Continuity equation constraint and the form of electric-type transition operator

The decomposition of electromagnetic vector potentialA=B+S is studied, which enables one to include the constraint dictated by continuity equation into the electric-type transition operator. A class of decompositions is obtained and discussed. All previously known decompositions belong to this class. The alternative approach used recently by Friar and Fallieros is also considered.Author thanks dr. M. Gmitro, dr. J. Kvasil and dr. . Burdík for valuable discussions.     

Deuteron electromagnetic form factors in transverse plane with a phenomenological Lagrangian approach

A phenomenological Lagrangian approach is employed to study the electromagnetic properties of deuteron. The deuteron is regarded as a loosely bound state of a proton and a neutron. The deuteron electromagnetic form factors are expressed in light-front representation in the transverse plane. The transverse charge density of the deuteron is discussed.     

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the non-perturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20 -25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q ² ~ 1...2 GeV².     

Analysis of the quadrupole mass filter with quadrupole excitation by the envelope equation method

The method of the envelope equation has been developed to describe the stability of the motion of ions in a quadrupole mass filter in the presence of periodic excitations of the feeding voltage. Dynamic equations that describe the variations in the envelope of ion vibrations in the vicinity of the vertex of the first common stability region have been obtained and reduced to the form of the Mathieu equations. The splitting of the stability diagram of the motion of ions into stability islands due to excitation has been described. The results of the approximate theory have been confirmed by an exact analysis of the stability diagram for rational values of the relative excitation frequency. The boundaries of the applicability domain for the developed theory limited by first-order resonances have been determined.     

The average transverse distance between partons as measured by nucleon form factors

The values of $\text{d}\text{F}{}_1\text{(q}{}^2\text{)}\text{d}\text{q}{}^2$ at q²=0 for the neutron and the proton provide a measure of the average transverse separations squared, 〈$\text{y}{}^2$〉, between a u or d quark and the rest of the partons in a nucleon. Using the measured values of the form factors (together with parton x-distributions), we find that 〈$\text{y}{}^2\text{= 17.4}\text{GeV}{}^{\mathrm{?2}}$ for u quarks and 16.4 GeV^?2 for d quarks in a proton. We speculate that the small difference between u and d quarks is caused by “quark pairing” and discuss other possible experimental signatures of quark pairing.     

Trajectory length constraint and the Klein-Gordon equation

It is shown that the relativistic constraint of the length of possible trajectories in the method of integrals over the trajectories results in the Klein-Gordon equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 63–65, December, 1984.     

The Dirac equation in exterior form

Using the correspondence between the Clifford and exterior algebras we write the Dirac equation in terms of differential forms. The covariances of the theory are then examined. We show in detail the correspondence with usual matrix methods.     

Upwind schemes for the wave equation in second-order form

We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d’Alembert’s exact solution. We construct conservative finite difference approximations, although finite volume approximations are also possible. High-order accuracy is obtained using a space-time procedure which requires only two discrete time levels. The advantages of our approach include efficiency in both memory and speed together with accuracy and robustness. The stability and accuracy of the approximations in one and two space dimensions are studied through normal-mode analysis. The form of the dissipation and dispersion introduced by the schemes is elucidated from the modified equations. Upwind schemes are implemented and verified in one dimension for approximations up to sixth-order accuracy, and in two dimensions for approximations up to fourth-order accuracy. Numerical computations demonstrate the attractive properties of the approach for solutions with varying degrees of smoothness.     

On the standard form of the Bloch equation

The requirement is often made in non-equilibrium statistical mechanics that a transport equation should be derived as that which governs the subdynamics relative to a (small) part of a (large) conservative dynamical system close to equilibrium. We show that such a requirement on the Markovian relaxation of a 1/2-spin imposes that this process be described by a Bloch equation of a very specific form, which we call standard. We show that this reduced dynamics is quasi-free if, and only if, the relaxation time is maximally anisotropic.Research supported in part by NSF grant MCS 76-07286     

Field equation for the transverse motion of a two-layered plate

An approximate theory is developed for the transverse motion of a two-layered plate. The two layers are assumed to be elastic, isotropic, homogeneous and welded to each other. The theory is similar to the Timoshenko-Mindlin model for a single-layered plate in which corrections are included for rotary inertia and shear deformation. A single equation of transverse motion is derived that predicts the first four antisymmetric modes and is applicable to practical problems. Phase velocities of these modes are numerically analyzed for a plate consisting of a copper layer and a steel layer.     

Spin-dependent potentials in the linearized collective Schrödinger equation for nuclear quadrupole vibrations

The linearized collective Schrödinger equation for nuclear quadrupole surface vibrations incorporates a new spin degree of freedom with a spin value of 3/2. We use this equation to describe the low energy spectrum of certain even-odd Ir nuclei which have a spin 3/2 in their ground state. For that purpose we explicitly introduce collective spin-dependent potentials which simulate the interaction of the valence nucleon with the core. The linearized Schrödinger equation is transformed into an effective Schrödinger equation with collective spin-dependent potentials. Already collective spin-orbit couplings of SO(3) and SO(5) type are sufficient to reproduce the lowest excited states of even-odd Ir nuclei.     

全光纤加速度地震检波器敏感元件横向振动限制的研究

简要介绍了全光纤加速度地震检波器的工作原理和敏感元件的结构特征 ,详细描述了质量块横向振动限制膜片的设计理论。实验结果表明 :采用双膜片限制质量块横向振动的检波器的频谱较未加限制膜片的频谱有明显改善     

Rational solutions of the Korteweg-de Vries equation in wronskian form

The rational solutions of the Korteweg-de Vries equation are obtained as limits of the soliton solutions in wronskian form and these solutions are verified by direct substitution using a novel determinantal identity.     

Octet-baryon form factors in the diquark model

We present an alternative parameterization of the quark-diquark model of baryons which particularly takes care of the most recent proton electric form-factor data from the E136 experiment at SLAC. In addition to electromagnetic form factors of the nucleon, for which good agreement with data is achieved, we discuss the weak axial vector form factor of the nucleon as well as electromagnetic form factors of and hyperons. Technical advance in calculating the pertinent analytic expressions within perturbative quantum chromodynamics is gained by formulating the wave function of the quark-diquark system in a covariant way. Finally, we also comment on the influence of Sudakov corrections within the scope of the diquark model.Sponsored in part by the Bundesministerium für Forschung und Technologie, Germany, under contract number 06 Wu 737     

On the general form of the Benjamin-Bona-Mahony equation in fluid mechanics

In the study of many problems of mechanical and physical sciences, various versions of the Benjamin-Bona-Mahony (BBM) equation or the regularized-long-wave equation have been proposed. In this paper, we obtain the solitary-wave solutions to the general form of the BBM equation, which fully cover the variety of the BBM solitary waves previously reported. This work has been supported by the China Talent Fund, by the Cheung Kong Scholars Programme of China, by the Cheung-Kong-Scholar Research Concerted Fund of Beijing University of Aeronautics and Astronautics, and by the Doctoral Education Fund in Basic Sciences of Beijing University of Aeronautics and Astronautics.