善用对称 化繁为简——例谈“对称”操作在物理解题中的运用

从操作的层面，结合具体的问题情境，介绍了高中物理解题中常用的4种构造对称的方法即时间反演、顺势延展、由因索果、对称分割．这些“对称”操作方法有效地简化了运动过程、运算方法和电路结构，使物理问题的求解变得更简单．

Mei Symmetry and Hojman Conserved Quantity of Nonholonomic Controllable Mechanical System

A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the corresponding holonomic mechanical system, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomie controllable mechanical system are obtained. An example is given to illustrate the application of the results.

A Scheme for Spin Manipulation in a Quantum Dot with Both Charge and Spin Bias

We propose a scheme for the effective polarization and manipulation of electron spin by using a quantum dot with both charge and spin bias. Using the equation of motion for Keldysh nonequilibrium Green function, we study the spin accumulation and polarization for the system. Through analytical analysis and a few numerical examples, it is demonstrated that fairly large spin accumulation and polarization can be produced due to the breaking symmetry of the chemical potential for different electron spin in the leads. Moreover, the direction and the strength of the spin polarization can be conveniently controlled and tuned by varying the charge bias or the gate voltage.

Single Platform Integration Environment for Turbine Rotor Design and Analysis

The present article covers briefly state of the art software interoperability technical solutions and the development of the first module of a new single platform D ＆ A （design ＆ analysis） tool for simulation and prediction of stress and burst behavior of turbine rotating disc a preliminary design stage. This platform singularity requires integration of multiple CAD （computer assisted design） ＆ FEA （finite element analysis） tools processing in batch mode and driven from a SPIE （single platform integration environment）. This first module is also to demonstrate, for an axial turbine disc hub axi-symmetric component, feasibility and usefulness of such a platform at preliminary design stage. Expected benefits of the D ＆ A single platform are to improve output accuracy, reduce cycle time, improve process quality and improve resource productivity.

Experimental and Numerical Investigation of Centrifugal Pumps with Asymmetric Inflow Conditions

Most of the times pumps operate off best point states.Reasons are changes of operating conditions,modifications,pollution and wearout or erosion.As consequences non-rotational symmetric flows,transient operational conditions,increased risk of cavitation,decrease of efficiency and unpredictable wearout can appear.Especially construction components of centrifugal pumps,in particular intake elbows,contribute to this matter.Intake elbows causes additional losses and secondary flows,hence non-rotational velocity distributions as intake profile to the centrifugal pump.As a result the impeller vanes experience permanent changes of the intake flow angle and with it transient flow conditions in the blade channels.This paper presents the first results of a project,experimentally and numerically investigating the consequences of non-rotational inflow to leading edge flow conditions of a centrifugal pump.Therefore two pumpintake-elbow systems are compared,by only altering the intake elbow geometry:a common single bended 90°elbow and a numerically optimized elbow(improved regarding rotational symmetric inflow conditions and friction coefficient).The experiments are carried out,using time resolved stereoscopic PIV on a full acrylic pump with refractions index matched(RIM)working fluid.This allows transient investigations of the flow field simultaneously for all blade leading edges.Additional CFD results are validated and used to further support the investigation i.e.for comparing an analog pump system with ideal inflow conditions.

CPT-Frames for Non-Hermitian Hamiltonians

Based on the PT-symmetric quantum theory, the concepts of PT-frame, PT-symmetric operator and CPT-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of a PT-symmetric linear operator are both symmetric with respect to the real axis and the eigenvalues of an unbroken PT-symmetric operator are real. For a linear operator H on Cd, it is proved that H has unbroken PT- symmetry if and only if it has d different eigenvalues and the corresponding eigenstates are eigenstates of PT. Given a CPT-frame on K, a new positive inner product on K is induced and called CPT-inner product. Te relationship between the CPT-adjoint and the Dirac adjoint of a densely defined linear operator is derived, and it is proved that an operator which has a bounded CPT-frame is CPT-Hermitian if and only if it is T-symmetric, in that case, it is similar to a Hermitian operator. The existence of an operator C consisting of a CPT-frame is discussed, These concepts and results will serve a mathematical discussion about PT-symmetric quantum mechanics.

Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so"apparently"not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates.The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1＋1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.

Dual-wavelength erbium-doped fiber laser with asymmetric fiber Bragg grating Fabry-Perot cavity

A novel dual-wavelength fiber laser with asymmetric fiber Bragg grating(FBG) Fabry-Perot(FP) cavity is proposed and experimentally demonstrated. A couple of uniform FBGs are used as the cavity mirrors, and the third FBG is used as intracavity wavelength selector by changing its operation temperature. Experimental results show that by adjusting the operation temperature of the intracavity wavelength selector, a tunable dual-wavelength laser emission can be achieved. The results demonstrate the new concept of dual-wavelength lasing with asymmetric FBG FP resonator and its technical feasibility.