Spectral characteristics of an open cavity with a metal-dielectric inhomogeneity

We propose a new method for studying the spectral characteristics of open cavities containing circular metal-dielectric cylinders. As a result, an algorithm for calculating the natural-frequency spectrum of such a class of electrodynamic structures is developed. A numerical comparative analysis of the spectral properties is carried out for a two-mirror, confocal, open cavity with a circular metal-dielectric cylinder and a similar cavity with the corresponding radial-layered dielectric cylinder. Acad. A. Ya Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences, Kharkov, Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 10, pp. 1336–1347, October 1998.     

On Multiple Scattering of Radiation by an Infinite Grating of Dielectric Circular Cylinders at Oblique Incidence

A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of the “well-known scattering coefficients of an isolated dielectric cylinder at oblique incidence” and “Schl?milch series”. In addition, a generalized sum-integral grating equation is acquired for the multiple scattered amplitude of a cylinder at oblique incidence in the grating in terms of the scattering coefficients of the insulating dielectric circular cylinder at oblique incidence.      

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken φ⁴ theories in 1+1 dimensions.     

Wave-number-based assessment of the doubly asymptotic approximation. I. Frequency domain wet surface impedance

The doubly asymptotic approximation (DAA) is a canonical relationship for the interaction between surface normal velocity and pressure. Its validity for a slender hemicapped cylinder is examined by formulating a frequency domain version of DAA using the global basis functions employed in the wave-number-based formulation of the surface variational principle [K. Wu and J. H. Ginsberg, ASME J. Vib. Acoust. 120, 392-400 (1998)]. The wet surface impedance matrix, which relates the spectral representation of normal velocity to a corresponding representation of pressure, is obtained according to a second-order version of DAA and according to the surface variational principle. Comparison and interpretation of the results reveals that DAA fails to account for highlights associated with transition from supersonic to subsonic surface waves as the surface wavelength decreases with frequency held constant.     

Representing multiple discrimination cues in a computational model of the bottlenose dolphin auditory system

A computational model of the dolphin auditory system was developed to describe how multiple discrimination cues may be represented and employed during echolocation discrimination tasks. The model consisted of a bank of gammatone filters followed by half-wave rectification and low pass filtering. The output of the model resembles a spectrogram; however, the model reflects temporal and spectral resolving properties of the dolphin auditory system. Model outputs were organized to represent discrimination cues related to spectral, temporal and intensity information. Two empirical experiments, a phase discrimination experiment [Johnson et al., Animal Sonar Processes and Performance (Plenum, New York, 1988)] and a cylinder wall thickness discrimination tasks [Au and Pawolski, J. Comp. Physiol. A 170, 41-47 (1992)] were then simulated. Model performance was compared to dolphin performance. Although multiple discrimination cues were potentially available to the dolphin, simulation results suggest temporal information was used in the former experiment and spectral information in the latter. This model's representation of sound provides a more accurate approximation to what the dolphin may be hearing compared to conventional spectrograms, time-amplitude, or spectral representations.     

基于稀疏表示模型和自回归模型的高光谱分类

针对高光谱分类中对光谱信息和空间信息利用不足的问题,提出了一种基于稀疏表示模型和自回归模型相结合的分类算法。该算法利用稀疏表示模型和自回归模型,设计联合字典:在光谱维上,利用稀疏表示模型将高光谱的每个光谱向量表示为字典中训练样本的稀疏线性组合;在空间维上,利用自回归模型对每个光谱向量的8邻域进行约束。针对不同样本分别构造一个字典,在减少计算量的同时减小重构误差,最后在最小重构误差和邻域相关性的约束下求解稀疏表示问题,以最小重构误差为准则实现高光谱数据的分类。仿真结果表明,该方法能够有效地提高高光谱数据的分类精度。     

Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular shell elements with five degrees of freedom per node. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of an open curved thin structure in terms of the cross spectral density of random pressure fields. The cross spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis and Païdoussis (J. Sound Vib. 25 (1972) 1–27) using cylindrical elements and a hybrid finite element method.     

Quantum extension of the Jarzynski relation: analogy with stochastic dephasing

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary time scale and the corresponding equilibrium free energy difference is generalized to quantum systems. Using the adiabatic representation, we show that this relation holds for isolated systems as well as for systems coupled to a bath described by a master equation. A close formal analogy is established between the present "classical trajectory" picture over populations of adiabatic states and phase fluctuations (dephasing) of a quantum coherence in spectral line shapes, described by the stochastic Liouville equation.     

The analytic properties of the box diagram amplitude. II.

A spectral representation is obtained for the box diagram amplitude for both real and complex values of the kinematical invariants s and t. By starting with a particular normal threshold spectral representation obtained in a previous paper [1] and analytically continuing in the external masses and then in s and t, the various forms of the spectral representation are obtained for all possible mass configurations involving externally stable particles. In particular, a spectral representation is established for all s in the upper half-complex-plane and for almost all real t.     

Acoustic scattering by an elastic elliptic cylinder in water: numerical results and experiments

The acoustic scattering from an elastic elliptic cylinder immersed in water and excited by a normally incident plane wave is considered in this paper. The purpose is to determine, theoretically and experimentally, the pressure scattered by this cylinder. A model based on the theory of elasticity is described briefly. It consists in carrying out expansions in Fourier series of the expressions relating to the conditions of continuity (displacements and constraints) at the surface of cylinder. These expressions form a system of equations. The resolution of this system enables us to obtain the scattering coefficient, then the pressure scattered by the cylinder. The numerical results obtained from this model are compared with experimental results obtained by means of an experimental short-pulse method presented in the literature. An good agreement between the results is noted.     

Circumferential normal modes in an empty elastic cylinder

The so-called circumferential normal modes propagating in an empty elastic cylinder are considered. A dispersion equation for the wave numbers of these waves, an equation for the critical frequencies, and expressions for the eigenfunctions of such a waveguide are derived. Solutions to these equations are obtained by numerical methods for different values of the parameter d representing the relative thickness of the cylinder. An analysis of the solutions is performed, and the main properties of the dispersion curves are described, including those for the low-frequency waves of the new type, which correspond to the branches in the form of open loops. Individual normal modes are identified on the basis of the calculations and subsequent analysis of eigenfunctions.     

A generalization of the Kac-Moody algebras with a parameter on an algebraic curve and perturbations of solitons

The Lie-algebraic approach for the dynamic systems associated with a generalization of the Kac-Moody algebras on Riemann surfaces is developed. A technique of solving the inverse scattering problem of operators with spectral parameters on Riemann surfaces is presented. Some equations associated with generalized Kac-Moody algebras are presented. The connection between their hamiltonian structure and deformed Lax representation is discussed as well as its applications to some special perturbations of integrable systems.     

A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

柱输运管中扩散超声速辐射波的能流

采用于敏关于直角坐标系下两平板间粒子传输的辐射能流计算的理论模型，给出了柱输运管中与径向位置相关的谱辐射能流的计算公式.研究结果表明，由于管壁的自由程远小于传输介质的自由程，从而导致辐射能流中几何因子随径向变化，并认为这是最近关于扩散超声速辐射波实验中测得的辐射波强度随径向呈拱形分布的又一个重要原因.另外，还给出对横截面平均的谱辐射能流、以及当辐射与物质处于局部热动平衡时的辐射能流的计算公式，并将其中的几何因子与人们传统的通过几何自由程获得的几何因子进行了比较.为方便数值模拟，还给出了辐射能流公式中含有多 关键词： 柱管中扩散超声速辐射波传输 辐射能流 几何因子     

Damped waves in a cylinder shadow

The sound field in the region of a deep shadow behind an impedance cylinder is analyzed for the case of plane wave diffraction by the cylinder surface. The main part of the field is represented by a cylindrical wave that has a complex index determined from the boundary conditions and decays with the angular coordinate. An expression for the amplitude of this wave is determined by extracting it from the total field formed in the shadow region. It is demonstrated that this wave approximates more closely the total field behind the cylinder, as compared to the least damped wave in the field representation obtained on the basis of the Watson transform. A way to improve the sound barriers is indicated.     

Measurement of an aeroacoustic dipole using a linear microphone array

It is shown that the standard beamformer technique is inadequate for both the source location and the measurement of a simple dipole and that this is due to the assumption of monopole propagation in the calculation of the phase weights used to steer the focus of the array. A numerical simulation is used to illustrate the problem and to develop a correction to the signal processing algorithm to account for the dipole propagation characteristic. This is then applied to array measurements for an aeroacoustic dipole produced by a cylinder in a cross flow. The resulting source map and the beamformed spectrum are shown to give a true representation of the source energy and frequency content. A secondary effect of this correction is that the array becomes insensitive to other source types so that in addition to acting as a spatial filter, the array can perform as a source filter. This work also demonstrates how an array measurement can be misinterpreted if applied without consideration of the source mechanism.     

基于稀疏表示的谱线自动提取方法

谱线提取在光谱分析中起着非常重要的作用,它对后续的光谱分类和参数测量有着直接的影响。文章提出了一种基于稀疏表示的谱线自动提取方法。首先,用基于稀疏表示的小波去噪方法去除噪声,该方法通过对光谱信号对应的小波系数进行稀疏化处理来达到去噪的目的,其优点是在处理小波系数时虽然将其作为整体进行考虑,但依然能保持小波系数的局部特性不变,所以在去噪的同时很好地保持了特征谱线的信息。其次,利用小波变换与样条拟合相结合的方法拟合出较为满意的伪连续谱,该方法在拟合过程中,先将强谱线扣除掉,从而使得拟合结果非常接近真实的连续谱。最后,通过对归一化后的谱线光谱设置自适应局部阈值来提取特征谱线。实验结果表明该方法切实有效。     

Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations

The paper deals with the problem of reconstruction of microstructural information from known effective complex permittivity of a composite material. A numerical method for recovering geometric information from measurements of frequency dependent effective complex permittivity is developed based on Stieltjes analytic representation of the effective permittivity tensor of a two-component mixture. We derive the Stieltjes representation for the effective permittivity of the medium using the eigenfunction expansion of the solution of a boundary-value problem. The spectral function in this representation contains all information about the microgeometry of the mixture. A discrete approximation of the spectral measure is derived from a rational (Padé) approximation followed by its partial fractions decomposition. The approach is based on the least squares minimization with regularization constraints provided by the spectral properties of the operator. The method is applied to calculation of volume fractions of the components in a mixture of two materials in a Bruggeman effective medium analytic model which has a continuous spectral density and to analytical models of two-phase composites with coated cylindrical and ellipsoidal inclusions. The numerical results of reconstruction of spectral measure for a mixture of silver and silicon dioxide and a composite of magnesium and magnesium fluoride show good agreement between theoretical and predicted values. The approach is applicable to geological materials, biocomposites, porous media, etc.     

Fiber Grating Based Optical Recirculating Filter with an Optimized Response

A novel optical recirculating filter for RF applications is described, which exploits a specially designed fiber grating with a ramped spectral profile to enable optimization of the filter response. The design overcomes the limitations imposed by loss in conventional fiber recirculating filters. Additionally, a tunable free spectral range is demonstrated by using the device in a grating array. Both theoretical and experimental results are presented and discussed.     

Fiber Grating Based Optical Recirculating Filter with an Optimized Response

A novel optical recirculating filter for RF applications is described, which exploits a specially designed fiber grating with a ramped spectral profile to enable optimization of the filter response. The design overcomes the limitations imposed by loss in conventional fiber recirculating filters. Additionally, a tunable free spectral range is demonstrated by using the device in a grating array. Both theoretical and experimental results are presented and discussed.