Experiments on the solution of the helmholtz equation using the finite element method and a variational approach in the case of domains of complicated boundary shape

Domains of ‘exotic’ boundary shape are of interest in several technological applications—acoustic and electromagnetic waveguides, solid propellant rocket cross-sections, printed circuit boards, etc.The present paper describes some experiments performed to determine the eigenvalues of a vibrating, ideal membrane.It is shown that the finite element method yields results which are in very good agreement with values determined by means of an analytical approach in the case of a membrane of a cardioidal shape.     

A boundary perturbation method for circularly periodic plates with a core

Fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically. A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem. The method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions. Clamped, simply supported, and free circular cores are considered. Approximate analytical formulations of the fundamental frequency for such plates with core are obtained.     

Circular Polarized Soliton Propagating at a Small Angle to Strong Bias Magnetic Field in a Ferromagnetic System

A variant of the derivative nonlinear Schrödinger equation for the low frequency circular polarized wave, propagating at a small angle to the bias magnetic field in a ferromagnetic system, is derived by the reductive perturbation expansion method. Bright and dark solitons are obtained.     

Vibration of a membrane having a circular outer boundary and an eccentric circular inner boundary

In this paper, a method of solving vibration problems for a membrane having a circular outer boundary and an eccentric circular inner boundary is presented. The frequency equation for the membrane is given, and the dependence of the natural frequency on the eccentricity is obtained. It is shown that the result obtained from this analysis in the limit of the eccentricity being zero coincides with that of a membrane with a concentric circular inner boundary.     

用频域法实现圆环形目标物的计数

研究了用频域法实现圆环形目标物计数的方法。对空域中含有圆环形目标物的二值图像，经傅里叶变换后在频域内进行滤波，再经傅里叶反变换后取一阈值进行处理，则对应于圆环形目标物即变为一个实心体，然后对实心体进行计数即可实现对圆环形目标物的计数。对该方法进行了数学描述，并分别用模拟图像和实际图像进行了实验。结果表明，该方法消除噪声的效果好，对部分封闭圆的检测同样有效，且可用于目标物有粘连的情况。该方法对圆环形目标物的尺寸相差不大的情况更为有效。     

Vibration and stability of a circular cylindrical shell subjected to a torque

An analysis is presented for the vibration and stability of a circular cylindrical shell subjected to a torque. The displacements of a circular shell are written in a series of beam eigenfunctions satisfying the boundary conditions. The kinetic and strain energies of the shell are evaluated analytically, and the frequency eauation of the shell is derived by the Ritz method. The method is applied to circular cylindrical shells under two types of boundary conditions at the edges; the natural frequencies and the divergence torques are calculated numerically, and the effects of the thickness ratio, length ratio and edge conditions on the vibration and stability are studied.     

Multiplication of the drive signal frequency in a relativistic microwave amplifier with a rod slow-wave structure

A theory is developed for the one-dimensional nonlinear multimode simulation of a Cerenkov maser of special configuration (antenna-amplifier [1, 2]) where a tubular relativistic electron beam propagates along a circular waveguide with a dielectric rod. The operating mode is the fundamental azimuthally asymmetric HE ₁₁ mode. Harmonics at the input signal frequency can be amplified because they fall into the amplification bands for higher modes. At certain parameters, the output power at the second or third harmonic may considerably exceed that of the amplified signal at the fundamental frequency. The powers of output harmonics can be efficiently controlled by varying the point of electron beam extraction from the interaction region, as well as by varying the input frequency or by switching the polarization of the input signal from linear to circular.     

A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser

A novel circular polarized optical heterodyne interferometer using a Zeeman laser to measure optical rotation both in nonscattered and scattered chiral medium is proposed. A pair of correlated orthogonal circular polarized light waves of different temporal frequency propagating in the chiral medium at different speed is studied. This results in phase retardation between circular polarized light waves of which the phase difference is proportional to the optical rotation angle of a linear polarized light in a chiral medium. In the mean time, two orthogonal circular polarized light waves can be treated as a circular polarized photon pair that is able to reduce the scattering effect in a scattered chiral medium. Then the optical rotation angle can be measured in the scattering medium. In addition, a common-path configuration with respect to circular polarized light waves immune the background noise. This further improves the sensitivity on optical rotation measurement based on phase difference detection.     

Mode Matching Analysis for a New Millimeter Wave Omni-Directional Antenna Consisting of Circular Rod Corrugations Gloved with a Dielectric Shell

A new millimeter-wave omnidirectional antenna consisting of circular rod corrugations gloved with a dielectric shell is investigated. As an eigenvalue problem, the antenna is analyzed with the rigorous mode matching method. The radiation characteristics of the antenna are calculated in the Ka-band frequency range. A comparison of the leaky characteristics is made between the antennas with and without dielectric shell. It is found that the circular dielectric shell layer greatly affects the leaky characteristics of the antenna and the leakage constant increases considerably. In such a way, the length of the antenna can be reduced tremendously with higher radiation efficiency. This fact indicates that the proposed leaky wave antenna is of essentially practical significance for the case where the limitation in size and weight of system is strictly required. The effectiveness and reliability of the present analysis are verified by the calculated and experimental results given in the literature.     

Vibration of a viscoelastic plate having a circular outer boundary and an eccentric circular inner boundary for various edge conditions

In this paper, vibration problems of a circular viscoelastic plate having an eccentric circular inner edge are investigated. The frequency equations in complex forms for various edge conditions are obtained. Numerical calculations are carried out for both elastic and viscoelastic plates, and the non-dimensional natural frequencies and the logarithmic decrements are given for a number of cases.     

Vibration and stability of a circular plate of unidirectionally varying thickness

An analysis is presented for the vibration and stability of an elastically restrained circular plate of unidirectionally varying thickness subjected to an in-plane force. For this purpose, the transverse deflection of a circular plate of variable thickness is written in a series of the deflection functions of a uniform circular plate without the action of a force. The dynamical energies of the plate are evaluated analytically, and the frequency equation of the plate is derived by the Ritz method. The analysis is applied to circular plates of unidirectionally tapered or stepped thickness; the natural frequencies and the divergence loads are calculated numerically, and the effects of the varying thickness and edge conditions on the vibration and stability are studied.     

Ring-resonator-based frequency-domain optical activity measurements of a chiral liquid

Chiral liquids rotate the plane of polarization of linearly polarized light and are therefore optically active. Here we show that optical rotation can be observed in the frequency domain. A chiral liquid introduced in a fiber-loop ring resonator that supports left and right circularly polarized modes gives rise to relative frequency shifts that are a direct measure of the liquid's circular birefringence and hence of its optical activity. The effect is in principle not diminished if the circumference of the ring is reduced. The technique is similarly applicable to refractive index and linear birefringence measurements.     

Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002     

Large amplitude vibrations of circular plates carrying a concentrated mass

A finite element analysis for the large amplitude vibrations of circular plates carrying a concentrated mass is presented in this note. The variation of the fundamental frequency with the central amplitude is obtained for simply supported and clamped plates for various positions and various magnitudes of the concentrated mass.     

Calculation of the Dynamic Stark Effect in the Many-Level Approximation

A new method for calculating the dynamic Stark effect in a circular polarized electric field of arbitrary strength and frequency is proposed. The basic equations of the method are given. By way of illustration the results of calculation of the shift and splitting of energy levels of a He atom in a circular polarized electric field are considered.     

Free vibration of continuous polar orthotropic annular and circular plates

The free vibration of a polar orthotropic annular plate supported on concentric circles is analyzed by the Ritz method with use of Lagrange multipliers. A trial function for the deflection of the plate is expressed in terms of simple power series, and a frequency equation for the plate is derived by the condition for minimizing the total potential energy with the constraint equations included. In the numerical examples it is also shown that the method can directly yield quite accurate frequency values for a solid circular plate. Natural frequencies of annular and circular plates are calculated for wide ranges of the support location and orthotropic parameters.     

Weibel instability in plasma produced by a superintense femtosecond laser pulse

The Weibel instability increment is analytically derived for plasma produced at the barrier-suppression ionization of atoms and atomic ions by a superintense femtosecond laser pulse. The cases of linear and circular polarization are considered. Relativistic effects are discussed. It is found that the instability increment is larger for the circular polarization than for the linear polarization. This increment can attain the plasma frequency. Barrier-suppression ionization decreases the increment compared with the case of tunneling ionization. Relativistic effects also decrease the value of the increment. Estimates of the produced maximum quasistatic magnetic field are given.     

Specific features of the spectral properties of a cholesteric liquid crystal with a resonance defective nanocomposite layer

This paper reports on studying the spectral properties of a cholesteric liquid crystal with a defective layer of a nanocomposite consisting of metallic nanoballs dispersed in a transparent matrix and characterized by an effective resonance dielectric permittivity. The transmission, reflection, and absorption spectra of waves of both circular polarizations have been calculated, and the spectral splitting of the defective mode when its frequency coincides with the resonance frequency of the nanocomposite has been studied. An essential dependence of the splitting on the nanoball concentration in the defect has been established. It has been shown that, depending on the position of the resonance frequency with respect to the boundaries of the cholesteric band gap, an additional passband appears in the transmission spectrum, which corresponds to waves of the diffracting circular polarization, or an additional band gap for waves of both circular polarizations, which are substantially modified with variations of both the incidence angle of light and the cholesteric helix pitch.     

Linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide

In this work we investigate the linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide. The proposed device consists of a circular central core and many circular sectoral cores at the periphery, while the whole structure can be considered as a nonlinear multicore composite optical coupler. Hybrid guided modes in a circular sectoral dielectric waveguide are derived using circular harmonic expansion for the electromagnetic fields and the Point Matching Method (PMM) for the application of boundary conditions. Several cases are investigated varying some of the parameters of the geometry and the optical frequency in order to produce dispersion diagrams. In advance, the electric and magnetic field distributions for the fundamental guided modes are produced, while linear and nonlinear coupling coefficients as well as the sectoral waveguide mode effective area are derived.     

Resonant interaction of light with a banded domain structure

The distinctive features of the interaction of light with a banded domain structure produced by linear magnetooptical effects are discussed. A dispersion law for characteristic circular waves is found which contains regions of forbidden spatial frequencies in which the interaction of light with the structure is of a resonance nature. Dependences of the reflection and transmission coefficients and angle of rotation of the polarization plane on frequency and crystal size are obtained for these regions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 84–88, March, 1982.