On the Massive Wave Equation on Slowly Rotating Kerr-AdS Spacetimes

The massive wave equation ${\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0}The massive wave equation \square_gy- a\fracL3y = 0{\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0} is studied on a fixed Kerr-anti de Sitter background (M,g_M,a,L){\left(\mathcal{M},g_{M,a,\Lambda}\right)}. We first prove that in the Schwarzschild case (a = 0), ψ remains uniformly bounded on the black hole exterior provided that a < \frac94{\alpha < \frac{9}{4}}, i.e. the Breitenlohner-Freedman bound holds. Our proof is based on vectorfield multipliers and commutators: The total flux of the usual energy current arising from the timelike Killing vector field T (which fails to be non-negative pointwise) is shown to be non-negative with the help of a Hardy inequality after integration over a spacelike slice. In addition to T, we construct a vectorfield whose energy identity captures the redshift producing good estimates close to the horizon. The argument is finally generalized to slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing vectorfield T = ∂ _t with K=?_t + l?_f{K=\partial_t + \lambda \partial_\phi} for an appropriate λ ~ a, which is also Killing and–in contrast to the asymptotically flat case–everywhere causal on the black hole exterior. The separability properties of the wave equation on Kerr-AdS are not used. As a consequence, the theorem also applies to spacetimes sufficiently close to the Kerr-AdS spacetime, as long as they admit a causal Killing field K which is null on the horizon.     

Petrov Types of Slowly Rotating Fluid Balls

Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.     

Revolving superposed standing waves in a spinning Timoshenko Beam

The aim of the present paper is to study the revolving superposed standing waves in a spinning Timoshenko beam based on the results obtained by the first author with others in two recently published papers. The concept of superposed standing wave as normal mode and the knowledge about the helical feature of propagating wave will be used to depict a physical picture about the vibration of the spinning beam, from describing the basic constituent waves to showing the orthogonality property of the revolving normal modes. The wave-mechanics approach will be invoked throughout the study with an algebraic procedure used to reveal the two eigenvalues of the gyroscopic-coupling phase factor. A table for tabulating the phases of the centroidal positions of the beam in time and space due to the passing of a wave is invented, through which one could show the helical structure of the wave without ambiguity. From the present result, two types of revolving standing waves are identified, each manifesting as a gyroscopic precession in association with a frequency-splitting phenomenon, in either the clockwise or the anticlockwise direction. It is shown that the revolving waves should be represented by wavefunctions in a form of four-component column matrix vectors.     

On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow

In this paper, the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction. The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however, do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain. This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy. The analysis is further generalized to polyharmonic equations.     

Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity

Following the general formalism presented by Rezzolla, Ahmedov and Miller, ⁽¹⁾ we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller ⁽¹⁾ mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature.     

束测误差对阻尼系统的影响

讨论了束测误差对阻尼系统工作状况的影响．结果表明，束测误差将减低阻尼效果，增大为达到一定的阻尼速度所需阻尼系统功率，并导致闭轨畸变．给出了计算有关效应的公式．     

Smaller Output Beam Divergence in the Slowly Opened Q-Switch Operation

The mechanism of the slowly opened Q-switch operation was investigated thoroughly. Maximum energy extraction from the resonator could be optimized, and the smallest output beam divergence could be achieved. In this article, we present a detailed analysis that has numerically verified the mode-selection mechanism in the slowly opened Q-switch operation, and the degree of the smaller output laser beam divergence that has been achieved. The mechanism of the slowly opened Q-switch operation is the inherent advantage of the passive saturable absorber in this operation. We can use the maximum energy extraction and the smallest output beam divergence results of the slowly opened Q-switch operation to design and optimize various passive saturable absorbers: plastic dye sheets, LiF:F₂⁻ color center crystals, Cr4⁺: YAG crystals, RG1000 color glass filters, and the single crystal semiconductor saturable absorber wafers that are in developed in our microchip laser systems.     

基于旋转液体特性实验的激光双次反射法测重力加速度

旋转液体特性实验是大学物理实验中典型的综合实验项目,本文利用激光束在旋转液体表面的双次反射时的特性,确定了测量重力加速度的新方法。通过对比实验发现,本设计减少了原有单次激光反射测量重力加速度时的物理量数目,并有效提高了测量结果的精确度。     

基于CT算法的旋转多丝靶二维束剖面测量

介绍了一种用于低能电子束的基于CT算法的二维束剖面测量方法及其初步实验结果.该束剖面测量方法首先利用多丝靶进行旋转获得不同角度下的一维束剖面信息,然后采用CT算法对这些信息进行处理重建出二维束剖面.本文对该束剖面测量方法的原理进行了详细分析,并通过实验初步验证了该束剖面测量方法的可行性.     

Microsecond Microwave Radiation Bursts from a Relativistic Electron Beam Rotating in a Plasma

Coherent curvature radiation from an intense relativistic electron beam rotating in a plasma yielded in the past [1] only very short bursts of microwave radiation. Here we report on extension of the microwave-burst duration to the full width of the beam pulse for two different electron beams: a) 1 MV, 50 kA, 110 ns b) 0.6 MW, 15 kA, 1 , ?s. We show that the short bursts in the past resulted from sudden changes in the plasma density caused by ionization of neutrals, present in the drift tube, by the beam itself. This density change caused a shift away from the resonance condition necessary for coherent radiation. The extension of the pulsewidth was achieved by introducing a plasma gun which did not emit many neutrals. The radiation is mostly in the Ka band (? ? 1 cm) and the power level was ~1 MW.     

Nonlinear Dynamical Stability of Newtonian Rotating and Non-rotating White Dwarfs and Rotating Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady- state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating white dwarf and high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. Also, we prove nonlinear dynamical stability of non-rotating white dwarfs with general perturbation without any symmetry restrictions. This paper is a continuation of our earlier work ([26]).     

Probing Beam Collective Effects in the Damping Ring of the VEPP-5 Injection Complex

Physics of Particles and Nuclei Letters - The in-depth understanding of beam collective effects in the damping ring (DR) of the VEPP-5 injection complex at BINP is essential for optimizing its...     

Stability of Novel Time-Sharing Dual Optical Tweezers Using a Rotating Tilt Glass Plate

A novel realization of time-sharing optical tweezers （TSOT） is demonstrated using a tilt glass plate. Objects are trapped in the time-sharing dual traps; each of them acts like a single beam gradient trap with an effective stiffness. The effective stiffness of TSOT is experimentally measured through analysis of dynamical images. In comparison, it is numerically calculated by adopting the Monte Carlo technique. Both simulation and experimental results agree well with each other and show a good linear relationship between the effective stiffness and trap switching frequency in the range from 5 Hz to 70 Hz.     

Slowly, Rotating Non-Stationary, Fluid Solutions of Einstein's Equations and Their Match to Kerr Empty Space-Time

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and theinduced rotation of local inertial frame is exhibited.     

Effects of Hall Currents and Gyroviscosity on the Stability of a Finitely Conducting Rotating Viscous Plasma of Variable Density

The Rayleigh-Taylor instability of an incompressible viscous, finitely conducting, rotating plasma of variable density has been investigated in the presence of the effects of Hall currents and finite ion Larmor radius. The proper solution for a semi-infinité plasma layer having exponentially varying density in the vertical direction has been obtained by making use of a variational principle which is shown to characterize the problem. The dispersion relation has been solved numerically. It is found that gyroviscosity, viscosity and coriolis forces have stabilizing influence whereas Hall currents and resistivity have a destabilizing influence.     

Assessment of Timoshenko Beam Models for Vibrational Behavior of Single-Walled Carbon Nanotubes Using Molecular Dynamics

In this paper, we study the flexural vibration behavior of single-walled carbon nanotubes (SWCNTs) for the assessment of Timoshenko beam models. Extensive molecular dynamics (MD) simulations based on second-generation reactive empirical bond-order (REBO) potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-to-diameter ratios, boundary conditions, chiral angles and initial strain. The effectiveness of the local and nonlocal Timoshenko beam models in the vibration analysis is assessed using the vibration frequencies of MD simulations as the benchmark. It is shown herein that the Timoshenko beam models with properly chosen parameters are applicable for the vibration analysis of SWCNTs. The simulation results show that the fundamental frequencies are independent of the chiral angles, but the chirality has an appreciable effect on higher vibration frequencies. The SWCNTs is very sensitive to the initial strain even if the strain is extremely small.     

Stability of a Rotating Compressible Stratified Plasma in the Presence of Hall Currents and Magnetic Resistivity

The dynamic instability in a horizontal layer of a rotaing compressible plasma of variable density has been investigated to examine the influence of the simultaneous presence of the effects of Hall currents and finite magnetic resistivity. The linearized stability analysis has been carried out through the normal mode technique. By making use of the existence of a variational principle which is shown to characterize the problem, proper solutions have been obtained for a semiinfinite plasma in which there is an exponential density gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that both the resistivity and the Hall currents have a destabilizing influence as the growth rate of the unstable disturbances increases with increasing values of the parameters characterizing these effects. On the other hand, the Coriolis forces are found to have a stabilizing influence for in this case the growth rate decreases with increasing rotation.