Fluctuations in diffuse field-field correlations and the emergence of the Green's function in open systems

Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.     

Interface scattering as a source for diffuse interference in cuprous oxide on copper

Interference in the diffuse reflectance (IDR) from thermally oxidized copper is considered. It is demonstrated that the diffuse reflectance scales with the value of the time-averaged square of electric field, 〈E²〉 at the oxide/metal interface. The appearance of IDR is therefore a sensitive probe of interface roughness created by the oxidation.     

基于声压场描述的扩散声场多自由度互易原理研究

应用于复杂结构中频声振分析的扩散场多自由度互易原理采用位移变量描述系统,实质为弹性波场互易原理,应用于声波场时会造成模型自由度数不必要的增加。建立基于声压描述的扩散声场受挡模型,利用声辐射模态描述扩散声场中结构的表面受挡声压;据此提出基于声压描述的扩散声场多自由度互易原理,发现扩散声场中结构表面受挡声压的互谱矩阵与该结构在自由空间中振动辐射声波的声阻矩阵成正比。该互易原理与传统的单自由度互易原理表达形式相似,但适用于任意自由度结构。该互易原理可用于扩散声场中复杂结构的表面受挡声压的自谱及相关分析,仿真研究表明当边界元网格尺寸小于声波波长的1/6(线性单元)或1/3(二次单元)时,数值解与理论解完全吻合。      

On the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies

A recent paper has shown that under certain conditions the cross-spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of (i) the energy of the wave field, and (ii) the direct field dynamic stiffness matrix of the boundary. This "diffuse field reciprocity relation" was derived using wave mechanics, and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing. This issue is addressed here by deriving an extended version of the reciprocity relation using modal methods, and the conditions required for the extended version to reduce to the existing relation are delineated. It is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem, and that this anomaly is resolved by using the present extended version of the relation. A supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix.     

影响光谱辐亮度标定因素的分析

在利用漫反射板标定光谱辐亮度的实验装置中,标准灯完全可以近似为点光源。通过对进入光谱仪的辐射通量的数值积分,可以对应求出仪器的实测光谱辐亮度的计算公式。计算表明,实测光谱辐亮度并不等于漫反射板表面的光谱辐亮度,而有一个随标定条件变化的微小差值。通过计算,对光谱仪与漫反射板的距离、光谱仪入射挟缝的光轴与漫反射板法线的夹角以及标准灯与漫反射板的距离等影响光谱仪标定的因素进行分析,得到了最佳的标定条件。讨论了理想标定情况、光谱仪视场趋于一点的极限情况和采用实际的双向反射分布函数已知的漫反射板标定时,实测光谱辐亮度的计算情况。     

An effect of curvature of rotating diffuse objects on the dynamics of speckles produced in the diffraction field

The time correlation function is analyzed of the speckel intensity fluctuation produced in the Fresnel diffraction field from a rotating diffuse object under illumination of a Gaussian laser beam. The dependence of the curvature radius of the rotating diffuse object on the time correlation length of the speckle intensity fluctuation is especially explored by taking into account the size of the detecting aperture. The theoretical results are confirmed experimentally for detecting apertures with various sizes. It is shown that a detecting aperture with an appropriate size is required. It becomes useful for determining the radius of curvature of the rotating diffuse object from measurements of the time correlation length of the speckle intensity fluctuation.     

Spatial-temporal correlation of a diffuse sound field

The spatial correlation function of the sound in a diffuse field is a quantity widely used in many reverbrant room acoustic applications. Although results for the spatial and temporal correlation for pure-tone and band-limited diffuse fields have already been developed, these have not been generalized for other signal types. This work presents a generalized derivation of the diffuse field spatial-temporal correlation which can be used for stationary random signals with given power spectral density. It is shown that the spatial-temporal correlation depends entirely on the temporal correlation of the signal exiting the diffuse field, or alternatively on its power spectral density. A simulation using the plane wave model is presented for tonal and broadband diffuse sound fields.     

Experimental Study of the Creation of a Fire‐rod I: Temporal Development of the Electron Energy Distribution Function

Positive voltage steps are applied to a planar electrode (collector) immersed in a magnetized discharge plasma column with its surface perpendicular to the magnetic field lines. If the voltage step and the neutral gas pressure are high enough additional ionization occurs in front of the collector and a fire‐rod is created. Time resolved measurements of the plasma response are performed by a one‐sided plane Langmuir probe using standard boxcar technique. The temporal development of the electron energy distribution function after the application of a positive voltage step to the collector is measured by a one‐sided plane Langmuir probe. In a magnetized plasma the electron energy distribution function is proportional to the first derivative of a plane Langmuir probe characteristics. It is found that immediately (∼1 μs) after the application of a positive voltage step to the collector a short lifetime electron population is created. This electron population disappears in approximately 2 μs. It is related to the anomalously large initial electron current collected by the collector “current overshoot”. When the initial current overshoot to the collector is terminated, a high potential (anode) plasma starts to form in front of the collector if the voltage step and the pressure are high enough. The formation of the anode plasma electron population is followed experimentally.     

Diffuse wavefields in cylindrical coordinates

A diffuse wavefield is normally defined in terms of plane waves--to quote one textbook definition "plane waves are incident from all directions with equal probability and random phase." In some vibro-acoustic problems the response of a two-dimensional component such as a plate is more conveniently expressed in terms of cylindrical waves, and it is not immediately obvious what properties should be assigned to the cylindrical waves to constitute a diffuse field. It is shown here that a diffuse wavefield can be modeled as a summation of statistically independent cylindrical waves, apart from the fact that each outgoing wave of a particular order is fully correlated to an incoming wave of the same order. A simple relationship is derived between the energy flow P in each wave component and the energy density e of the wavefield: P = ec(g)/k, where c(g) is the group velocity and k is the wavenumber. This result is shown to hold true for both bending waves and in-plane waves (longitudinal and shear) in a plate. The work has application to the calculation of coupling loss factors in statistical energy analysis.     

Influence of density stratification on stability of a two-layer binary-fluid system with a diffuse interface

A system of two layers separated by a diffuse interface which is created due to a phase separation in a binary liquid in the gravity field, is considered. The influence of the density stratification and the gravity on the stabilization of the solution is studied. The stability of two-layer base solutions with respect to long-wave disturbances in the framework of the linear stability analysis is investigated in the case of small density ratio and large Galileo number. It is found that the action of gravity can stabilize the equilibrium state.     

Sensitive Response of the Quantum Entropies to Jaynes-Cummings Model in Presence of a Second Harmonic Generation

The behavior of a modified Jaynes-Cummings Hamiltonian model (two-level atom in interaction with an electromagnetic field) in the presence of degenerate parametric amplification is introduced. We have examined two different cases, one when the field frequency ω is not equal to the splitting photon frequency ε for which the off-resonance case is considered. In the second case we have taken each frequencies to be equal (ω = ε) and considered the system to be at exact resonance. The wave function for both cases is obtained and the result used to calculate the density matrix from which we manage to discuss the field entropy as well as the phase entropy. It is shown that the system is sensitive to any change in the splitting photon frequency ε.     

Splitting Scheme Integration of the Two-and-One-Half-Dimensional Vlasov Equation

A numerical splitting scheme technique is applied to the integration of the Vlasov equation in two-space and three velocity dimensions. Calculations are performed for a cold, stationary ion, mobile electron plasma in the presence of a constant external magnetic field. Results for Landau damping and the two-stream instability are presented in both one and two velocity dimensions. The Landau damping results show a plateau structure in the electron velocity distribution function in both the parallel and perpendicular directions formed as a result of the damping of a high initial electric field propagating at 45° to the parallel velocity axis. The two-stream velocity distribution function shows pitch angle scattering and velocity diffusion for an electron beam initially propagating at 45° to the magnetic field direction through a low-temperature equal density background. The two-stream distribution function evolves to a stable quasi-isotropic plateau structure similar to that found in auroral sounding rocket data.     

Stark效应对J-C模型腔场谱的影响

研究了计及Stark效应的J-C模型的腔场谱,通过求解本征方程导出了腔场谱的计算公式,给出了腔场处于光子数态时的数值结果,讨论了Stark效应和初始场强对标准J-C模型腔场谱的影响.发现在初始场为真空场时,两个Rabi峰的高度相等,随着Stark位移参数的增大,两峰都向低频方向移动,且频差逐渐增大;在初始场较强的情况下,Stark移动参数增大时会导致双峰的对称性消失,通过测量两峰的相对高度也可确定Stark位移参数的大小;在Stark效应较强初始场递增的情况下两峰仍向左移,但峰间距越来越小;在弱场情况下,Stark效应使两峰呈现左高右低或左低右高的峰结构.总之,改变Stark位移参数β1、β2的大小以及初始场强的强弱,可得到不同的谱线结构.     

On the possibility of using acoustic reverberation for remote sensing of ocean dynamics

The two-point correlation function of diffuse noise fields produced by distributed random sound sources carries useful information on the medium of sound propagation. Such information can be used for performing passive acoustic tomography of the ocean. In a number of cases that are important for practice, the noise field in the ocean is predominated by contributions of individual point sources. Here, a theoretical study is presented on the possibility of determining the sound speed and current velocity in the water column by the correlation processing of reverberation signals measured by two vertical receiving arrays. In other words, we study the possibility of replacing the diffuse noise produced by a great number of delta-correlated sources by waves generated by a localized source and scattered at the rough surface and bottom of the ocean for sensing the medium. The correlation function of scattered waves is calculated by using the method of small perturbations. It is shown that the correlation processing of the scattered waves offers an opportunity of measuring the acoustic nonreciprocity and reconstructing the field of sound speed in the fluid, without using any acoustiLc transceivers.     

Random field of internal stresses from point defects in a crystal

The variance and correlation function are calculated for the internal stress field created by point defects situated independently at random lattice points in a crystal. For equal concentration dilatations, the amplitude of the internal stresses in a fcc lattice is several times the amplitude in an fcc lattice. It is shown that the stress field is practically uncorrelated and its probability density function is represented by an Edgeworth asymptotic series. An asymptotic representation of the stress distribution is proposed in the form of a superposition of a discrete stress spectrum and a normally distributed background.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 43–47, August, 1982.The author is deeply indebted to M. A. Shtremel' for steadfast interest in the work and a useful discussion of the results.     

Ground-state density of the pauli operator in the large field limit

The ground-state density of the Pauli operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in the large field limit, the naturally rescaled ground-state density function is bounded from above by the megnetic field, and under some additional conditions, the limit density function is equal to the magnetic field. A restatement of this result yields an estimate on the density of complex orthogonal polynomials with respect to a fairly general weight function. We also prove a special case of the paramagnetic inequality.Part of this research was conducted during the U.S.-Sweden Workshop on Spectral Methods sponsored by the NSF under grant INT-9217529. Partial support by NSF grant PHY90-19433 A02 is also acknowledged.     

A new concept for the origin of the Schaefer-Bergmann diffraction patterns

The origin of the Schaefer-Bergmann diffraction patterns is interpreted by the concept of a diffuse acoustic field occuring in high Q-factor crystals like the sound field in large low-loss auditoriums. It is shown that the inhomogeneous illumination of the patterns obtained by crystals with high symmetry or with weak anisotropy is due to interference phenomena in the diffuse field.     

Light exiting from real photonic band gap crystals is diffuse and strongly directional

Any photonic crystal is in practice periodic with some inevitable fabricational imperfections. We have measured angle-resolved transmission of photons that are multiply scattered by this disorder in strongly photonic crystals. Peculiar non-Lambertian distributions occur as a function of frequency: due to internal diffraction, wide angular ranges of strongly reduced diffuse transmission coincide with photonic stop bands, while enhancements occur for directions outside stop gaps. We quantitatively explain the experiment with a model incorporating diffusion and band structure on equal footing. We predict that in the event of a photonic band gap, diffuse light at frequencies near band gap edges can exit only along isolated directions. Angle-resolved diffuse transmission appears to be the photonic equivalent of angle-resolved photoelectron spectroscopy.     

On aperture averaging of speckle patterns

Statistical parameters of the power of a nonuniform (speckled) light field measured by a photodetector with a finite receiving aperture were investigated. Such a field was created by passing coherent laser radiation through a multimode optical fiber and then scanned across the aperture. It was demonstrated that the mean square deviation of the received power is defined by a parameter equal to the ratio of the aperture diameter to the characteristic dimension of the spatial variations of the light field. If this ratio is more than 2, the above deviation does not exceed values permissible for devices using spatially coherent light (e.g., for free-space optical communication systems).     

Effects of strong electric fields in a polyacetylene chain

In this work, we study the effects related to the creation of electron/hole pairs via application of an external electric field that acts on a pristine trans-polyacetylene molecular chain at zero-temperature. This phenomenon is termed Schwinger–Landau–Zener (SLZ) effect and arises when a physical system, which can even be the vacuum, is under the action of a strong, static and spatially homogeneous electric field. Initially, we investigate how the electrical conductivity of the polyacetylene changes with the applied field, by considering the carriers production as well as the variation of the interband gap according to certain ab initio models. Next, we analyse the competition between the SLZ effect and another one associated with the incidence of an uniform electric field on one-dimensional crystals – the Bloch oscillations. We evaluate the conditions in which these latter can be destroyed by the particles created through the same field that induces them, and verify the possibility of occurrence of the Bloch oscillations inside the trans-polyacetylene with frequencies equal to or higher than the terahertz scale.