signals a different place in the screw-implant interface as the factor of the greater weight in this study. The location indicated that von Mises stress concentrations are not exclusive to the contact regions studied, moving to an area that is not in direct contact with the non-linear contact interfaces. In addition, the direction of load with an angle of 15 degrees presented the highest values of von Mises stress.

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

Line-element based nonlinear adaptive piecewise compensating correction for LVDT sensors

In order to solve the linear variable differential transformer （LVDT） displacement sensor nonlinearity of overall range and extend its working range, a novel line-element based adaptively seg- menting method for piecewise compensating correction was proposed. According to the mechanical structure of LVDT, the output equation was calculated, and then the theoretic nonlinear source of output was analyzed. By the proposed line-element adaptive segmentation method, the nonlinear output of LVDT was divided into linear and nonlinear regions with a given threshold. Then the com- pensating correction function was designed for nonlinear parts employing polynomial regression tech- nique. The simulation of LVDT validates the feasibility of proposed scheme, and the results of cali- bration and testing experiments fully prove that the proposed method has higher accuracy than the state-of-art correction algorithms.

基于氢氧同位素的平原湖荡地表水与地下水转化研究

地表水与地下水间的相互转化以及量化地下水补给量是湖泊水循环研究的重要内容。本文采集了元荡湖区域湖水、地下水样品,测试了其氢氧稳定同位素组成和水化学组成,运用Piper三线图分析其水化学类型、通过钻孔实测的地下水埋深绘制元荡湖区域旱季(2022年12月)和雨季(2023年6月)的地下水水位等值线图,结合电导率(EC)和溶解性总固体(TDS)定性分析地表水-地下水之间的转化关系,利用同位素水量平衡方程、线性端元混合模型定量评价了湖水、地下水、河水和降水之间的转化量。结果表明,研究区湖水和地下水的水化学类型均为HCO_(3)^(-)·SO_(4)^(2-)·Ca^(2+)·Na^(+)·Mg^(2+),旱季和雨季湖水均受到地下水的补给,拟合得到的湖水旱季、雨季氢氧稳定同位素线性回归方程表明雨季斜率较小,蒸发更为强烈。湖水主要由河水、地下水和降水补给,其三者在旱季的补给比例分别为59%、26%和15%,在雨季的补给比例分别为23%、39%和38%。本文成果为元荡湖区域以及太湖流域的综合治理提供了科学依据。

高温超导直线同步电机电磁力仿真与实验研究

无铁芯超导直线同步电机(superconducting linear synchronous motor,SLSM)具有推力密度高、工作气隙大等优势,是超导磁浮列车的动力核心。由于会不可避免地受到弯道、道岔、横风和电源谐波等因素的影响,磁浮列车在运行过程中将发生多自由度运动,使电机次级姿态发生滚转或偏移,致使超导直线电机的电磁力性能发生改变,进而影响列车的运行稳定性。针对多变电机次级姿态下高温超导直线同步电机的三维力特性展开研究,首先分析悬浮车体多自由度运动对直线电机次级姿态的影响,并建立计算SLSM三维电磁力的有限元模型;其次,通过搭建超导同步直线电机样机,实验验证模型的有效性;最后,基于该模型研究无铁芯SLSM次级在发生横向偏移、法向偏移、侧滚、俯仰以及偏航条件下的三维电磁力输出特性及其变化规律,为超导磁浮列车运行性能优化提供了理论依据。