Exact solutions of the Dirac equation with Pschl-Teller double-ring-shaped Coulomb potential via the Nikiforov-Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.

Deformation Analysis on Shear-Bending of Ring-Shaped Piezoelectric Actuator

Deformation of a simple single piezoelectric actuator is usually quite small.A ring-shaped piezoelectric actuator with large piezoelectrically generated displacement was proposed.The thickness of the actuator was1 mm,and the inner and outer diameters were 4 mm and 40 mm,respectively.The ring-shaped actuator was made of BiScO_3-PbTiO_3(BS-PT)ceramic and polarized in radial direction.An electric field was applied to thickness direction and a large shear-bending deformation emerged.Then Rayleigh-Ritz method and Bessel functions were adopted to analyze the shear-bending deformation.Results show that under an electric field of 7.5kV/cm,the maximum displacement at the inner edge of the actuator reached 5.07μm,which agreed well with the corresponding experimental results.

Formation Mechanism of the Ring-shaped Structure of Plasma Bullet

The formation of plasma bullets’ring-shaped structure in atmospheric pressure helium is analyzed by using a coupled fluid model.The model consists of a two-dimension neutral gas flow module and a one-dimension plasma dynamics module.The obtained radial distributions of the electron’s number density and the nitrogen’s metastable number density have different structures under different types of reactions or air contents in the model.It shows that total electron impact ionization plays an important role in sustaining the discharge,and together with Penning process,they lead to the shifted-off structure of electron number density.Meanwhile,the ring structure of plasma bullets forms mainly due to the excitation reaction of nitrogen molecule on air contents.

Exact solutions of the Klein-Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm＂ functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.

Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential

Poschl-Teller double-ring-shaped Coulomb （PTDRSC） potential, the Coulomb potential surrounded by PSschl- Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ,θ and τ coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schr6dinger equation with PTDRSC potential are presented. The normalized φ,θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

AERODYNAMIC ANALYSIS OF CIRCULAR PLATE-SHAPED AND CIRCULAR RING-SHAPED SQUEEZE FILM BEARINGS

Aerodynamics of circular plate- and circular ring-shaped squeeze film hearings is analyzed in detail, yielding analytic expressions for the pressure distribution of these hearings. Several formulae for these hearings are modified using the developed method. The paper also gives numerical results oj pressure distribution and load-hearing capacities of these hearings.

STUDY ON THE RING SPINNING SYSTEM WITH A FIXED BELL SHAPED BALLOON CONTROLLER

On the basis of analyzing the typical kinds of balloon controllers used now, this article provides a new type one named Fixed Bell Shaped Balloon Controller. Experiments have been made to verify the function of it. Results indicated that the facility has quite good effect on the improvement of yarn quality and properties in addition to controlling yarn tension.

The Calibration and Use of a New Ring-Shaped Ionization Chamber for Monitoring and Dosimetry of X-Ray Beams

Today, dosimeters are used generally for dosimetry of the diagnostic X-ray beam. Ionization chambers are appropriate instruments for monitoring and also the dosimetry of X-ray beam in medical diagnostic equipment. The present work introduces design and investigation of a new ring-shaped monitor chamber with a PMMA body, graphite-coated PMMA windows (0.5 mm thick), a special graphite-foil central electrode (0.1 mm thick, 0.7 g/cm3 dense) that creating two sensitive volumes and a central hole for crossing the radiation beam with less attenuation. The results of performance tests conducted at the Nuclear Science and Technology Research Institute, AEOI in Karaj- Iran proved the high short and long-term stability, the very low leakage current, the low directional dependence and very high ion collection efficiency through the special design of the collecting electrode. Moreover, the FLUKA Monte Carlo simulations certified the negligible effect of central electrode on this new ring-shaped monitor chamber. According to the results of the performance tests, the new monitor chamber can be used as a standard dosimeter in order to monitor X-ray beam in primary standard dosimetry laboratories.

Advances in Compact Manufacturing for Shape and Performance Controllability of Large-scale Components-A Review

Research on compact manufacturing technology for shape and performance controllability of metallic components can reanze the simplification and high-reliability of manufacturing process on the premise of satisfying the requirement of macro/micro-structure. It is not only the key paths in improving performance, saving material and energy, and green manufacturing of components used in major equipments, but also the challenging subjects in frontiers of advanced plastic forming. To provide a novel horizon for the manufacturing in the critical components is significant. Focused on the high-performance large-scale components such as bearing rings, flanges, railway wheels, thick-walled pipes, etc, the conventional processes and their developing situations are summarized. The existing problems including multi-pass heating, wasting material and energy, high cost and high-emission are discussed, and the present study unable to meet the manufacturing in high-quality components is also pointed out. Thus, the new techniques related to casting-rolling compound precise forming of rings, compact manufacturing for duplex-metal composite rings, compact manufacturing for railway wheels, and casting-extruding continuous forming of thick-walled pipes are introduced in detail, respectively. The corresponding research contents, such as casting ring blank, hot ring rolling, near solid-state pressure forming, hot extruding, are elaborated. Some findings in through-thickness microstructure evolution and mechanical properties are also presented. The components produced by the new techniques are mainly characterized by fine and homogeneous grains. Moreover, the possible directions for fin＇ther development of those techniques are suggested. Finally, the key scientific problems are first proposed. All of these results and conclusions have reference value and guiding significance for the integrated control of shape and performance in advanced compact manufacturing.

Electronic states of InAs/GaAs tyre-shape quantum ring

In the framework of the effective mass theory, this paper calculates the electron energy levels of an InAs/GaAs tyre-shape quantum ring （TSQR） by using the plane wave basis. The results show that the electron energy levels axe sensitively dependent on the TSQR＇s section thickness d, and insensitively dependent on TSQR＇s section inner radius R1 and TSQR＇s inner radius R2. The model and results provide useful information for the design and fabrication of InAs/GaAs TSQRs.

GENERAL SOLUTION FOR U-SHAPED BELLOWS OVERALL-BENDING PROBLEMS

The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping, et al. and the solution for ring plates. The results evaluated in this paper are compared with those on EJMA (standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxilz, et al.

Nonlinear mechanics of a ring structure subjected to multi-pairs of evenly distributed equal radial forces

Combining the elastica theory, finite element (FE) analysis, and a geometrical topological experiment, we studied the mechanical behavior of a ring subjected to multi-pairs of evenly distributed equal radial forces by looking at its seven distinct states. The results showed that the theoretical predictions of the ring deformation and strain energy matched the FE results very well, and that the ring deformations were comparable to the topological experiment. Moreover, no matter whether the ring was compressed or tensioned by N-pairs of forces, the ring always tended to be regular polygons with 2N sides as the force increased, and a proper compressive force deformed the ring into exquisite flower-like patterns. The present study solves a basic mechanical problem of a ring subjected to lateral forces, which can be useful for studying the relevant mechanical behavior of ring structures from the nano- to the macro-scale.

SYNTHESIS,CHARACTERIZATION AND NANOPARTICLE FORMATION OF STAR-SHAPED POLY(L-LACTIDE)WITH SIX ARMS

Well-defined star-shaped poly(L-lactide)with six arms(sPLLA)was synthesized via the ring-opening polymerization of L-lactide using dipentaerythritol as initiator and stannous octoate as catalyst in bulk at 125~C.The effects of molar ratios of both monomer to initiator and monomer to catalyst on the molecular weights of as-synthesized sPLLA polymers were in detail investigated.The molecular weights of sPLLA polymers linearly increased with the molar ratio of monomer to initiator,and the molecular weight dist...

基于环形多模谐振器的双频滤波功分器设计

本文设计了一种基于环形多模谐振器的零点可控双频滤波功分器。通过微扰加载,实现双频滤波器功能;利用枝节加载,提高了带宽和带外选择性;采用融合设计方法,将该滤波器与功分器进行集成,完成双频滤波功分器设计;通过在输出端口间引入电阻,提高端口间隔离度。为了验证设计的正确性,设计、加工和测试了该功分器,实测结果和仿真结果基本吻合,当功分器S_(11)<-10 dB时,工作频段分别为2.14~2.52 GHz和4.54~4.84 GHz,端口间隔离度最大达到45 dB。

基于ANSYS Workbench的O形橡胶密封圈有限元分析

为了研究O形橡胶密封圈(以下简称O形圈)的压缩率与接触压强的关系,首先通过ANSYS Workbench有限元分析软件对装置结构进行必要的模型简化,其次进行关键的边界条件设置及载荷的施加等操作,最后完成非线性静态有限元分析。采用后处理分析技术,得到该装置结构的变形量及von Mises应力分布图。结合实际工况,分析螺栓预紧力、O形圈压缩率及接触压强之间的关系,保证介质(含压气体或液体)密封的接触压强满足工况需求,确保介质密封的有效性和可靠性。

非均质环形谐振子结构性能分析方法

传统环形谐振子结构特性分析方法是基于均质弹性力学理论的,无法准确描述非均质材料力学特性对环形谐振子结构静、动态性能的影响规律。基于圆弧形结构的欧拉梁理论,根据非均质本构关系,运用Hamilton原理,提出一种非均质环形谐振子结构性能分析方法。利用非均质环形谐振子理论和布勃诺夫-伽辽金法,获得非均质环形谐振子静态弯曲问题和动态转动问题的理论解。然后,分析了材料的非均质力学特性对环形谐振子弯曲挠度、二阶弯曲角频率及进动系数的影响规律。典型非均质材料性能分析结果表明,传统方法对于二阶弯曲角频率计算误差达59%以上,而所提方法能够精确预测非均质谐振子结构的静、动态响应,计算出二阶弯曲角频率。

高温合金环件形性协同锻造工艺参数群智能寻优方法与应用研究

准确快速地选取锻造工艺参数的最优组合方法,对实现难变形材料高温合金环类锻件的形性协同控制具有重要的意义。基于传统锻造工艺参数设计依赖设计人员经验、目标函数选择困难和寻优过程耗时等特点,提出了一种基于群智能寻优的工艺参数优化组合设计方法,实现了难变形高温合金环类锻件形性质量提升。论文以高温合金环形件模锻成形工艺参数最优组合为研究对象,以实现环锻件形性协同控制为目标,设计了考虑环锻件平均等效应变、等效应变标准差以及材料利用率的多目标参数模型;通过对各目标参数进行加权处理,获得了环锻件的综合目标模型;根据中心复合试验法及有限元模拟结果,确定了各目标参数与工艺参数之间的回归关系;利用麻雀搜索算法对综合目标模型进行智能寻优,获得了环锻件锻造工艺参数组合。生产试制结果表明:采用基于群智能寻优麻雀搜索算法获得的工艺参数组合,锻造后环锻件本体晶粒度达到9~10级,晶粒度差值小于1级,有效提高了环形锻件的变形均匀性,实现了高温合金环类锻件形状和性能的形性协同。