Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function W=Tr(Δρ)( an ensemble average of the density operator ρ，Δis the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states.In doing so,converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise,The entangled states are defined in the enlarged Fock space with a fictitious freedom.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

使用转变关系在之中平常，正常，和 antinormalordering 为多模式波色子指数的二次的多项式操作员(BEQPO “ s ) ，我们在场为 BEQPO 的任意的矩阵元素的分析表示” s。作为一个初步的应用程序，我们关于波色子获得分区功能的准确表达式二次的多项式系统，在粒子数字的矩阵元素，坐标，和动量表示，和为 BEQPO 的 P 表示“ s。

Matrix elements in the SU(1,1)⊗SO(6)limit of the proton-neutron symplectic model

The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.

Research on convergence of the nuclear matrix elements for 2νββ decays

In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are presented for the half-lives,nuclear matrix elements(NMEs),phase space factors(G2ν),and convergence of the NMEs.The theoretical results agree well with the experimental data.In addition,we predict the half-lives of 2νββ decays for four nuclei.We focus on the convergence of the NMEs by analyzing the number of contributing intermediate 1+states(NC)for the nuclei of interest.We assume that NC is safely determined when the accumulated NMEs saturate 99.7%of the final calculated magnitude.From the calculations of the involved nuclei,we discover a connection between NC and the total number of intermediate 1+states(NT).According to the least squares fit,we conclude that the correlation is NC=(10.8±1.2)×N(0.29±0.02)T.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, the time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classify the high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution(TFD) with non-negative matrix factorization(NMF), and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform(STFT). Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network(ANN), NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Finite Element Analysis of Push-Out Test of SiC Fiber Reinforced Titanium Matrix Composites

Based on the interphase layer model and the spring layer model, an improved interface model was developed to evaluate the interfacial shear strength of Titanium matrix composites(TMCs) and to analyze the effects of various parameters on the interfacial properties. The results showed that the improved interface model is more suitable for calculating the interfacial properties of SiC fiber reinforced titanium matrix composites. The interfacial shear strength of SiC/Timetal-834 predicted is 500 MPa. In addition, in order to better understand the interfacial properties of composites, some push out phenomenon were analyzed.

CALCULATION OF MATRIX ELEMENTS IN THE MODEL POTENTIAL THEORY OF ATOMIC STRUCTURE

Ⅰ. INTRODUCTIONRecently, Zheng suggested a new model potential to describe the electronic motion in a multi-electron atom or ion in his serial papers. Applying this new version of model po-

Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.

Computation of products of phase space factors and nuclear matrix elements for double beta decay

Nuclear matrix elements(NME) and phase space factors(PSF) entering the half-life formulas of the double-beta decay(DBD) process are two key quantities whose accurate computation still represents a challenge. In this study, we propose a new approach of calculating these, namely the direct computation of their product as an unique formula. This procedure allows a more coherent treatment of the nuclear approximations and input parameters appearing in both quantities and avoids possible confusion in the interpretation of DBD data due to different individual expressions adopted for PSF and NME(and consequently their reporting in different units) by different authors. Our calculations are performed for both two neutrino(2 vββ) and neutrinoless(0 vββ) decay modes, for five nuclei of the most experimental interest. Further, using the most recent experimental limits for 0νββ decay half-lives,we provide new constraints on the light mass neutrino parameter. Finally, by separating the factor representing the axial-vector constant to the forth power in the half-life formulas, we advance suggestions on how to reduce the errors introduced in the calculation by the uncertain value of this constant, exploiting the DBD data obtained from different isotopes and/or decay modes.

Theoretical Study on Electron Transfer Matrix Element in Oxidation of α-Amino Carbon-Centered Radical by O_2

As a successive work of our previous paper, 1 the electron transfer matrix element (V rp) in the oxidation of the simplified model molecule of α-amino carbon-centered radical by O 2 has been investigated with ab initio calculation at the level of UHF/6-31++G**. Based on the optimized geometries of the reactant and the ion-pair complex obtained previously, the reaction heat and the inner reorganization energy have been obtained by constructing the potential energy curves of reactant and product states considering the solvent effect with the conductor-like screening model (COSMO). The solvent reorganization energy has been estimated using Lippert-Mataga relationship. The calculated results show that the value of V rp is several times larger than that of RT, which means that the model reaction is an adiabatic one. Theoretical investigation indicates that the solvent effect on the direct electron transfer (ET) process of oxidation of α-amino carbon-centered radical by oxygen is remarkable.

Effects of rare earth element lanthanum on the microstructure of copper matrix diamond tool materials

Effects of rare earth element La on the microstructure of Cu matrix diamond tools were researched under the conditions of various materials componentsand the process parameters in order to improve materials properties. SEM, XPS and X-ray were used to investigate the fracture section, microstructure and the element valence in materials. The results shown that the combination of rare earth element La and transition element Ti is advantageous to the bonding state between diamond particles and matrix, so it can improve the materials properties. Suitable sintering temperature is 790℃.

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

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THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element The Hilbert stress subspace of the assumed stress modes is established So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt’s method Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly The numerical examples show that the method is

Coupling matrix element of electron self-exchange reactions in solution

On the basis of the common feature among the electron transfer process and the ion hydration process as well as the relevant experimental kinetic data of electron transfer reaction,a new accurate hydration potential function scheme for the determination of electron transfer coupling matrix element is presented.The coupling matrix element between two hydrated ions of the reacting system in solution is calculated.The results and the applicability of this scheme are discussed.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

Damage prediction for magnesium matrix composites formed by liquid-solid extrusion process based on finite element simulation

A damage prediction method based on FE simulation was proposed to predict the occurrence of hot shortness cracks and surface cracks in liquid-solid extrusion process.This method integrated the critical temperature criterion and Cockcroft & Latham ductile damage model, which were used to predict the initiation of hot shortness cracks and surface cracks of products, respectively.A coupling simulation of deformation with heat transfer as well as ductile damage was carried out to investigate the effect of extrusion temperature and extrusion speed on the damage behavior of Csf/AZ91D composites.It is concluded that the semisolid zone moves gradually toward deformation zone with the punch descending.The amplitude of the temperature rise at the exit of die from the initial billet temperature increases with the increase of extrusion speed during steady-state extrusion at a given punch displacement.In order to prevent the surface temperature of products beyond the incipient melting temperature of composites, the critical extrusion speed is decreased with the increase of extrusion temperature, otherwise the hot shortness cracks will occur.The maximum damage values increase with increasing extrusion speed or extrusion temperature.Theoretical results obtained by the DeformTM-2D simulation agree well with the experiments.

NORMALIZED ELEMENT NODE TOPOLOGICAL MATRIX OF FINITE ELEMENT MESHES

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精密导向膜片设计与优化

针对微振动模拟器中精密导向机构行程小、精度高的要求,提出了一种具有精密导向作用的柔性膜片。首先,基于柔度矩阵法对柔性膜片的轴向与径向柔度进行建模;其次,基于柔性膜片的结构参数对其轴向和径向柔度进行参数化分析;接着,以高轴向柔度、高轴向/径向柔度比和低应力为目标,建立了优化设计模型,并对其进行优化,优化结果表明轴向柔度优化率为233%,轴向/径向柔度比优化率为172%,最大应力优化率为32%。优化后柔性膜片的各目标性能都得到较大提升;最后,通过有限元分析与实验进行验证。有限元分析与实验结果相对于理论分析的相对误差分别为6.7%和7.8%。理论分析与优化方法为柔性膜片提供了一个简单有效的设计思路。