Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Rayleigh approximation for axisymmetric scatterers

The Rayleigh approximation is known to be designed only for small ellipsoidal scatterers. We suggest an approach that allows one to find a simple, often analytical, long-wavelength approximation for nonellipsoidal particles. We apply the approach to axisymmetric scatterers and utilize Chebyshev particles to study the main properties of the obtained approximation. To a certain degree, it can be considered as an extension of the Rayleigh approximation to nonspheroidal scatterers.     

Comments on “the scattering of light and phase transition in solutions of tertiary butyl alcohol in water”

In two independent experiments, we have measured the Rayleigh factor of tert-butanol-water mixtures as a function of concentration. Our results are in strong disagreement with those of Vuks and Shurapova in that we find only a single maximum in the Rayleigh factor at mole fraction 0.125 in alcohol. We find that the Rayleigh factors of solutions in the immediate vicinity of 0.03 mole fraction of alcohol depend strongly upon the purity of the components and treatment of the solutions prior to measurement. A possible explanation for this behavior is given.     

Rayleigh scattering and atomic dynamics in dissipative optical lattices

We investigate Rayleigh scattering in dissipative optical lattices. In particular, following recent proposals [S. Guibal, Phys. Rev. Lett. 78, 4709 (1997)]; C. Jurczak, Phys. Rev. Lett. 77, 1727 (1996)]], we study whether the Rayleigh resonance originates from the diffraction on a density grating and is therefore a probe of transport of atoms in optical lattices. It turns out that this is not the case: the Rayleigh line is instead a measure of the cooling rate, while spatial diffusion contributes to the scattering spectrum with a much broader resonance.     

Resonant rayleigh scattering from bilayer quantum Hall phases

We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor nu = 1. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.     

How fast can cracks propagate?

We have performed atomic simulations of crack propagation along a weak interface joining two harmonic crystals. The simulations show that a mode II shear dominated crack can accelerate to the Rayleigh wave speed and then nucleate an intersonic daughter that travels at the longitudinal wave speed. This contradicts the general belief that a crack can travel no faster than the Rayleigh speed.     

Convective instability of a water-vapor-saturated atmospheric layer. The formation of localized and periodic cloud structures

The classical Rayleigh problem of convective instability is generalized to the case of water vapor condensation in the atmosphere. We present an analytical solution demonstrating a fundamental difference between moist convection and Rayleigh convection: the curve of the critical Rayleigh number versus the number characterizing the intensity of condensation heat release consists of two parts, with spatially localized neutral solutions corresponding to one of them. Spatially periodic neutral solutions correspond to the second part of the curve; these are characterized by a significant localization of the regions of ascending motions. The theory describes the nucleation and development of individual convective clouds and ordered cloud structures.     

The propagation dynamics of ultraviolet light filament with Rayleigh scattering in air

In this paper we present for the first time the effects of Rayleigh scattering on the long distance propagation of ultraviolet （UV） light filament in air based on the stationary analysis. The simulation results show that the effects of Rayleigh scattering on the propagation of UV laser filaments may not be ignored. These influences are slightly dependent on the laser wavelength. We also compare the UV filament propagations at different input powers in the presence and the absence of the Rayleigh scattering and discuss the mechanisms of power loss and beam defocusing. In the absence of Rayleigh scattering, the filament propagation is determined by the oscillating behaviour of the beam size. In the presence of the scattering, the propagation lengths of filament are close to each other at different initial powers and determined by the Rayleigh scattering.     

Probing microcavity polariton superfluidity through resonant Rayleigh scattering

We study the motion of a polariton fluid injected into a planar microcavity by a continuous wave laser. In the presence of static defects, the spectrum of the Bogoliubov-like excitations reflects onto the shape and intensity of the resonant Rayleigh scattering emission pattern in both momentum and real space. We find a superfluid regime in which the Rayleigh scattering ring in momentum space collapses as well as its normalized intensity. We show how collective excitation spectra having no analog in equilibrium systems can be observed by tuning the excitation angle and frequency.     

Landau–Ginzburg theory for ‘star’-shaped droplets

ABSTRACT

Molecular simulations have shown that when a nano-drop comprising a single spherical central ion and a dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. A linear continuum model of the ‘star’-shapes comprised electrostatic and surface energy is not sufficient to describe these shapes. We employ combined molecular dynamics, continuum electrostatics and macroscopic modelling in order to construct a unified free energy functional that describes the observed star-shaped droplets. We demonstrate that the Landau free energy coupled to the third-order Steinhardt invariant mimics the shapes of droplets detected in molecular simulations. Using the maximum likelihood technique we build a universal free energy functional that describes droplets for a range of Rayleigh fissility parameter. The analysis of the macroscopic free energy demonstrates the origin of the finite amplitude perturbations just above the Rayleigh limit. We argue that the presence of the finite amplitude perturbations precludes the use of the small parameter perturbation method for the analysis of the shapes above the Rayleigh limit of the corresponding spherical shape.     

On scaling laws in turbulent magnetohydrodynamic Rayleigh-Benard convection

We invoke the concepts of magnetic boundary layer and magnetic Rayleigh number and use the rates of magnetic energy dissipation in the bulk and the boundary layers to derive some scaling laws expressing how the Nusselt number depends on the magnetic Rayleigh number, Prandtl number and magnetic Prandtl number for the simple case of turbulent magnetohydrodynamic Rayleigh-Benard convection in the presence of a uniform vertical magnetic field.     

Ultraviolet high-spectral-resolution Rayleigh-Mie lidar with a dual-pass Fabry-Perot etalon for measuring atmospheric temperature profiles of the troposphere

We report what is believed to be the first demonstration of measurement of tropospheric temperature profiles in daytime by use of a high-spectral-resolution Rayleigh-Mie lidar at an eye-safe wavelength of 355 nm. Atmospheric temperature is determined from the linewidth of the Rayleigh spectrum. Two Rayleigh signals are detected with Fabry-Perot etalon filters with a dual-pass optical layout. The Mie signal is detected with a third etalon filter for correcting the Mie component in the Rayleigh signals. The temperature statistical uncertainties are below 1 K up to a height of 3 km in nighttime and 2 km in daytime with a relatively compact system that uses laser energy of 180 mJ and a 25-cm telescope. Good agreement between lidar and radiosonde measurements is obtained.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

A self-gain random distributed feedback fiber laser based on stimulated Rayleigh scattering

We reported a narrow linewidth (~ 4 kHz) fiber laser with a mirror-less open cavity based on stimulated Rayleigh scattering (STRS) in a non-uniform fiber. Because of its variable core size and dispersion along the fiber, the threshold of the stimulated Brillouin scattering was increased by ~ 7 dB compared with that of conventional single mode fiber, which allows higher order Rayleigh scattering. The self-gain is initiated by the spontaneous Rayleigh scattering and amplified via STRS, and the distributed feedback mechanism is formed by different orders of Rayleigh scattering counter-propagating as the “random mirror reflection” in the non-uniform fiber.     

On the Heat Transfer in Rayleigh–Bénard Systems

In this paper we discuss some theoretical aspects concerning the scaling laws of the Nusselt number versus the Rayleigh number in a Rayleigh–Bénard cell. We present a new set of numerical simulations and compare our findings against the predictions of existing models. We then propose a new theory which relies on the hypothesis of Bolgiano scaling. Our approach generalizes the one proposed by Kadanoff, Libchaber, and coworkers and solves some of the inconsistencies raised in the recent literature.     

Elastic characterization of platinum/rhodium alloy at high temperature by combined laser heating and laser ultrasonic techniques

We demonstrate an innovative pump–probe technique combined with laser heating to determine the velocity of a surface Rayleigh wave at high temperature. Laser ultrasonics in a point-source–point-receiver configuration was combined with laser heating to evaluate the elastic properties of micron size specimens. The measurements of the velocity of the surface Rayleigh wave (SRW) were conducted at 1070 K.     

The attenuation of rayleigh surface waves by surface roughness

This paper presents a calculation of the attenuation length of Rayleigh surface waves in the presence of surface roughness. We consider Rayleigh waves on the surface of a semi-infinite isotropic elastic continuum, and the method we use produces the contribution to the attenuation rate proportional to the square of the rms amplitude of the roughness. We obtain explicit expressions for the contribution to the attenuation rate from roughness-induced scattering into bulk transverse and longitudinal acoustic waves, and into Rayleigh waves. Our derivation makes use of a Green's function method. When the wavelength λ of the Rayleigh wave is long compared to the transverse correlation length a that characterizes the surface roughness, all contributions to the attenuation rate are proportional to the fifth power of the frequency. When λ is comparable to or smaller than a, the attenuation constant varies more slowly with frequency. For a model of the surface roughness, we present numerical calculations of the relative magnitude and frequency dependence of the various contributions to the attenuation rate. The Green's functions used here may be applied to a number of calculations. A derivation of their form is provided in an Appendix.     

Optimizing illumination's complex coherence state for overcoming Rayleigh's resolution limit

We suggest tailoring of the illumination's complex degree of coherence for imaging specific two-and three-point objects with resolution far exceeding the Rayleigh limit. We first derive a formula for the image intensity via the pseudo-mode decomposition and the fast Fourier transform valid for any partially coherent illumination(Schell-like, non-uniformly correlated, twisted) and then show how it can be used for numerical image manipulations. Further, for Schell-model sources,we show the improvement of the two-and three-point resolution to 20% and 40% of the classic Rayleigh distance,respectively.     

Accuracy analysis on Rayleigh lidar measurements of atmospheric temperature based on spectroscopy

We make a detailed analysis on the linearity and accuracy of the relationship between the full-width at half-height （FWHH） of the atmosphere molecules Rayleigh scattering spectrum and the square root of the atmospheric temperature. A simulation of the FWHH of the atmosphere molecules Rayleigh scattering spectrum is made based on the S6 Atmosphere Model and U.S. Standard Atmosphere Model. The calcu- lated temperature is compared with the initial simulation temperature. The result shows that the FWHH of the atmosphere molecules Rayleigh scattering spectrum is nearly proportional to the atmospheric temperature. The goodness-of-fit index of the fitting curve is 0.9977 and the maximum absolute error of measured atmospheric temperature is about 2 K.     

Fluctuations in fluids out of thermal equilibrium

After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed.