Rayleigh Theory Research Articles

Theory of plasma confinement in devices with pure toroidal field

Equilibrium, stability, and confinement in currentless toroidal device is studied in the terms of the flow-fluctuation cycle. In the initial seed equilibrium provided by the limiter, Rayleigh–Taylor (RT) fluctuations grow appreciably. These fluctuations are additional source of rotational transform in two ways. First, they directly drive a poloidal flow via Reynolds stress which improves the equilibrium. Second, the flow modifies the rms level profile in such a way that the ponderomotive force due to the fluctuations impedes the free fall. Detailed linear theory of Rayleigh–Taylor fluctuations with poloidal flow is presented and criteria for flow stabilization are identified. Using the exact eigenfunction of fluctuations, an exact ordinary differential equation for poloidal flow is derived and solved using an ansatz. Finally, the relevance of this analysis to the recently proposed low to high confinement mode transition theories is discussed.

Time-domain theory of resonant Rayleigh scattering by quantum wells: Early-time evolution.

A polariton-based theory of resonant Rayleigh scattering in quantum wells, i.e., the linear elastic scattering of light, near an excitonic resonance is developed to establish the connection between disorder associated with interface defects and the angular dependence of the temporally scattered light under sub-ps resonant excitation of the quantum well. The disorder model is motivated by the development of islands during epitaxial growth of heterostructures. The interplay of the length scales describing the island size and the spatial correlation between islands leads to nontrivial dynamics in the angular dependence of the temporal rise of the resonantly scattered light. It is found that the spatial correlations between defects scatter a substantial part of the photogenerated excitons to large-wave-vector nonradiative surface-polariton states. Hence scattering into these states is not directly observable using the usual far-field optical techniques, but rather contributes to the long-time behavior of the light emitted in time-resolved photoluminescence spectroscopy. \textcopyright{} 1996 The American Physical Society.

Theory of Scholte, leaky Rayleigh, and lateral wave excitation via the laser-induced thermoelastic effect

The analysis of the laser-induced thermoelastic excitation of acoustic waves propagating along a plane interface between two elastic media is presented. The general solution for the interface motion is derived. The detailed description of the liquid–solid interface motion caused by the photoexcited leaky Rayleigh, Scholte and lateral wave in the liquid is given both in frequency and time domain. The presented theory predicts that laser-induced thermoelastic stresses in the liquid and the solid can contribute in phase to the excitation of a Scholte wave and that the lateral wave excitation is suppressed when the light penetration depth and Scholte wave penetration depth in the liquid are equal. The obtained analytical solutions provide necessary theoretical background for the optimization of the laser-induced generation of interface waves in experiments.

Theory of resonant rayleigh scattering of excitons in semiconductor quantum wells

Disorder-induced Rayleigh scattering of excitons in quantum wells is investigated theoretically. For classical excitions (long-range spatial correlation), the disorder average can be performed exactly. For the full problem, a kinetic equation with «weak memory» for the excition distribution is derived which coincides with the classical result in the appropriate limit. The theoretical results are compared with recent experimental data on femtosecond time-resolved luminescence explaining well the finite rise time and the heavy-light-hole beating.

Sodium/Calcium‐Montmorillonite Suspension and Light Scattering

AbstractLight scattering method was used to determine clay concentration in aqueous suspensions. Because light scattering of nonabsorbing solid particles in suspension depends on particle size and shape in addition to the particles' concentration, these two factors should be considered in determination of clay concentration in suspension. this study was conducted to determine the effect of adsorbed ion composition and clay particle size and shape on light scattering of montmorillonite suspensions. Light scattering of montmorillonite suspensions at various particle size, clay concentrations, and equivalent fraction of exchangeable sodium (EFES) was determined at a wavelength of 550 nm. Light scattering of montmorillonite suspensions depended strongly on particle size and EFES. The scattered light intensity decreased as the particle size of the clay platelets decreased and dropped sharply with increasing EFES in the range below 0.2. The relative number of particles in a given volume of suspension at any given EFES value was smaller than predicted by the theory. This deviation indicated that Rayleigh's theory is not valid for such systems. Clay concentration, therefore, cannot be adequately determined by light scattering when changes in ionic composition and electrolyte concentration alter the particle size and shape of montmorillonite in aqueous suspension.

Acoustic properties of fibrous materials

The acoustic behaviour of fibrous materials which depends upon physical structural parameters has been investigated experimentally. Numerous values of characteristic impedance and propagation constant have been determined for materials having different fibre diameter and density. For quantitative estimation of acoustic energy losses in media a term equal to the real part of the characteristic impedance has been introduced as a ‘structural characteristic’. From comparative analyses of experimental results and taking into account the viscous boundary layer thickness present in Rayleigh's theory an empirical expression of structural characteristic has been derived as a function of porosity and fibre diameter. Empirical relationships between acoustic parameters and structural characteristic have been obtained also. This model can be used to predict values of the sound absorption coefficient.

Capillary Instability of a Jet of Liquid Metal

A system based on ink-jet technology has been used to demonstrate the controlled generation of monodispersed 100 μm diameter molten solder droplets. Oxide formation on the surface of the molten solder jet was shown to have a drastic effect on the droplet formation process. If the oxygen is not removed from the environment, no jet break up occurs. The growth rate of a radial disturbance on a capillary jet of molten solder is similar in magnitude to that predicted by Rayleigh and Weber theory, but the agreement is not good enough to say that these theories are valid for the liquid metal jet.

Characterization of SiC whiskers through infrared-absorption spectroscopy

The infrared-absorption spectra of commercially available SiC whiskers were measured. The spectra were dominated by the small particle resonances associated with finite ionic crystals. Analysis of these resonances allowed characterization of both morphological and electronic properties of the whiskers. The data were analyzed using Rayleigh and Mie theories as well as an effective medium model based on the Maxwell–Garnett approximation. It was possible to determine whisker radius and identify whiskers with a high free-carrier density and a core-shell structure. The effects of decreasing aspect ratio were also studied. The results showed that infrared-absorption spectroscopy provides an effective and relatively simple means to characterize SiC whiskers.

Rayleigh scattering by energetic photons: Development of theory and current status

We present in this article a brief summary of the status and the history of development of the theory of Rayleigh scattering—the elastic scattering of X- and γ-rays from bound electrons of an atom. The usefulness and the limitations of the commonly used theories are discussed. We compare recent experiments and simpler theories with the state-of-the-art theoretical S-matrix calculations. A practical simple scheme to obtain cross sections of accuracy comparable to the S-matrix predictions is described.

Distribution of Crest Amplitudes in Severe Seas With Breaking

A theoretical model is presented for the probability distribution of wave crest amplitudes in severe seas states with wave breaking. As the severity of a sea state increases, nonlinearities cause an increase in the amplitudes of the largest wave crests with a subsequent modification of the distribution of wave crest amplitudes from the linear Rayleigh theory. In this paper, a theory for the probabilities of these nonlinear crest amplitudes is first reviewed based on earlier work. The further limitations on these nonlinear crest amplitudes by wave breaking are then considered. As a result, a theoretical model is presented to account for both: 1) the nonlinear increase in the highest wave crests, and 2) the selective reduction of some fraction of these high crests due to wave breaking. This model is then verified using several sets of laboratory data for severe breaking seas having approximate JONSWAP wave spectra.

Degree of linear polarization method for determination of intrinsic optical anisotropy of southern bean mosaic virus

AbstractSouthern bean mosaic virus (SBMV) is a spherical plant virus. It possesses an intrinsic (structural) anisotropy due to the orientation of valence bonds of the amino acid and/or nucleic acid residues. According to the light scattering theory of Rayleigh and Gans for optically anisotropic spheres, the degree of linear polarization of the scattered light depends on the intrinsic anisotropy, the relative refractive index of the sphere to the solvent, the scattering angle, and the inclination angle of linearly polarized incident light to the scattering plane. By using the theoretical expression of the degree of linear polarization, the intrinsic anisotropy parameter of southern bean mosaic virus in the compact spherical state was calculated with the appropriate experimental values. This novel method should be useful in elucidating the internal structure of spherical viruses and other spherical complexes of macromolecules. © 1993 John Wiley & Sons, Inc.

Theoretical approach to the humping phenomenon in welding processes

The conjecture which explains the humping phenomenon in terms of Marangoni convection is discussed and rejected. Instead, Rayleigh's theory of the instability of a free liquid cylinder due to surface tension is applied. The width-to-length ratio of the weld pool has to exceed 1/2 pi to avoid humping. The growth time of a disturbance is found to be approximately the same as the growth time of a hump. The analysis of a bounded cylinder provides a new stability criterion which allows the introduction of a bounding function to distinguish between arc and laser welding. The weld pool dimensions are estimated in terms of a simple heat conduction model. The threshold value predicted theoretically for the travel speed above which humping commences agrees well with the experimental value. It decreases with increasing power, which is in qualitative agreement with experimental results.

Growth kinetics of the photosynthetic bacterium Chlorobium thiosulfatophilum in a fed‐batch reactor

Hydrogen sulfide dissolved in water can be converted to elementary sulfur or sulfate by the photosynthetic bacterium Chlorobium thiosulfatophilum. Substrate inhibition occurred at sulfide concentrations above 5.7 mM. Light inhibition was found at average light intensities of 40,000 lux in a sulfide concentration of 5 mM, where no substrate inhibition occurred. Light intensity, the most important growth parameter, was attenuated through both scattering by sulfur particles and absorption by the cells. Average cell and sulfur particle sizes were 1.1 and 9.4 microm, respectively. Cells contributed 10 times as much to the turbidity as sulfur particles of the same weight concentration. The light attenuation factor was mathematically modeled, considering both the absorption and scattering effects based on the Beer-Lambert law and the Rayleigh theory, which were introduced to the cell growth model. Optimal operational conditions relating feed rate vs. light intensity were obtained to suppress the accumulation of sulfate and sulfide and save light energy for 2- and 4-L fed-batch reactors. Light intensity should be greater for the same performance (H(2)S removal rate/unit cell concentration) in larger reactors due to the scaleup effect on light transmission. Knowledge of appropriate growth kinetics in photosynthetic fed-batch reactors was essential to increase feed rate and light intensity and therefore cell growth. A mathematical model was developed that describes the cell growth by considering the light attenuation factor due to scattering and absorption and the crowding effect of the cells. This model was in good agreement with the experimental results.

EXPERIMENTAL STUDY ON OSCILLATORY THERMOCAPILLARY CONVECTION

The transition processes from steady flow into oscillatory flow in a liquid bridge of the half floating zone are studied experimentally. Two methods of noncontacted diagnoses are developed to measure the distribution of critical Marangoni numbers described by the onset of the oscillation at the free surface of the liquid bridge. The experimental results obtained for both cases of the upper rod heated and the lower rod heated agree with the prediction by Rayleigh's instability theory. The sensitive relations between the relatively fat or slender liquid bridge and the onset of oscillatory convection are also discussed to reveal the insight of the pressure distribution near the free surface. The experiments have been performed in a small liquid bridge, where the Bond number is much smaller than 1, alld the results can be used to simulate the experiment in the microgravity environment.

Interim guidance for prediction of wave run-up on beaches

A method of predicting wind wave run-up (for any desired quantile or statistic value) on smooth linear mild slopes has been presented. The method is based on a re-analysis of an extensive laboratory measurement run-up data base of Mase [(1989), Random wave run-up height on gentle slopes. J. WatWay, Port, Coastal, Ocean Engng Div., ASCE 115, 649–661] and Mase and Iwagaki [(1984), Run-up of random waves on gentle slopes. Proceedings of the 19th Coastal Engineering Conference, ASCE, pp. 593–609]. The predictive run-up measurement equation is based on a modified dimensionless form of the Hunt [(1959), Design of seawalls and breakwaters. Proc. J. WatWay Harbour Div., ASCE, 85, 123–152] formula with a linear intercept term (which appears to be due to mild slope wave set-up). Values of the slope coefficient in the run-up predictive equation are based on the Rayleigh probability distribution in accordance with findings from the present re-analysis of the Mase data set. Run-up prediction for a given quantile or statistic value is then found utilizing the slope coefficient based on Rayleigh theory combined with the predictive linear equation found herein for the average run-up height R mean in a stationary wave train. In the case of rough slopes and permeable beaches, it is obvious that the true run-up would be reduced from the predicted values of run-up given by the smooth slope method provided herein. At present the extent of such reduction is a matter of speculation. As an interim measure, it is recommended that conservative design practice be followed by using the run-up values predicted via the method given herein unless sufficient justification for run-up reduction based on laboratory or field findings can be provided.

Resonant light scattering by fractal clusters.

A scale-invariant theory of resonant Rayleigh scattering by fractal clusters is developed. Our main result is that the scattering cross section is greatly enhanced, because of the presence of very high local fields, which are correlated and strongly fluctuating. Simulations dealing with two examples of fractal structures, namely, random walk and cluster-cluster aggregates, are presented. The numerical results confirm the theoretical predictions of the scaling behavior for both absorption and scattering, and allow us to obtain the corresponding exponents. In addition to the results for scattering, the large scale of the simulations of the present work provides a comprehensive confirmation and a substantial extension of a recent study by Markel, Muratov, Stockman, and George [Phys. Rev. B 43, 8183 (1991)].

Absorption and scattering of light by polydisperse aggregates

The absorption, scattering, and differential scattering cross sections are presented for polydisperse aggregates of prescribed fractal dimension and uniform primary particle size. These optical properties are formulated for polydisperse aggregates in terms of the primary particle diameter, the appropriate moments of the discrete size distribution function, and the mean-square radius of gyration. The absorption and scattering cross sections are compared with Rayleigh theory in the small size limit and with the results of the computational simulations of Mountain and Mulholland [Langmuir 4, 1321 (1988)] for intermediate and large aggregates. The differential scattering cross sections are well correlated by the law of Guinier together with a power-law expression for the larger sizes. The cross sections that are described herein apply in particular to polydisperse fractallike aggregates that are formed by cluster-cluster aggregation and possess a size scale that is pertinent to laboratory experiments and industrial processes.

Linear stability analysis of gas-liquid interface

This paper extends the Rayleigh theory to study the interface instability of axisymmetric gas-liquid flows. The dispersion equations of cylindrical liquid sheets were derived and numerical solutions were obtained. Two families of instability curves were found; one for symmetric disturbances and the other for antisymmetric disturbances. Two limiting cases can be recovered from derived dispersion equations. The equation recovers the Rayleigh instability of round jets for symmetric disturbances and recovers the hollow jet or submerged jet instability for antisymmetric disturbances. Effects due to ambient fluid density and ambient fluid velocity on liquid-sheet instabilities were examined.

Coherent fluorescent emission and scattering from a uniform cylinder.

The coherent light inelastically scattered from an ideal fluorescent cylinder illuminated by an arbitrary electromagnetic wave is analyzed using an extension of Rayleigh's theory. Scattering coefficients are solved specifically for a plane wave illuminating the cylinder normal to the axis of the cylinder. The resulting inelastically scattered radiation is not entirely unlike that of elastically scattered radiation from a perfect cylinder. These results are illustrated by numerical calculations for several specific, but arbitrary, cases.

The role of net angular momentum in pump/probe spectroscopy: Absorption, refringence, scattering, and nuclear resonance

Applied net angular momentum ( J) has the same role in spectroscopy as applied magnetic flux density ( B), both having the same parity and motion reversal symmetry. This simple statement appears to have profound consequences, especially in the context of nonlinear optics, where J can be generated by a pump laser. These are explored for pump/probe spectroscopy involving absorption, refringence, and scattering in the semiclassical Rayleigh theory. It is shown that there are phenomena analogous to those induced by B, exemplified by the spin chiral class of circular and axial birefringence/dichroism (analogues of the Faraday and Wagnière/Meier effects produced by B); and pump laser-induced Rayleigh/Raman optical activity (analogues of scattered optical activity induced by B). Nuclear effects of the pump laser-induced J are introduced as nuclear electromagnetic resonance (NER).