The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

Explicit Exact Solutions for the (2+1)-Dimensional Higher-Order Broer-Kaup System

Using the modified extended tanh-function method, explicit and exact traveling wave solutions for the (2+1)-dimensional higher-order Broer-Kaup (HBK) system, comprising new soliton-like and period-form solutions, are obtained.     

带电线性谐振子在非对易空间中的Wigner函数

在利用Wigner函数性质的基础上, 考虑到空间变量的对易关系中包含了坐标 坐标的非对易性, 得到了带电线性谐振子在非对易空间中的Wigner函数。 Based on the property of wigner function, the Wigner function of charged Linear Harmonic Oscillator in non commutative space was obtained by considering the noncommutative of the coordinate coordinate in the relation of space variable.     

Application of a modified Lindstedt–Poincaré method in coupled TDOF systems with quadratic nonlinearity and a constant external excitation

An analytical approach is developed for the nonlinear oscillation of a conservative, two-degree-of-freedom (TDOF) mass-spring system with serial combined linear–nonlinear stiffness excited by a constant external force. The main idea of the proposed approach lies in two categories, the first one is the transformation of two nonlinear differential equations of a two-mass system using suitable intermediate variables into a single nonlinear differential equation. Another is the treatment a quadratic nonlinear oscillator (QNO) by the modified Lindstedt–Poincaré (L-P) method presented recently by the authors. The first-order and second-order analytical approximations for the modified L-P method are established for the QNOs with satisfactory results. After solving the nonlinear differential equation, the displacements of two-mass system can be obtained directly from the governing linear second-order differential equation. Unlike the common perturbation method, the modified L-P method is valid for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical expressions valid for small as well as large amplitudes of oscillation. In short, this new approach yields extended scope of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to the previous approaches such as the perturbation and classical harmonic balance methods. Two examples of nonlinear TDOF mass-spring systems excited by a constant external force are selected and the approximate solutions are verified with the exact solutions derived from the Jacobi elliptic function and also the numerical fourth-order Runge–Kutta solutions.     

具有约束层阻尼贮液圆柱容器的耦振与减振特性分析

该文在对空圆柱层合壳(不充液)振动分析研究的基础上,借助线性势流理论,进一步考虑液固耦合效应,导出了敷有CLD贮液圆柱层合壳谐耦振的一阶常微分矩阵方程,该方程右边多了液动压力项.由于它不能预先给定,导致方程中出现未知项.为了克服这一困难,文中研究了液动压力的解式,并采用新型齐次扩容精细积分技术,提出了一种高效率和高精度的半解析半数值解法.进而还求解了CLD贮液圆柱容器在地面谐运动激励下的响应;通过大量数值计算分析了CLD的厚度、长度、敷设位置以及粘弹芯的复剪切模量对减振效果的影响.计算还表明了有液体的存在,这些影响和空容器时是不一样的.文中方法为CLD贮液容器的控制优化提供了有力手段.     

Fields induced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic bimaterials

The coupled elastic, electric and magnetic fields produced by an arbitrarily shaped three-dimensional dislocation loop in general anisotropic magneto-electro-elastic (MEE) bimaterials are derived. First, we develop line-integral expressions for the fields induced by a general dislocation loop. Then, we obtain analytical solutions for the fields, including the extended Peach–Koehler force, due to some useful dislocation segments such as straight line and elliptic arc. The present solutions contain the piezoelectric, piezomagnetic and purely elastic solutions as special cases. As numerical examples, the fields induced by a square and an elliptic dislocation loop in MEE bimaterials are studied. Our numerical results show the coupling effects among different fields, along with various interesting features associated with the dislocation and interface.     

Mutator for transferring a memristor emulator into meminductive and memcapacitive circuits

In this paper, a concise but effective interface circuit for transforming a memristor into meminductive and memcapacitive systems is designed. This newly proposed interface circuit, constructed by only two current conveyors, is equipped with three available ports, which can provide six connecting combinations in terms of one resistor, one capacitor, and one memristor. For the sake of confirming the design effectiveness, theoretical and simulation discussions are hence introduced and all the experimental waveforms provide conclusive evidence to validate the correctness of these new mutators. The most attractive features of this new interface circuit are the floating terminals and convenient practical implementation.     

An easy trick to a periodic solution of relativistic harmonic oscillator

In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.     

Spectral element analysis of herringbone‐grooved journal bearings with groove–ridge discontinuity

Many researchers have investigated the performance of herringbone‐grooved journal bearings (HGJBs). However, few have yet mentioned the issue of film thickness discontinuities in HGJBs with a finite number of grooves. Most studies have involved the application of a finite difference method for discretization. The present work utilizes the spectral element method to calculate the pressure distribution and dynamic coefficients of HGJBs, in which the thickness of the fluid film changes abruptly in the groove–ridge region. Conservation of mass is adopted to solve the problem. Additionally, the present method can be adopted for grooves with curvy geometry. The numerical results were compared with the analytical solution for a one‐dimensional slider bearing and an HGJB. It also shows that for the case of HGJB, the numerical result by the present method is more accurate than the numerical results found in the literature (Trans. ASME J. Tribol. 2000; 122 : 103–109, Int. J. Numer. Meth. Heat Fluid Flow 2002; 12 : 518–540). Furthermore, employing the present method with the Elrod algorithm can improve the accuracy of deriving loads of HGJBs when cavitation occurs. In addition, the result displays the efficiency of the present method by observing the CPU time. Therefore, the approach can be employed to compute the critical mass of a HGJB. The influence of changing groove angle, groove depth, groove width, and the eccentricity on the critical mass are discussed. Observing the variations in critical mass shows that when the eccentricity is small, a larger groove angle, a lower groove depth, and smaller groove width correspond to a higher critical mass of the HGJB. Copyright © 2010 John Wiley & Sons, Ltd.     

On the dynamics of a particle on a cone

A detailed study of the classical and quantum mechanics of a free particle on a double cone and a particle bound to its tip by a harmonic oscillator potential is presented.