Contribution from cosmological scalar perturbations to the angular velocity spectrum of extragalactic sources

The possibility of the influence of adiabatic scalar perturbations on the angular velocity spectrum of extragalactic sources is considered. The multipole expansion coefficients of the angular velocity field in terms of vector spherical harmonics are calculated. We show that there is no contribution from adiabatic perturbations to the angular spectrum for a spatially flat Universe at the dusty stage, while there is a contribution only to the electric multiple coefficients at the stage of ??-term domination. The cases of long-wavelength and short-wavelength perturbations are considered separately. The relationship between the multipole angular velocity spectrum and the primordial scalar perturbation spectrum is discussed.     

Collective generation of higher optical harmonics by dipole molecules

An analysis is made of the collective resonant generation of higher harmonics by a spatially extended system of two-level molecules possessing an intrinsic electron dipole moment in the excited state. Frequency and angular dependences of the scattered radiation are studied. It is shown that for moderately small numbers of harmonics their intensity depends comparatively weakly on the number (plateau) and the intensity of the emitted harmonics then falls sharply as the number increases. The angular distribution of the harmonics is strongly anisotropic. It is also shown that collective effects significantly change the time profile of the generated harmonic pulse. In addition, as a result of cooperative effects harmonics of a certain parity are suppressed in the low-frequency part of the radiation spectrum.     

Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source

The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.     

Characterizing the rotation of non symmetric objects in an optical tweezer

We present an optical tweezer based study of the rotation of microscopic objects with shape asymmetry. Thermal fluctuations and rotations are simultaneously monitored through laser back scattering. The rotation causes a modulation in intensity of the back scattered light incident on a quadrant photo detector. The resulting power spectrum is a modified Lorentzian with additional peaks located at the fundamental rotational frequency of the object and at the integer harmonics. The manifestation of these peaks reveals that the rotations are periodic but with varying angular velocity. We model our experimental results to illustrate the hydrodynamic interplay between the rotor and the surrounding medium that results in the time dependence of the angular speed of the former. Further, we demonstrate the use of video microscopy for characterization of low reflectivity rotors, such as biological cells. We propose through these studies that an analysis of these rotations can provide insights into the role of hydrodynamics at micron levels.     

The change in the sound wave energy due to the scattering by a medium rotating with acceleration

Scattering amplitudes and intensities of partial azimuthal harmonics and the total intensity of the scattered field are calculated for the case of transmission of longitudinal acoustic waves through a liquid rotating with acceleration. It is shown that the intensity of transmitted waves depends on the angular acceleration and does not depend on the angular velocity of the vortex rotation.     

Angular spectrum representation of the electromagnetic multipole fields, and their reflection at a perfect conductor

Angular spectrum representations are derived for electric and magnetic multipole fields of arbitrary order. The result involves generalized spherical harmonics and generalized vector spherical harmonics, and the representations are in the form of integrals over the k_∥-plane. The representations are especially useful for the study of reflection and transmission of multipole radiation by a plane interface. As an example, we have considered the reflection at a perfect conductor. The reflected field of a multipole field could be expressed in the form of an angular spectrum with a very simple relation to the angular spectrum of the source field. The radiation pattern of a multipole near the perfect conductor is obtained with the method of stationary phase. We also introduce a method for determining the mirror image of the source of an arbitrary multipole.     

Pseudo field modulation in EPR spectroscopy

This paper develops methodology for computer simulation of the effect on an experimental EPR spectrum that would occur if an additional field modulation were applied followed by eventual phase sensitive detection at the modulation frequency or at one its harmonics. The algorithm, which is called pseudomodulation, transforms the digitized spectrum and also filters the noise. If a second harmonic spectrum is desired in order to make subtle changes in curvature more apparent, it is shown that it is always preferable to obtain an experimental second harmonic spectrum. The signals are identical, but because of the filtering properties of the pseudomodulation algorithm, the noise is lower. Pseudomodulation should be applied to simulated spectra prior to fitting a model to data in order more precisely to simulate the experimental signal. It is argued that such fits ought to involve not only first harmonics but also higher harmonics, since the various harmonics are sensitive in different ways to input parameters in the spin Hamiltonian. Application of pseudomodulation to the EPR spectrum of the blue copper-protein azurin is described.     

具有速度谱分辨能力的角色散FP干涉测量技术

 发展了可用于速度谱诊断的角色散Fabry-Perot干涉测量技术,使不同频移探测激光形成的干涉条纹在空间分离,从而可对单一或混合运动源引起的多普勒频移成分进行检测,并给出物体速度谱分布。利用Fabry-Perot干涉测量技术,开展了激光驱动铝箔飞片实验。随着驱动激光能量的变化,观察到了铝箔飞片的不同速度谱分布,包括没有速度空间分散的速度谱、分裂成几片并以不同速度飞行的离散速度谱、碎片云或射流状态下的连续速度谱分布,此外还观测到了冲击下铝箔/玻璃界面分离引起的条纹分裂现象。     

Characterisation of parallel misalignment in rotating machines by means of the modulated signal of incremental encoders

There are many defects in rotating machines which, when analysed by means of the Fourier spectrum of transversal vibration, show several harmonics of the rotational speed, more specifically the first and the second, although higher harmonics may also be present. Misalignments, looseness, the breakage of fastening screws, broken mechanical seals, are just some of the problems. Nevertheless, the effects of some of these defects differ when the angular vibration is measured using an incremental rotating encoder, which offers an additional aid for diagnosing the problem.     

Even-harmonic generation due to beyond-Born-Oppenheimer dynamics

We calculate the harmonic spectrum generated by a model HD molecule in a strong laser pulse. The unequal nuclear masses lead to the emission of even harmonics, i.e., photon frequencies which are even multiples of the laser frequency. The effect does not occur within the Born-Oppenheimer approximation. In the high-frequency region, the even harmonics are almost of the same order of magnitude as the odd ones.     

Vibration analysis of a rotating system due to the effect of ball bearing waviness

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modelled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian contact theory is applied to calculate the elastic deflection and non-linear contact force, while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the non-linear governing equations of the rotor, which are solved by using the Runge–Kutta–Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e., the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing, but also between those of two or more ball bearings constrained by the rotor.     

On the non-synchronous rotation of binary systems

During the evolution of the binary system,many physical processes occur,which can influence the orbital angular velocity and the spin angular velocities of the two components,and influence the non-synchronous or synchronous rotation of the system.These processes include the transfer of masses and angular momentums between the component stars,the loss of mass and angular momentum via stellar winds,and the deformation of the structure of component stars.A study of these processes indicates that they are closely related to the combined effects of tide and rotation.This means,to study the synchronous or non-synchronous rotation of binary systems,one has to consider the contributions of different physical processes simultaneously,instead of the tidal effect alone.A way to know whether the rotation of a binary system is synchronous or non-synchronous is to calculate the orbital angular velocity and the spin angular velocities of the component stars.If all of these angular velocities are equal,the rotation of the system is synchronous.If not,the rotation of the system is non-synchronous.For this aim,a series of equations are developed to calculate the orbital and spin angular velocities.The evolutionary calculation of a binary system with masses of 10M⊙+6M⊙shows that the transfer of masses and angular momentums between the two components,and the deformation of the components structure in the semidetached or in the contact phase can change the rotation of the system from synchronous into non-synchronous rotation.     

Angular and frequency dependence of light diffracted by surface acoustic waves

The intensity of light diffracted by surface acoustic waves is described by its spectrum, which contains all the harmonics of the acoustic frequency. A formulation is given, mainly for the first harmonic angular dependence, taking into account most of the experimental parameters. Calculated results are compared with experimental data. Optimum conditions for detection are given for a wide range of frequencies.     

Measurement of the stress sensitivity of magnetostriction in electrical steels under distorted waveform conditions

Electrical steel laminations used in the construction of transformer cores are subject to stresses introduced during their construction and analysis of the effect of this on the magnetostriction of the lamination has been investigated previously. It has been shown that higher harmonics of magnetostriction are of greater importance than the fundamental when considering transformer noise. Whereas previous studies have concentrated on the magnetostriction harmonics generated by sinusoidal magnetization, this investigation seeks to understand the relationship between harmonics present in the magnetization waveform and those in the magnetostriction waveform. A measurement system has been designed based on a similar principle to one previously described. In this case, a single Labview Virtual Instrument (VI) is used for the control of the applied stress, controlled magnetization and measurement of magnetostriction together with other magnetic parameters such as specific total loss, specific apparent power, permeability, coercivity and remanence. An adaptive digital feedback algorithm is utilized for control of arbitrary waveform which may be constructed from discrete harmonics or read from an input waveform. As well as measuring peak magnetostriction the software utilizes an FFT to calculate the harmonics of magnetostriction at each stress point. The effect of harmonics introduced into the magnetization waveform on the magnetostriction harmonics will be shown at various applied stresses. A harmonic, Harm_B in the flux density waveform is shown to have the effect of producing a dominant harmonic in the magnetostriction given by (Harm_B+1)/2.     

真空磁绝缘传输线损失电子模拟

真空磁绝缘传输线建立磁绝缘状态的初始阶段,损失电子轰击阳极,发生轫致辐射。针对自限制流同轴圆筒模型,通过粒子模拟获得了损失前沿在能量传输方向的推进速度、电子到达阳极时的能谱和角分布情况,在此基础上采用蒙特卡罗方法模拟得到了轫致辐射所产生的X射线能谱。数值计算结果表明:电磁波损失前沿在能量传输方向的推进速度小于光速;损失前沿电子密度稳定。在自限制流磁绝缘传输线中,损失电子处在较宽的能量范围内,其电子偏移角度较小。建立了对应于同轴圆筒真空磁绝缘传输线的电子/光子输运模型,获得了损失电子轰击阳极产生的X射线能谱。     

Attosecond angle-resolved photoelectron spectroscopy

We report experiments on the characterization of a train of attosecond pulses obtained by high-harmonic generation, using mixed-color (XUV+IR) atomic two-photon ionization and electron detection on a velocity map imaging detector. We demonstrate that the relative phase of the harmonics is encoded both in the photoelectron yield and the angular distribution as a function of XUV-IR time delay, thus making the technique suitable for the detection of single attosecond pulses. The timing of the attosecond pulse with respect to the field oscillation of the driving laser critically depends on the target gas used to generate the harmonics.     

Three-mode optomechanical system for angular velocity detection

We propose a scheme for measuring the angular velocity of absolute rotation using a three-mode optomechanical system in which one mode of the two-dimensional(2 D) mechanical resonator is coupled to an optical cavity. When the total system rotates, the Coriolis force acting on the 2 D mechanical resonator due to the absolute rotation will affect the mechanical motion and thus change the phase of the output field from the cavity. The angular velocity of the absolute rotation can be estimated by monitoring the spectrum of the output field from the cavity via homodyne measurement. The minimum measurable angular velocity, which is determined by the noise spectrum, is calculated. The working range of the gyroscope for measuring angular velocity is discussed.     

Energy spectra of two interacting electrons in a quantum ring: rotating Wigner molecule

We study two interacting electrons confined within a quantum ring. For a narrow-width ring the radial motion is the fastest one and adiabatically decoupled from the angular motions. The role of the Coulomb interaction and the confining potential is to build a rotating Wigner molecule with the relative angular motion in form of harmonic oscillations. We calculate the electronic states and discuss the thermodynamical properties of two-electron quantum rings. It is shown that a strong correlation exists between the quantum numbers of rotation and oscillation of the Wigner molecule.     

Fourier transform profilometry based on defocusing

Sinusoidal fringe patterns are popularly used in conventional Fourier transform profilometry. There are numerous harmonics in the Fourier spectrum, so as to avoid spectrum overlapping; the maximum range of measurement is limited. The present paper studies FTP based on properly defocusing a binary square wave. There are only odd harmonics in the Fourier spectrum of a binary square wave, and the maximum range of measurement is expanded 1.5 times. Defocusing has a low-pass filtering effect and higher-order odd harmonics are suppressed. Therefore, the fundamental spectrum is easy to extract. The proposed method overcomes the filtering problem of conventional FTP. Measurement experiments show that the proposed method has a good measurement result and the measurement accuracy is improved.