等离子体中大幅波与低频振荡粒子非线性相互作用效应

本文从Vlasov-Maxwell方程组出发,保留高频场到四级项,导得了纵、横波大幅高频场与低频振荡粒子拍频作用的动力学方程组。结果表明,在空间一维情况下,对亚声波,高阶大幅高频场的存在使形成Soliton的有质动力凝聚作用削弱,而对超声波则更不存在Soliton解;在三维情况下,似乎使Caviton形成变慢。 关键词：     

Sixth order electron and muon (g−2)/2 from second order vacuum polarization insertion

We complete the analytic evaluation of sixth order contributions to electron and muon anomalous magnetic moments coming from second order vacuum polarization insertions into all the fourth order graphs.     

Spring pendulum: Parametric excitation vs an external force

The method of multiple scales is applied to obtain an approximate solution to the nonlinear dynamic equations describing a spring pendulum with the vertical oscillations of the suspension point up to and including the fourth order corrections. The solutions of these equations, where an external force enters the equations multiplicatively, are compared with the solution considered earlier, for the behavior of a spring pendulum subject to an external force, which enters the appropriate equations additively. It turns out that in lower orders in small parameter, the two solutions coincide for the case where the external force and viscous damping force are equally small, but they differ when the damping is much smaller than the external force.     

Effective pair potentials in fluids in the presence of three-body forces. II

Earlier calculations are extended to the second order in density thus providing the non-additive contributions to the fourth virial coefficient in the presence of a weak three-body force given by the triple-dipole dispersion potential of Axilrod and Teller. We compare the Percus-Yevick approximations of Rushbrooke and Silbert and of Rowlinson at the level of the fourth virial coefficient and find that the former is more accurate. We also compare our calculations of the effective pair potential of liquid argon with the results of Mikolaj and Pings obtained from X-ray diffraction measurements.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

非线性振动中周期与振幅和能量关系的级数表达式

针对一般的一维非线性振动问题,讨论了周期与振幅和能量关系的级数解法,给出了直到4阶的表达式和相关结果,并用单摆和中心力场的严格解进行了验证.     

Solution to the Ghost Problem in Fourth Order Derivative Theories

We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does indeed contain the negative norm energy eigenstates which are characteristic of higher derivative theories, in the limit in which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with either negative energy or negative norm. We confirm these results by quantizing the Pais–Uhlenbeck theory via path integration and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other.     

Complete fourth-order calculation of correlation energy for closed-shell molecules by diagrammatic RSPT

Starting from the diagrammatic version of Wigner's (2n+1) rule the formulae for the correlation energy of closed-shell molecules are derived. This approach allows to formulate in the very compact way the correlation energy through the fourth order of perturbation theory, a repeating evaluation of the same intermediate terms is completely removed.Some part of this work has been elaborated at the Department of Chemistry, Carnegie-Mellon University, and one of us (V. K.) is very obliged to Prof. J. A. Pople and Dr. R. Krishnan for many stimulating discussions concerning the complete fourth-order evaluation of the correlation energy.     

去耦覆盖层降噪性能评价指标的理论探讨

去耦覆盖层是降低水下结构声辐射的一个重要措施。为了给工程上去耦覆盖层降噪性能评价指标的选择提供理论参考,建立了点激励力作用下敷设去耦覆盖层的四端简支撑矩形板水下振动和声辐射理论模型,定义了可能表征去耦覆盖层降噪性能的五项评价指标。研究结果表明:只有振动传递损失相对独立于基板的长度、宽度和点激励力位置,而且能较好地描述去耦覆盖层隔离基板振动向水层传递的性能;而湿面均方振速插入损失较振动传递损失则能更好地反映辐射声功率插入损失,尤其在低频。作为评价指标,振动传递损失和湿面均方振速插入损失分别有各自的优点和缺点。      

Repulsive Casimir–Polder forces from cosmic strings

We investigate the Casimir–Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir–Polder force is derived in the general case of anisotropic polarizability. In dependence on the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir–Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation. We show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely with the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays with the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir–Polder potential on the orientation of the polarizability tensor principal axes also leads to a moment of force acting on the particle.     

Double perturbation calculations of spin-spin coupling constants using localized orbitals

The Fermi contact contribution to N.M.R. spin-spin coupling constants has been calculated to the fourth order by a double perturbation development starting from a fully localized determinant, according to the assumptions of the PCILO-CNDO method. The use of diagrammatic techniques greatly simplifies the evaluation. There is a cancellation of certain types of diagram. The coupling constant between bonded atoms appears in the second order through a contribution which only depends on the appropriate bond orbital. The next orders involve the other bonds and correlation effects. For nonbonded atoms, the first contribution appears in the fourth order and results from direct delocalization through space, involving only the bonds on the two atoms.

An analytical and numerical comparison with previous calculations is performed for H-H and C-H coupling constants on small organic molecules. The relative importance of the various processes is discussed for the J _HH vicinal coupling constants of ethylene.     

Higher order tapered beam finite elements for vibration analysis

In this paper, explicit for mass and stiffness matrices of two higher order tapered beam elements for vibration analysis are presented. One possesses three degrees of freedom per node and the other four degrees of freedom per node. The four degrees of freedom of the latter element are the displacement, slope, curvature and gradient of curvature. Thus, this element adequately represents all the physical situations involved in any combination of displacement, rotation, bending moment and shearing force. The explicit element mass and stiffness matrices eliminate the loss of computer time and round-off-errors associated with extensive matrix operations which are necessary in the numerical evaluation of these expressions. Comparisons with existing results in the literature concerning tapered cantilever beam structures with or without an end mass and its rotary inertia are made. The higher order tapered beam elements presented here are superior to the lower order one in that they offer more realistic representations of the curvature and loading history of the beam element. Furthermore, in general the eigenvalues obtained by employing the higher order elements converge more rapidly to the exact solution than those obtained by using lower order one.     

Wire coating by withdrawal from a bath of fourth order fluid

This Letter looks an analysis for withdrawal of cylinder. The flow depends upon the wire velocity. The fluid considered is a fourth order fluid. The problem is modeled using cylindrical coordinates for velocity and pressure distributions. The solution of the governing equation is obtained using homotopy analysis method (HAM). The variations of the velocity, volume flow rate, radius of coated wire, shear stress and force on the total wire are presented graphically and discussed for emerging non-Newtonian parameter.     

Vibration-rotation theory and isotopic substitution in nonlinear triatomic molecules

In the interpretation of high-resolution data it is helpful to be able to relate the experimentally determined molecular constants, such as rotational constants, centrifugal distortion constants, and vibration-rotation interaction constants of a given molecule to those of its isotopically substituted variants. Results concerning the symmetric nonlinear triatomic molecule (XYX) have been given through the second order of approximation by previous workers. In this paper, extensions of the work to the fourth order of approximation and to the nonsymmetric nonlinear triatomic molecule (XYZ) are considered. These extensions are found to increase the algebraic complexity of the problem considerably, and results can generally be given in implicit form only. The approach used is one that emphasizes the isotopic invariants of the problem, i.e., those expressions which remain unchanged when applied to the various isotopic modifications of a given molecule under the assumption that the molecular force field and the molecular geometry remain unchanged under isotopic substitution.     

Source Theory Treatment of the Casimir Effect: A Review

The general method to calculate Casimir forces using Source Theory is reviewed. Included are such issues as point splitting, high frequency cut-offs and the inclusion of temperature. The details of calculations for planar, spherical and cylindrical geometries are presented. Finally, assuming spin zero photons, the Casimir force between perfectly conducting spheres is calculated. The large distance behavior is found to be proportional to the inverse distance to the fourth power, unlike the spin one behavior of to the eighth power.     

Hybrid High Low Frequency Separation (HLFS) method: Harmonic force fields of methyl halides

A parameter formulation of Wilson's High Low Frequency Separation (HLFS) Method is given in conjunction with isotopic frequencies in a third order vibrational problem. A new approximation scheme called the Hybrid HLFS Method is proposed which is superior to the pure HLFS method in the sense that it enables the evaluation of all twelve force constants. This, however, furnishes two sets of force fields out of which one is seen to be in better agreement with that obtained using various additional data.One of the authors (AJV) is grateful to the CSIR, New Delhi, for the award of a Junior Research Fellowship.     

Dynamic analysis of double-row self-aligning ball bearings due to applied loads,internal clearance,surface waviness and number of balls

In this paper, a three degrees of freedom (dof) model was established for a double-row self-aligning ball bearing (SABB) system, and was applied to study the dynamic behavior of the system during starting process and constant speed rotating process. A mathematical model was developed concerning stiffness and damping characteristics of the bearing, as well as three-dimensional applied load, rotor centrifugal force, etc. Balls and races were all considered as nonlinear springs, and the contact force between ball and race was calculated based on classic Hertzian elastic contact deformation theory and deformation compatibility theory. The changes of each ball?s contact force and loaded angle of each row were taken into account. In order to solve the nonlinear dynamical equilibrium equations of the system, these equations were rewritten as differential equations and the fourth order Runge–Kutta method was used to solve the equations iteratively. In order to verify accuracy of the dynamical model and correctness of the numerical solution method, a kind of SABB-BRF30 was chosen for case studies. The effects of several important governing parameters, such as radial and axial applied loads, normal internal, inner and outer races waviness, and number of balls were investigated. These parametric studies led to a complete characterization of the shaft-bearing system vibration transmission. The research provided a theoretical reference for new type bearing design, shaft-bearing system kinetic analysis, optimal design, etc.     

光栅压缩器中色散的矩阵计算

在ABCD矩阵基础上,通过引入角度色散项获得了可以方便描述色散系统的3×3阶矩阵.采用这种矩阵方程方便、准确地计算了标准光栅对压缩器中的二阶、三阶以及四阶色散,得到的结果与由常规积分法获得的结果相同.     

Weak turbulent Kolmogorov spectrum for surface gravity waves

We study the long-time evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in moderately small wave numbers. We numerically implemented the primitive Euler equations for the potential flow of an ideal fluid with free surface written in Hamiltonian canonical variables, using the expansion of the Hamiltonian in powers of nonlinearity of terms up to fourth order. We show that because of nonlinear interaction processes a stationary Fourier spectrum of a surface elevation close to <|eta(k)|(2)> approximately k(-7/2) is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.