Statistics of diffusive and localized fields in the vortex core

The statistics of the field structure in the vortex core surrounding phase singularities in random wave fields are measured and calculated for diffusive and localized waves. Excellent agreement is found between experiment and theory. The variation of phase with the geometric angle is deterministic, depending only upon the eccentricity of elliptical intensity contours, epsilon, whose probability distribution is shown to be universal. The distribution of vorticity is shown to reflect both the vorticity distributions within a Gaussian random wave field with a given value of the total transmission and the mesoscopic distribution of total transmission.     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

On the effect of fractional statistics on quantum ion acoustic waves

In this paper, I study the effect of a small deviation from the Fermi–Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi–Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits.     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Coherence function and mean field of plane and spherical sound waves propagating through inhomogeneous anisotropic turbulence

Inhomogeneity and anisotropy are intrinsic characteristics of daytime and nighttime atmospheric turbulence. For example, turbulent eddies are often stretched in the direction of the mean wind, and the turbulence statistics depends on the height above the ground. Recent studies have shown that the log-amplitude and phase fluctuations of plane and spherical sound waves are significantly affected by turbulence inhomogeneity and anisotropy. The present paper is devoted to studies of the mean sound field and the coherence functions of plane and spherical sound waves propagating through inhomogeneous anisotropic turbulence with temperature and velocity fluctuations. These statistical moments of a sound field are important in many practical applications, e.g., for source detection, ranging, and recognition. Formulas are derived for the mean sound field and coherence function of initially arbitrary waveform. Using the latter formula, we also obtained formulas for the coherence functions of plane and spherical sound waves. All these formulas coincide with those known in the literature for two limiting cases: homogeneous isotropic turbulence with temperature and wind velocity fluctuations, and inhomogeneous anisotropic turbulence with temperature fluctuations only. Using the formulas obtained, we have numerically shown that turbulence inhomogeneity significantly affects the coherence functions of plane and spherical sound waves.     

The phase statistics of a multichannel radar interferometer

The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σ_k=1^N S_k(t) S_k*(t+Δt) where, for example, the signals from each antenna in the kth pair are S_k(t) and S_k(t+Δt).

The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible to measure the phase of the coherence function of an electromagnetic wave field scattered from a randomly moving extended object (such as the ocean surface) using such a multichannel radar. This phase is related to asymmetry of the Doppler power spectrum. Furthermore, if this asymmetry is a result of surface currents on the ocean interacting with the surface waves which cause the electromagnetic scattering, then the surface currents may be measured in some sense.     

Statistics of shock waves in a two-dimensional granular flow

We have investigated the dynamics of shock waves in a single layer of uniform balls in a small-angle two-dimensional funnel. When the funnel half-angle 0 degrees < or approximately beta < or approximately 2 degrees, the flow is intermittent and kinematic shock waves are observed to propagate against the flow. We have used fast video equipment and image analysis methods to study the statistics of the shock waves. It is found that their speed and frequency increase with the distance from the outlet. In particular, the shock speed scales as the ratio of the local funnel width to the width of the funnel outlet. Various kinds of interactions between shock waves are observed, including repulsion. New shock waves are only created at those sites where a close-packed triangular packing of the monodisperse balls fits across the funnel.     

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.     

Non-Gaussian statistical models for scattering calculations

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Contribution to the statistical theory of wave localization in a two-layered medium

A very simple system of stochastic boundary-value wave equations that describes the interaction of two types of waves in a randomly inhomogeneous medium is studied. The statistics of the reflection and transmission coefficients for the incident and excited waves are discussed. It is shown that the excitation of waves is statistically equivalent to switching on damping for the initial incident waves which are localized in separate specific realizations. The parameters of the length of such localization are estimated in terms of the spectral density of the variations of the medium. It is also shown that for excited waves there is no dynamical localization, and the transmission coefficients for them are estimated. Zh. éksp. Teor. Fiz. 111, 2030–2043 (June 1997)     

氧碘化学激光器中相位扰动的模拟研究

 建立了含相位扰动的1维流场3维物理光学负载光腔模型。选用折叠非稳腔，模拟计算了斜激波中心距光轴不同距离时以及不同强度的斜激波对腔内光场相位分布和输出功率的影响。研究表明激光输出光束质量与腔内激波的分布位置和激波的强度有密切关系，应该避免激波中心近光轴时的强扰动效应引起的光束质量退变。实验装置的计算结果再现了实验现象。     

The radiation Q factors obtained from the partial derivatives of the phase of the reflection coefficient of an elastic plate

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.     

剪切波对时间反转调相的经颅聚焦超声的影响*

为研究颅骨中的剪切波对经颅聚焦超声的影响,该文利用Kelvin-Voigt固体声波方程并结合时间反转法,分别模拟了考虑剪切波和不考虑剪切波时,256-单元平面相控阵为实现超声经颅聚焦所需的相位调控,并将这两种相位调控都分别作用于考虑剪切波和不考虑剪切波时的聚焦情形。对这两种相位调控以及基于它们的经颅聚焦超声场的对比分析结果表明:聚焦深度较大时,剪切波对基于时间反转进行的相位调控影响较小;不过,剪切波对经颅聚焦超声场的强度分布影响较大,忽略剪切波会导致对焦域处声场聚焦强度的高估以及对颅骨附近声能量沉积的低估。     

Hidden Variables and the Nature of Quantum Statistics

It is shown that the nature of quantum statistics can be clarified by assuming the existence of a background of random gravitational fields and waves, distributed isotropically in space. This background is responsible for correlating phases of oscillations of identical microobjects. If such a background of random gravitational fields and waves is considered as hidden variables, then taking it into account leads to Bell-type inequalities that are fairly consistent with experimental data.     

Photon statistics upon consecutive parametric interactions of light waves with nonmultiple frequencies

Quasi-phase-matched consecutive three-frequency interactions between waves with nonmultiple frequencies are considered. The quantum theory of parametric amplification is developed in the approximation of an undepleted low-frequency pump field in the Heisenberg representation. It is shown that, with a certain choice of quasi-phase-matching orders, the regime of exponential increase in the mean number of photons of interacting waves can be realized. In this case, the photon statistics of generated waves is super-Poissonian one. The correlation of fluctuations of numbers of photons with different frequencies is also considered.     

Non-Gaussian statistical models for scattering calculations

Abstract

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

The Effects Induced by Turbulence and Dust Storms on Millimeter Waves

Dust storms and turbulence consist of a random medium system, its effects on milimeter waves propagation are studied. Attenuation of millimeter waves, its phase shift and cross- polar discrimination are presented. Results show that dust storms mainly effects XPD and phase shift of millimeter waves, turbulence chiefly produces attenuation, in mediocre fluctuation.     

FREQUENCY DISPERSION CHARACTERISTICS OF PHASE VELOCITIES IN SURFACE WAVE FOR ROTATIONAL COMPONENTS OF SEISMIC MOTION

When rotational components of ground motion produced by seismic surface waves are computed, the phase velocities must always be dealt with in earthquake engineering. In this paper, appropriate methods are presented to obtain the calculation formulas for the phase velocities of surface waves by applying the theory of elastic wave propagation. Frequency dispersion characteristics of phase velocities are discussed. The rocking component around a horizontal axis and the torsional component around a vertical axis, which are generated, respectively, by the Rayleigh and Love waves, are reasonably given. A procedure is developed to calculate the time histories of these rotational components.     

Interaction between Breathers and Rogue Waves in a Nonlinear Optical Fiber

We study the interaction between breather and N-order rogue waves in a nonlinear optical fiber.The impacts of the relative phase and the interaction distance between breathers and rogue waves are discussed in detail.Specifically,the breather can reduce the maximum hump value of high-order rogue waves greatly in the cases of nonzero relative phase or nonzero interaction distance.The characteristic of exclusion between breathers and rogue waves is described qualitatively in the situation of different interaction distances,which can be used to change the temporal-spatial distribution of rogue waves.Their interaction properties are characterized by the trajectory of localized waves' valleys and humps.It is shown that the interaction changes the dynamical evolution trajectory of rogue waves and breathers.These results provide some possible ways to control high-order rogue waves.