Rayleigh Theory Research Articles

Comparison of atmospheric hydrology over convective continental regions using water vapor isotope measurements from space

Global measurements of the 500–825 hPa layer mean HDO/H2O ratio from the Tropospheric Emission Spectrometer (TES) are used to expose differences in the dominant hydrologic processes in the Amazon, north Australian, and Asian monsoon regions. The data show high regional isotopic variability and numerous values unexpected from classical Rayleigh theory. Correlation analysis shows that mixing with boundary layer air, enhanced isotopic fractionation during precipitation, and subsiding air parcels contribute to intraseasonal isotopic variability. These local controls explain only 8–30% of total regional variance, which suggests that the isotopes are primarily indicators of moist processes that occur upstream. Seasonal trajectory analysis demonstrates that Rayleigh distillation in a Lagrangrian framework underestimates the observed isotopic depletion during the monsoons and suggests substantial recycling of water within or below clouds. The trajectory results for the dry seasons reveal that subsiding air parcels periodically introduce isotopically depleted air into the north Australia and Asian monsoon regions, whereas vigorous low‐level convection over the Amazon basin acts to quickly enrich and moisten dry subsiding air. The analysis indicates variations in the strength of convective detrainment into the lower to middle troposphere over all regions, which, during the dry seasons of the north Australian and Asian monsoon regions, correlate with increases in relative humidity. This study shows that isotopic measurements provide unique diagnostics of mechanisms that control the seasonal sources of water and that these provide a refined understanding of the differences in the characteristics of hydrologic budgets in these monsoonal regions.

Predictions of Rayleigh's diffraction theory for the effect of focal shift in high-aperture systems

In their work on diffraction [J. Opt. Soc. Am.51, 1050 1961], Osterberg and Smith have computed in an exact manner from the Rayleigh-Sommerfeld diffraction integral of the first kind the irradiance distribution along the axis of a converging spherical wave, and they found that in a scalar optical system of high relative aperture and finite value of Fresnel number, the central peak value of the axial irradiance may occur inside, at, or outside the geometrical focal point as the angular semiaperture of the system is less than, equal to, or greater than, respectively, a particular angle that falls near 70 degrees . These findings are now reexamined using a different assumption that takes into account diffraction at the edge of the aperture. Different results are obtained that agree well with the predictions of other theories of diffraction of light and give confidence to the common conclusions drawn by investigators of the effect of focal shift, that the point of the principal maximum of axial irradiance is not at the geometrical focus but shifted toward the aperture in systems of different relative aperture and finite value of Fresnel number.

Effect of surface tension on a liquid-jet produced by the collapse of a laser-induced bubble against a rigid boundary

The effect of surface tension on the behavior of a liquid-jet is investigated experimentally by means of a fiber-coupled optical beam deflection (OBD) technique. It is found that a target under water is impacted in turn by a laser-plasma ablation force and by a high-speed liquid-jet impulse induced by bubble collapse in the vicinity of a rigid boundary. The liquid-jet impact is found to be the main damage mechanism in cavitation erosion. Furthermore, the liquid-jet increases monotonously with surface tension, so cavitation erosion rises sharply with increasing surface tension. Surface tension also reduces bubble collapse duration. From the experimental results and the modified Rayleigh theory, the maximum bubble radius is obtained and it is found to reduce with increasing surface tension.

Dynamics of Cryogenic Jets: Non-Rayleigh Breakup and Onset of Nonaxisymmetric Motions

We report development of generators for periodic, satellite-free fluxes of monodisperse drops with diameters down to 10 microm from cryogenic liquids such as H2, N2, Ar, and Xe (and, as a reference fluid, water). While the break up of water jets can be described well by Rayleigh's linear theory, we find jet regimes for H2 and N2 which reveal deviations from this behavior. Thus, Rayleigh's theory is inappropriate for thin jets that exchange energy and/or mass with the surrounding medium. Moreover, at high evaporation rates, the axial symmetry of the dynamics is lost. When the drops pass into vacuum, frozen pellets form due to surface evaporation. The narrow width of the pellet flux paves the way towards various industrial and scientific applications.

Theory of Rayleigh scattering from metallic carbon nanotubes

We present a microscopic calculation of the Rayleigh (elastic light) scattering spectra for single-walled carbon nanotubes. Combining density-matrix formalism and the tight-binding model, we obtain results for nanotubes of arbitrary chiral index. In agreement with experiment, the calculated Rayleigh spectra of metallic nanotubes show a double-peaked structure resulting from the trigonal warping effect, with the low-energy feature exhibiting greater intensity. We explain the intensity ratios by the wave-vector dependence of the optical matrix elements. Also in accord with experiment, the Rayleigh line shape of each peak is asymmetric, with an enhanced cross section for lower photon energies. This behavior arises from contributions of the nonresonant optical susceptibility to the Rayleigh scattering process.

Ultratransparent glass ceramics: The structure factor and the quenching of the Rayleigh scattering

Glass ceramics with nanocrystals present a transparency higher than that expected from the theory of Rayleigh scattering. This ultratransparency is attributed to the spatial correlation of the nanoparticles. The structure factor is calculated for a simple model system, the random sequential addition of equal spheres, at different volume filling factor. The spatial correlation given by the constraint that particles cannot superimpose produces a diffraction peak with a low S(q) in its low-q tail, which is relevant for light scattering. The physical mechanism producing high transparency in glass ceramics is demonstrated to be the low density fluctuation in the number of scatterers.

Optimized liquid DEP droplet dispensing

Dielectrophoretic droplet dispensing on a substrate relies on initial actuation of the liquid to form a uniform, sessile rivulet along the length of coplanar electrodes, and subsequent capillary-driven instability to form the droplets after the voltage is removed. Periodic bumps disposed along the length of the structure promote droplet formation by establishing an initial, static perturbation from which the instability evolves. Droplet uniformity, essential for applications in the laboratory-on-a-chip, is promoted if the bumps are spaced close to the most unstable wavelength predicted by Rayleigh's cylindrical jet theory. Proper sizing of the bumps guarantees good coverage by the droplets without compromising reliable droplet formation. Finally, if one of the coplanar electrodes is divided into two electrically addressable sections, and then if the voltage application to the sections is sequenced to trap liquid along the active structure, precisely positioned droplet dispensing of very uniform volume results. The experiments reported in this paper demonstrate the effectiveness of these enhancements. To achieve further improvements, the analytical approaches taken in the present work will have to be supplemented or replaced by numerical simulations of the capillary-driven transient hydrodynamics.

Angular-dependent metal-enhanced fluorescence from silver colloid-deposited films: opportunity for angular-ratiometric surface assays

We describe an exciting opportunity for Metal-Enhanced Fluorescence (MEF)-based surface assays using an angular-ratiometric approach to the observed enhanced emission from fluorophores in close proximity to silver colloids deposited on glass substrates. This approach utilizes the radiationless energy transfer (coupling) between the excited states of the fluorophore and the induced surface plasmons of the silver colloids, and the subsequent angular-dependent fluorescence emission from the fluorophore-silver colloid system. Since MEF is related to surface plasmons' ability to scatter light, angular-dependent light scattering from three different silvered surfaces and glass substrates were investigated using two common excitation angles, 45 and 90 degrees . The scattered light from silvered surfaces with a high loading was observed at wider angles on both sides of the glass substrates, while forward scattering (from the back of the glass) was dominant for the silvered surfaces with low loading, as explained by both Mie and Rayleigh theories. When silver colloids were placed between the fluorophore and glass interface, the coupled fluorescence emission through the higher refractive index glass (and in air), increased in an angular-dependent fashion, following closely the angular-dependent light scattering pattern of the silver colloids themselves. Similar observations for fluorescence emission from fluorophores deposited onto glass surfaces alone were made, but at much narrower angles on both sides of the fluorophore-glass interface and were simply explained by Lambert's cosine law. As the loading of silver on glass was increased, the enhanced fluorescence emission was observed at wider angles (towards 0 and 180 degrees ) at both sides of the silvered surfaces. Glass surfaces without silver colloids were used as control samples to demonstrate the benefits of MEF for enhancing fluorescence signatures in an elegant, angular-dependent fashion. Finally, the utility of the angular-dependent MEF phenomenon for intensity-based angular-ratiometric surface assays is demonstrated.

Temperature and magnetic field dependencies in a model of diamagnetic hysteresis in beryllium

A model of a diamagnetic hysteresis loop of strongly correlated electron gas in dHvA effect conditions is developed. It is shown that in the framework of Rayleigh theory for magnetization loop, the coercive force and remnant magnetization at every stage of the dHvA oscillations are characterized by strong dependencies on temperature, magnetic field and Dingle temperature.

Experimental investigation of the collapse of laser-generated cavitation bubbles near a solid boundary

The oscillation of a laser-generated single cavitation bubble near a solid boundary is investigated by a fiber-optic diagnostic technique based on optical beam deflection (OBD). The maximum bubble radii and collapse time for each oscillation cycle are determined from a sequence of bubble oscillations. Furthermore, by combining the revised Rayleigh theory, the prolongation factor κ at different dimensionless parameter γ ( γ = L / R max , where R max is the maximum bubble radius and L is the distance of a cavity inception point from a boundary) is obtained. In addition, the prolongation factor of the collapse time versus laser energy is also derived, which are valuable in the fields of hydraulic cavitation, laser lithotripsy and laser ophthalmology.

A reagentless optical biosensor based on the intrinsic absorption properties of peroxidase

During the reversible reaction between peroxidase (HRP) and H(2)O(2), several peroxidase intermediate species, showing different molecular absorption spectra, are formed which can be used for H(2)O(2) determination; when H(2)O(2) is generated in a previous enzymatic reaction, the substrate involved in this reaction can also be determined. On this basis, a new family of fully reversible reagentless optical biosensors containing HRP is presented; glucose determination is used as a model. The biosensor (which can be used for at least 6 months and/or more than 750 measurements) is prepared by HRP and glucose oxidase entrapment in a polyacrylamide gel matrix. A mathematical model (in which optical, kinetic and transport aspects are considered) relating the measured absorbance with the substrate concentration is also presented together with a simple methodology for characterization of this kind of biosensor. Regarding the optical model, the Kubelka-Mulk theory of reflectance does not give good results and the biosensors are better described by the Rayleigh theory of polymer solutions. Under working conditions, linear response ranges from 1.5x10(-6) to 3.0x10(-4)M glucose and CV was about 4%. This biosensor has been applied for glucose determination in fruit juices and synthetic serum samples without sample pretreatment.

Quantitative Scattering of Melanin Solutions

The optical scattering coefficient of a dilute, well-solubilized eumelanin solution has been accurately measured as a function of incident wavelength, and found to contribute <6% of the total optical attenuation between 210 and 325 nm. At longer wavelengths (325–800 nm), the scattering was less than the minimum sensitivity of our instrument. This indicates that ultraviolet and visible optical density spectra can be interpreted as true absorption with a high degree of confidence. The scattering coefficient versus wavelength was found to be consistent with Rayleigh theory for a particle radius of 38 ± 1 nm. Our results shed important light on the role of melanins as photoprotectants.

Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture using Borgnis potentials II Application to the study of focal shift

Focal shift of the converging spherical wavefront light diffracted by a circular aperture is numerically studied with the method of calculating the vector diffractive field by using Borgnis potentials given in Part I [J. Opt. Soc. Am. A23, 872 (2006)]. The quantitative dependence of the focal shift on the geometric parameters is discussed. The focal shift is mainly determined by the Fresnel number (N(f)) on the geometric focusing plane of the converging light, and an empirical formula between the fractional focal shift and the Fresnel number is deduced for N(f)<2. The focal shift of the same geometry is also studied on the basis of the scalar Rayleigh theory of diffraction, and its comparison with and difference from the result of our method are presented.

Experimental study of optical second-harmonic scattering from spherical nanoparticles

Optical second-harmonic (SH) generation from the surface of spherical particles of radii much smaller than the optical wavelength has been investigated experimentally. Angle- and polarization-resolved measurements from dye-coated polystyrene spheres have been obtained for radii of 55 and $85\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The SH signals obey general axial- and polarization-selection rules. The polarization-resolved angular patterns agree with the electromagnetic theory of SH Rayleigh scattering that describes the process in terms of locally excited quadrupolar and nonlocally excited dipolar emission. The experimental results differ significantly from those predicted for a local dipole-allowed SH scattering process.

Impact of a liquid-jet produced by the collapse of laser-induced bubbles against a solid boundary

The mechanical effect induced by the collapse of cavitation bubbles in the neighborhood of a solid boundary is investigated by focusing a Q-switched laser pulse on a metal target in water. By means of a fiber-coupling optical beam deflection technique, the displacement generated by liquid-jet impact at the final stage of the bubble collapse is detected at the epicenter of the rear metal surface. Furthermore, combining a widely used laser-ablation model with the detection principles of this detector, the transient impact-force value loading on the target material can be easily estimated. Besides, according to experimental results and the modified Rayleigh theory, the maximum bubble radius and the liquid-jet pressure are also obtained, which are in good agreement with the results of other studies. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1525–1528, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21706

Diffraction of complex harmonic plane waves and the stimulation of transient leaky Rayleigh waves

This paper describes the interaction of complex harmonic plane waves on a periodically corrugated surface. It is shown that the ability of complex harmonic plane waves to stimulate leaky Rayleigh waves on a corrugated surface is similar to the ability of harmonic inhomogeneous waves to stimulate leaky Rayleigh waves on a smooth interface. Because the experimental generation of harmonic inhomogeneous waves is more complicated and less flexible than the generation of complex harmonic waves, the combination of complex harmonic plane waves with a diffraction grating therefore offers an excellent alternative. The theoretical model developed here is based on the well-known and experimentally verified complex harmonic wave theory and the famous Rayleigh decomposition of the diffracted field. The numerical examples are given for combinations of frequency and corrugation dimensions that justify the use of the Rayleigh theory. A study of the influence of a complex frequency on the generation of Scholte-Stoneley surface waves is performed as well.

Dispensing picoliter droplets on substrates using dielectrophoresis

Liquid dielectrophoresis is exploited to initiate rapid, transient flow of aqueous liquids along co-planar electrodes patterned on insulating substrates. The flow induced by the non-uniform electric field leads to a new electrostatic equilibrium. A reduced-order model predicts the transient motion of the rivulet. When the field is removed, capillary instability breaks up the rivulet into regularly spaced droplets. Periodic circular bumps patterned on the structure, when spaced according to the most unstable wavelength based on Rayleigh's inviscid theory for the cylindrical liquid jet, lead to uniformly spaced and sized droplets. A correction factor, based on the dimensionless Ohnesorge number, accounts successfully for the effect of viscosity.

Vibrational Energy Flow Analysis of Corrected Flexural Waves in Timoshenko Beam – Part I: Theory of an Energetic Model

In this paper, an energy flow model is developed to analyze transverse vibration including the effects of rotatory inertia as well as shear distortion, which are very important in the Timoshenko beam transversely vibrating in the medium‐to‐high frequency ranges. The energy governing equations for this energy flow model are newly derived by using classical displacement solutions of the flexural motion for the Timoshenko beam, in detail. The derived energy governing equations are in the general form incorporating not only the Euler‐Bernoulli beam theory used for the conventional energy flow model but also the Rayleigh, shear, and Timoshenko beam theories. Finally, to verify the validity and accuracy of the derived model, numerical analyses for simple finite Timoshenko beams were performed. The results obtained by the derived energy flow model for simple finite Timoshenko beams are compared with those of the classical solutions for the Timoshenko beam, the energy flow solution, and the classical solution for the Euler‐Bernoulli beam with various excitation frequencies and damping loss factors of the beam. In addition, the vibrational energy flow analyses of coupled Timoshenko beams are described in the other companion paper.

The historical bases of the Rayleigh and Ritz methods

Rayleigh's classical book Theory of Sound was first published in 1877. In it are many examples of calculating fundamental natural frequencies of free vibration of continuum systems (strings, bars, beams, membranes, plates) by assuming the mode shape, and setting the maximum values of potential and kinetic energy in a cycle of motion equal to each other. This procedure is well known as “Rayleigh's Method.” In 1908, Ritz laid out his famous method for determining frequencies and mode shapes, choosing multiple admissible displacement functions, and minimizing a functional involving both potential and kinetic energies. He then demonstrated it in detail in 1909 for the completely free square plate. In 1911, Rayleigh wrote a paper congratulating Ritz on his work, but stating that he himself had used Ritz's method in many places in his book and in another publication. Subsequently, hundreds of research articles and many books have appeared which use the method, some calling it the “Ritz method” and others the “Rayleigh–Ritz method.” The present article examines the method in detail, as Ritz presented it, and as Rayleigh claimed to have used it. It concludes that, although Rayleigh did solve a few problems which involved minimization of a frequency, these solutions were not by the straightforward, direct method presented by Ritz and used subsequently by others. Therefore, Rayleigh's name should not be attached to the method.

Validation d’un banc hydrodynamique pour la caractérisation de produits de contraste ultrasonores (PCUS)

Purpose Validation of an experimental ultrasound system on erythrocyte suspensions with variable levels of aggregation and application to the echogenicity quantification of UCA under quasi-physiologic flow conditions. Materials and Methods The system is constituted with a Couette cell with variable applied shear rates, an ultrasound emitter/receiver and a digital scope for radio-frequency signal acquisition. Ultrasound indices (UI) were defined for the two experimental established protocols based on the gold standard laser methodology. Washed red cells with or without variable Dextran 70 kD concentrations were used to simulate a wide particle size range. A preliminary application to UCA was conducted with Levovist ® for calibration of the system. Results For each protocol, applied ten times on identical whole blood samples, a student t-test revealed no significant variation for all UI. Results on washed red cells were in good agreement with Rayleigh's theory of ultrasound backscattering. Significant correlations were obtained between laser and UI for washed red cells with different Dextran concentrations. An elevation of 12.13 dB in backscattered intensity was obtained after addition of Levovist ®. Conclusion The constituted Couette system allowed reproducible and accurate echogenicity quantification of small scatterers such as UCA in quasi-physiologic blood flow conditions.