Theoretical and numerical analysis of electron motion in a three-dimensional undulator field

The results of numerical calculations of electron trajectories in the three-dimensional ideal magnetic field of an undulator are given. These trajectories can be regarded as exact results in our case. It is shown that, in a series of cases, results of the calculation of trajectories using approximate analytical formulas significantly differ from those obtained using numerical methods. The obtained numerical results show that the influence of the undulator on the dynamics of the electron beam is very complicated and cannot be reduced only to the focusing properties of the undulator magnetic field or wiggler.     

Quantitative three-dimensional holographic interferometry for flow field analysis

Holographic interferometry offers the potential for quantitative, wholefield analysis of three-dimensional compressible flows. The technique is non-intrusive, does not require the introduction of seeding particles, and records the entire flow information within the pulse duration of a Q-switched ruby laser (˜30ns). At present, however, holographic interferometry is mainly used qualitatively due to the practical restrictions of data recording, acquisition and processing.To address the potential of holographic flow analysis a prototype multi-channel interferometer has been designed and preliminary wind tunnel results have been obtained. The proposed configuration uses specular illumination which, unlike comparable diffuse systems, does not suffer from fringe localisation and speckle noise. Beam collimation and steering through the flow field is achieved in a single operation by the use of holographic optical elements (HOEs). The resulting design is compact, light efficient, has aberration compensation, and the recorded data are conducive to both tomographic analysis and direct comparison to computational fluid dynamics (CFD) predictions.Holograms have been recorded of simple two-dimensional and axisymmetric compressible flows, to compare the accuracy of holographic density measurements with data from conventional pressure sensors and CFD codes. Data extraction from the holograms, and the elimination of rigid body motion, was achieved using digital Fourier transform fringe analysis. The introduction of phase errors by image processing has been investigated by analysing simulated fringe patterns generated from a combination of experimental amplitude information and computer generated phase data.     

气泡在超声场中绕圈运动的高速摄影及其图像分析

借助高速摄影和图像分析技术对首次发现的附壁气泡的绕圈现象进行了实验研究,重点研究游移气泡的运动轨迹、附壁气泡的布阵过程、气泡的来源以及气泡的振动细节.研究发现游移绕圈气泡的运动轨迹呈现出不稳定、不规则、不光滑的特点.阵列气泡源于游移气泡,而游移气泡变成阵列气泡的方式主要是通过合并增大体积,从而减小所受的Bjerknes...     

激光支持等离子体流场的2维动态数值模拟

 采用高温气体（等离子体）电离度的一种近似计算方法,以及具有五阶精度的广义Godunov差分格式-加权本质无振荡格式,给出了高温气体状态方程的简便描述,并考虑激光与等离子体的相互作用和能量耦合模拟了强激光与固体靶相互作用时激光支持靶面等离子体流场的动态物理过程,并同理论模型结果进行了比较。结果表明：不考虑2维膨胀效应的理论模型结果比2维数值计算结果偏大,但两者只有接近一倍的差距,并无数量级的差别。考虑了膨胀效应的2维数值计算结果是可信的。     

Acoustical analysis of pipes with flow using invariant field functions

An analysis of the pressure field within a pipe is carried out using simplified formulations of pipe acoustics. The fluid contained within the pipe is considered non-viscous, while the flow velocity of the fluid is assumed to be smaller than the speed of sound.The analysis is limited to frequencies which are well below the pipe ring frequency, i.e., at which only simple waves can propagate. Expressions and diagrams are given which specify the applicable frequency range in each particular case.Three invariant functions of the internal pressure field are evaluated. These functions allow for the determination of the following quantities: base pressure spectrum (spatial mean r.m.s. value), lower and upper bounds of the pressure spectrum for the entire pipe, pressure spectrum at an arbitrary position, speed of sound in the contained fluid and fluid flow velocity.Experimental identification of these quantities requires simultaneous measurement at three points. A few measurements carried out on one air-filled and one water-filled pipe have demonstrated the potential of pipe invariant functions for acoustical analysis.     

重力场,运动积分与可积性

讨论了重力场中质点系统的运动积分及其中的Runge-Lenz型运动积分与分离变量方法中分离系数之间的关系,也讨论了系统的可积性以及它与运动积分之间的关系等问题.     

二维及三维流场的光学测量方法

对于复杂的非定常流动 ,流场的测量往往要求无干扰、非接触 ,并且能够瞬时记录流场的二维甚至三维信息。对近年来流场测量领域发展快速、应用广泛的几种光学测量方法 ,如 PIV技术及其由此发展而来的 DPIV和 HPV技术 ,做一些介绍和比较。     

Exact quantum mechanical description of the motion of spin-1/2 particles and of spin motion in a uniform magnetic field

The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum mechanical equation for the motion of the particles in a strong magnetic field is derived. Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998)     

Particle motion in a toroidal field

Particle motion on a toroidal surface is considered. The classically permissible ranges of particle motion are analyzed and trajectories determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 57–60, April, 1990.In conclusion the author thanks V. V. Rumyantsev and A. M. Bykov for evaluating the study.     

Electromagnetic field of a rotating magnetic dipole and electric-charge motion in this field

In this paper, we present the results of a study of the electromagnetic field in the near and intermediate zones of a magnetic dipole rotating in free space. Examples of solving the relativistic equations of the charged-particle motion in this field are given. The energy, which can be acquired by the particles during acceleration, is estimated.     

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1$\delta \rho /\rho \le 1$. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ?1$\delta \rho /\rho ?1$. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.     

Multi-bubble motion behavior of electric field based on phase field model

By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation,electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble.The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong(E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method(LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.     

Brownian motion in a rotating flow

The Langevin equations for a particle of an arbitrary shape and the correlation functions for the fluctuating forces, torques, or force-torque acting on the particle in a rotating flow are derived from the semimicroscopic level of coarse graining by using fluctuating hydrodynamics. In order to obtain the solution of the Navier-Stokes Langevin equation valid over the entire flow region, use is made of the method of matched asymptotic expansions in ( _f a²/v)^1/2 1. The cases of slow and rapid rotation are analyzed. It is shown that the fluctuation-dissipation theorems hold up to the order of ( _f a²/v)^1/2 in both slow and rapid rotation, and that the diffusivity tensor depends on the angular velocity of the fluid and becomes anisotropic.     

Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory

We study a single particle diffusing on a triangular lattice and interacting with a heat bath, using boundary conformal field theory (CFT) and exact integrability techniques. We derive a correspondence between the phase diagram of this problem and that recently obtained for the 2-dimensional 3-state Potts model with a boundary. Exact results are obtained on phases with intermediate mobilities. These correspond to nontrivial boundary states in a conformal field theory with 2 free bosons which we explicitly construct for the first time. These conformally invariant boundary conditions are not simply products of Dirichlet and Neumann ones and unlike those trivial boundary conditions, are not invariant under a Heisenberg algebra.     

Kinetic energy flow analysis of high-energy heavy-ion collisions: The classical equation of motion approach

The results of a kinetic energy flow analysis carried out on the basis of the classical equation of motion model are presented for the reactions Ne + U, Ca + Ca and Nb + Nb at 400 MeV/nucleon. The model satisfactorily reproduces the global values of the events and the side-splash effect observed in the experiment. The flow angle turned out to be sensitive to the effective NN potential model which parametrizes the compression dynamics.     

Probe particle motion in a Schwarzschild field

The motion of probe particles and light beams in a specified Schwarzschild metric is considered for the full range of radial coordinate r: 0 r . The singularity at r=r^g is elininated by shifting the integration contour to the complex plane [4, 5, 6]. There is then possible a class of finite motions with particle passage through the center. Light rays emitted by the probe particle during such motion are constructed, and difficulties with the causality principle occurring in both the T- and R-regions are evaluated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 44–50, October, 1977.     

Multi-bubble motion behavior of uniform magnetic field based on phase field model

Aiming at the interaction and coalescence of bubbles in gas–liquid two-phase flow, a multi-field coupling model was established to simulate deformation and dynamics of multi-bubble in gas–liquid two-phase flow by coupling magnetic field, phase field, continuity equation, and momentum equation. Using the phase field method to capture the interface of two phases, the geometric deformation and dynamics of a pair of coaxial vertical rising bubbles under the applied uniform magnetic field in the vertical direction were investigated. The correctness of results is verified by mass conservation method and the comparison of the existing results. The results show that the applied uniform magnetic field can effectively shorten the distance between the leading bubble and the trailing bubble, the time of bubbles coalescence, and increase the velocity of bubbles coalescence. Within a certain range, as the intensity of the applied uniform magnetic field increases, the velocity of bubbles coalescence is proportional to the intensity of the magnetic field, and the time of bubbles coalescence is inversely proportional to the intensity of the magnetic field.