Rayleigh Theory Research Articles

LaUV: A Physics-Based UV Light Simulator for Disinfection and Communication Applications

The sterilization properties of the C-band of the ultraviolet (UV) light have been well-known for many years; however, their application has become more vital and widespread today due to the Covid-19 pandemic. Nevertheless, minimal work has been devoted to simulating UV-C propagation for surface disinfection in indoor environments. UV light has also been proposed for non-line-of-sight (NLOS) outdoor communication applications, where a number of simulators have been developed, but with several simplifications. The current work presents a fully-featured simulator for UV light propagation, called LaUV, designed mainly for indoor settings, capable of calculating measurable parameters that can be used for indoor surface disinfection and communication applications. LaUV considers atmospheric absorption and scattering according to Rayleigh and Mie theory, and reflections from rough surfaces. The scattering cross-section and probability density function of the scattering angles (phase function) are calculated accurately for any wavelength, concentration, and diameter distribution of spherical scattering particles (aerosols and droplets). Examples are presented for indoor environments, including empty rooms and rooms with furniture, for different environmental conditions and surface albedos. Interesting initial conclusions can be drawn, considering the spatial distribution of UV exposure for surface disinfection applications and channel modeling for line-of-sight (LOS) and NLOS communication, demonstrating the versatility and the potential applications of the proposed simulator.

Analiza slobodnih transverzalnih oscilacija dva elastično povezana nosača slojem Keerovog tipa izloženog dejstvu aksijalnih pritisnih sila

Free transverse vibration of a Rayleigh double-beam system with the effect of compressive axial load with a Keer layer in-between is studied in this paper. It is assumed that the two beams of the system are continuously joined by the Keer layer. The equations of the motion for this system are described by a set of three homogenous differential equations. The classic Bernoulli-Fourier method was used for solving this system of differential equations. In the research found in literature on the subject of the Keer model, the most common methods used are the theories of Timoshenko and Euler-Bernoulli. It is for that exact reason that the research goal of this paper is determining analytical and numerical characteristics (natural frequency, associated amplitude ratio) of the considered model by applying the Rayleigh theory. What is also researched is the effect of elastic in-between layer on system's frequency and amplitudes. The numerical analysis of the system was performed using software tools. The numerical results obtained are shown in the form of a plot diagram. Presented numerical results in this paper confirm those obtained in the literature.

Temperature effects on transient behaviour of a free-falling liquid gallium drop

The present investigation presents the results of an experimental study of a free-falling liquid gallium drop in a quiescent water. Experiments were performed with different drops size in the range of 2.67 mm to 5.56 mm. All experiments were carried out under isothermal conditions, where the liquid Gallium temperature equals the temperature of the quiescent water inside the column. The temperature of both phases was investigated in the range of 30 °C to 70 °C. The study focuses on the transient behaviour of the falling drops and their aspect ratio as well as the effect of size, viscosity ratio and temperature. The captured high speed images are studied to quantify the evolution of the aspect ratio of the falling Gallium drops in time. Transient oscillations of the aspect ratio are found to exhibit a decaying trend in time. Amplitude and frequency of these oscillation were analysed. The frequency of aspect ratio oscillations were found to decrease with Eötvös number following the fD-3/2 law according to Rayleigh theory The free fall velocity of the Gallium drop is found to be highly correlated to the aspect ratio oscillations. Furthermore, whilst the oscillations amplitude was found to be sensitive to viscosity ratio, the frequency of oscillations was not affected in any noticeable way. The trends reported are limited to the range of experimental conditions investigated in this study.

The role of the “monopole” instability in the evolution of two-dimensional turbulent free shear layers

The role of instability in the growth of a two-dimensional, temporally evolving, “turbulent” free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot–Savart relation. The initial evolution of perturbations in a constant vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman–Rubach–Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan, Narasimha, and Hari Dass [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)] and a universal value of the ratio of dominant spacing of structures (Λf) to the layer thickness (δω). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing “base” flow. The model of Morris, Giridharan, and Lilley [“On the turbulent mixing of compressible free shear layers,” Proc. R. Soc. London, Ser. A 431, 219–243 (1990)], which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of Λf/δω achieved in the universal self-preserving state.

Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study

In engineering structures, to having the projected structure to serve all the engineering purposes, the theory to be used during the modeling stage is also of great importance. In the present work, an analytical solution of the free vibration of the beam composed of functionally graded materials (FGMs) is presented utilizing different beam theories. The comparison of supposed beam theory for free vibration of functionally graded (FG) beam is examined. For this aim, Euler-Bernoulli, Rayleigh, Shear, and Timoshenko beam theories are employed. The functionally graded material properties are assumed to vary continuously through the thickness direction of the beam with respect to the volume fraction of constituents. The governing equations of free vibration of FG beams are derived in the frameworks of four beam theories. Resulting equations are solved versus simply supported boundary conditions, analytically. To verify the results, comparisons are carried out with the available results. Parametrical studies are performed for discussing the effects of supposed beam theory, the variation of beam characteristics, and FGM properties on the free vibration of beams. In conclusion, it is found that the interaction between FGM properties and the supposed beam theory is of significance in terms of free vibration of the beams and that different beam theories need to be used depending on the characteristics of the beam in question.

Flame-acoustic response measurements in a high-pressure, 42-injector, cryogenic rocket thrust chamber

This work presents measurements of acoustically driven flame dynamics in a 42-element, cryogenic oxygen-hydrogen rocket thrust chamber under supercritical injection conditions. The experiment shows self-excited combustion instabilities for certain operating conditions, and this work describes the nature of the flame dynamics driving the acoustic field, as far as it can be ascertained from state-of-the-art optical measurements. Optical access has been realized in the combustion chamber with both fibre-optical probes and a viewing window. The probes collect point-like measurements of filtered OH* radiation. Their signals were used to calculate the gain and phase of intensity oscillations with respect to acoustic pressure for both stable and unstable operating conditions. Through the window, synchronized high-speed imaging of the flame in filtered OH* and blue radiation wavelengths was collected. The 2D flame response was related to the local acoustic pressure to investigate the distributed intensity and phase relationships. The flame response from OH* measurements is in agreement with the theory of Rayleigh. For stable conditions the oscillations of combustion and pressure were out of phase, whereas for an excited chamber 1T mode the oscillations were closely in phase. The integrated Rayleigh index from blue imaging was not consistent with the OH* results. The reason lies in the depth of field captured by this type of imaging, and must be used in a complementary fashion together with OH* imaging. The flame response values and 2D visualization presented in this work are expected to be of value for the validation of numerical modelling of combustion instabilities.

Vibration analysis of mass nanosensors with considering the axial-flexural coupling based on the two-phase local/nonlocal elasticity

The influences of considering coupled axial-flexural vibrations on efficiency of cantilever mass nanosensors, modeled by Rayleigh and Timoshenko beam theories, are investigated in the frame work of a paradox-free nonlocal theory, i.e. two-phase local/nonlocal elasticity. However, the effects of axial-flexural coupling due to eccentricity of attached mass have been ignored in previous studies on mass nanosensors. Governing equations, boundary conditions, and corresponding compatibility conditions are derived by means of Hamilton’s principle and differential law of two-phase elasticity. Next, The Generalized Differential Quadrature Method (GDQM) as well as Generalized Integral Quadrature Method (GIQM) are utilized to attain the discretized two-phase formulation and coupled vibration characteristics of mass nanosensor. Several analogical studies are performed in detail to confirm the credibility of the present formulation and results. Comparisons between the uncoupled and coupled vibrations disclose that there are significant errors in obtaining the natural frequencies of corresponding mass value when the axial and transverse vibrations are considered separately. Therefore, the coupling of axial-lateral displacements resulted from the added mass eccentricity must be considered. This work can be a useful step forward to examine the coupling effects on vibration behavior of mass nanosensors, and it can be helpful to design the nanosensors with higher accuracy.

A Fast Single-Image Dehazing Algorithm Based on Dark Channel Prior and Rayleigh Scattering

The scattering of atmospheric particles significantly alters images captured under hazy weather condition. Images appear distorted, blurry and low in contrast attenuation, which extensively affects computer vision systems. There has been development of several prior based methods to address this problem. However, these methods come at a high computational cost. We present a fast, single image dehazing method based on dark channel prior and Rayleigh scattering. Firstly, we present a simple but effective methodology for estimating the atmospheric light through the computation of average, minimum and maximum of the pixels in each of the three RGB colour channels. Then, using the theory of Rayleigh scattering, we model a scattering coefficient to estimate the initial transmission map. Also, a fast-guided filter is adopted to refine the initial transmission map due to inaccurate halo edges. Finally, we restore the haze-free image through the atmospheric scattering model. Extensive qualitative and computational experiments on hazy outdoor images demonstrate that the proposed method produces excellent results whiles achieving a faster processing time.

Aspect Ratio-Dependent Dynamics of Piezoelectric Transducers in Wireless Acoustic Power Transfer.

Acoustic power transfer (APT) for wireless electronic components has received growing attention as a viable approach to deliver power to remotely located small electronic devices. The design of an efficient APT system requires accurate models to describe its individual components as well as the interaction between them. Most of the analytical models available to represent the bulk piezoelectric transducers used in APT are limited to either thin rod or thin plate transducers. However, transducers with moderate aspect ratios are often used, especially at the receiver end. In this work, in addition to reviewing standard theories, models based on the Rayleigh and Bishop rod theories are developed to analyze transducers [transmitter (TX) or receiver (RX)] with various aspect ratios. Results from these models are compared with experimental data and finite-element analysis to determine the range of aspect ratios in which they are valid. In addition, fluid loading effects on the predictions of all models are investigated, and the generated pressure fields by the transducers with different aspect ratios are compared. The resulting models are used to analyze the effect of aspect ratio on the performance of the transducer when operated as a TX or an RX in an APT setting.

Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory

The main objective of the present work is devoted to the study of both free and time-dependent forced axial vibration simultaneously in single-walled carbon nanotubes subjected to a moving load. The governing equation is derived via Hamilton’s principle. Classical theory, along with the Rayleigh and Bishop theories, is used to analyze the nonlocal vibrational behaviors of single-walled carbon nanotubes. A Galerkin method is established to solve the derived equations. The boundary conditions are assumed to be clamped-clamped and clamped-free. Firstly, the variation of nondimensional natural frequencies is calculated based on the classical theory, and the effect of the nonlocal parameter, the mode number and the length is illustrated and schematically compared for clamped-clamped and clamped-free boundary conditions. Besides, the obtained nondimensional responses are compared with the results of another study to validate the accuracy of the used method. Ultimately, the dynamic axial displacement due to the moving load in the time domain has been studied for the first time. Furthermore, the effects of the thickness, length, velocity of the moving load, excitation frequency, and the nonlocal parameter based on the classical, Rayleigh, and Bishop theories are investigated in this paper. Also, the influence of the nonlocal parameter on the variations of maximum axial displacement with respect to the velocity parameter for the aforementioned boundary conditions and theories is evaluated relative to each other.

Light absorption by polluted snow cover: Internal versus external mixture of soot

The effect of impurities on spectral absorption coefficient of snow, snow absorptance and albedo is modeled and analyzed for the practically important case of soot particles. A combination of physical processes of snow formation in the atmosphere and periodic partial melting of snow cover can lead to various morphologies of contaminated snow. Therefore, both the internal mixing of soot in ice grains and the external mixing when soot is between the grains are considered. The geometrical optics approximation for large semi-transparent particles, the Rayleigh theory for small soot particles, the Maxwell-Garnett theory for the effective optical constants of ice containing soot, and the Mie theory generalized for absorption and scattering of light by two-layered spherical particles are employed. Calculations showed that a possible uneven distribution of soot in ice grains can lead to significant differences in the values of the absorption coefficient of snow cover in the visible region of the spectrum.

Modelling of Electromagnetic Scattering at Infrared Wavelengths by Pristine Ice Crystals

Cirrus clouds substantially impact Earth's atmospheric system, including its radiative budget, both of which enormously influence all scales of weather regions and processes. The shapes of ice crystals are ultimately determined by incident coordinate systems and relevant geometric models, specifically computational geometry and applied mathematics. and incident coordinate systems determine the shapes of ice crystals (Takano, Y. and Liou, K.N., 1995. Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals. Journal of the Atmospheric Sciences, 52 (7), pp.818–837.). However, the scattering solution present in the infrared's spectrum area a complex dilemma. In previous attempts to solve scattering methods, such as Rayleigh theories, Mie and T-matrix methods, various established methods have been explored. However, it is important to note that such methods are faulty at infrared wavelengths because of size parameters, which can often exceed 100, consequently resulting in intensive computation. This paper presents a new approach based on physical optics and attempts to evaluate scattering by smooth prismatic dielectric ice crystals—specifically those which are electrically large. This method suggests that the total scattered amplitude in any trend can be measured by applying the reaction theorem to a volume interval from understanding internal field distribution. Subsequently, it is possible to convert this integral to an integral over an equivalent surface current distribution, thus, enabling total surface field analysis. The scattered field solution of the proposed physical optics method has been compared with ray-launching geometrical optics. Overall, the recommend method shows a good agreement when the scatterer is considered sizably large in comparison to wavelength. The proposed method exhibits good potential to be applied for ice crystals with rough surface structure.

Full-scale 3D-modelling of the radiative heat transfer in rotary kilns with a present bed material

This work discusses the development and use of a detailed 3D radiative heat transfer model of a rotary kiln with a present bed material, used for iron ore pelletizing. A discrete ordinates method is used to solve the radiative heat transfer equation with radiative properties calculated using a weighted-sum-of-grey-gases (WSGG) model for gases and Mie and Rayleigh theory for particles including fuel, ash and soot. Measurement data gathered from a pilot-scale test furnace, comprising temperature, gas composition and particle concentration, is used in combination with temperature data and operation parameters gathered from a conventional rotary kiln to model a full-scale rotary kiln with a present bed material. The modelled cases have a thermal input of about 37 MWth and in addition to radiative heat transfer, conductive heat transfer within, as well as between, the bed and wall material are included in the model along with convective heat transfer from the gas and heat release from exothermic reactions in the bed. The model also considers the rotational wall and includes a simplified mixing model of the bed material as well as heat losses from the outside wall of the rotary kiln due to radiation and convection. For two different flames, one coal and one oil flame, surface temperatures are calculated on the inside and outside of the rotary kiln and compared to measurements. The model appears to predict the inner wall and bed surface temperatures well with errors less than 11%. The total heat transfer to the present bed material was also studied revealing that more than 80% originated from the radiative heat transfer within the furnace.

Nonlocal longitudinal, flapwise, and chordwise vibrations of rotary doubly coaxial/non-coaxial nanobeams as nanomotors

The advancement in both experiment and theory of rotating nanomotors provides a vital base for succeeding nano-electro-mechanical system technology. This paper deals with nonlocal dynamic modeling of double-nanobeam-systems with coaxial and non-coaxial patterns rotate with a rigid shaft accounting for longitudinal, flapwise, and chordwise vibrations. The full lateral interactions of doubly adjacent nanobeams due to three-dimensional vigorous van der Waals forces are considered in the framework of linear vibrations. Using Hamilton’s principle, the nonlocal equations of motion of the nanosystem are constructed by employing Rayleigh and Timoshenko beam theories. By exploiting the size-dependent mode shapes, the unknown deformation fields are appropriately discretized, the Galerkin approach is applied, and the natural frequencies associated with the longitudinal, in-plane, and out-of-plane motions are evaluated. The roles of various crucial factors, including geometrical properties of the nanosystem, nonlocality and shear effects, angular velocity, radius of the shaft, and intertube distance, in the free dynamic response of the rotating nanosystem are explained and discussed comprehensively. Further, the size-dependent critical angular velocity pertinent to the initial dynamic instability of the nanosystem is also introduced and the effects of influential parameters on this key factor are displayed.

Tunable and large plasmonic field enhancement in core-shell heterodimer/trimer

ABSTRACTHeterodimer/trimer are two/three closely adjacent nanoparticles dissimilar in shape or size, and represent a simple nanoscale geometry which gives rise to a remarkably rich set of properties. The core-shell nanostructure has advantages of tunability and stability over a similar homogeneous particle. We theoretically demonstrate tunable and significant field enhancement in both heterodimer and heterotrimer systems using core-shell geometry with a metal shell and dielectric core and compared our results with core-shell homodimer and homotrimer. The analytical modeling is based on the Rayleigh theory for small particles and Foldy–Lax multi-scattering theory for multiple particles. It is shown that the E-field can be enhanced in core-shell dimer/trimer due to the plasmonic resonance in the metal shell, which can be easily tunable by changing the core-shell ratio, composition of the core and shell, relative size and distance between the particles, and wavelength of the incident light. We report significant maximum field intensity enhancement near the particles. Moreover, this tunable nanostructures with high field intensity can be useful as potential bio-sensing applications.

Aftereffect of high-order nonlinearity on extreme wave occurrence from deep to intermediate water

Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave and they have become an important topic in engineering and science. However, it is not clear the behavior of extreme waves in deep-water shoaling toward shallow water; the transient behavior of high-order nonlinearity on the slope and its effect on the wave pressure acting on the breakwater. In this study, a series of experiments with several bathymetry configurations from deep to shallow water were conducted for unidirectional random waves. The dependence of the kurtosis on the extreme wave occurrence weakens if dimensionless water depth kh is shallower than 1.363, but the amplified extreme wave still remains until the surf zone. The aftereffects of the deep-water third-order nonlinearity in greater water depth give remarkable influences on random wave height distribution on the slope. Additionally, from the point of view of the design for breakwaters, it is possible to evaluate the uncertainty of wave pressures with the deviation from the Rayleigh theory through the extreme wave occurrence depending on the kurtosis changing.

Vertical profile observations of water vapor deuterium excess in the lower troposphere

Abstract. We use airborne measurements of water vapor (H2Ov) stable isotopologues and complementary meteorological observations to examine how boundary layer (BL) dynamics, cloud processing, and atmospheric mixing influence the vertical structure of δD, δ18O, and deuterium excess (d excess =δD–8×δ18O) in the BL, inversion layer (INV), and lower free troposphere (FT). Flights were conducted around two continental US cities in February–March 2016 and included vertical profiles extending from near the surface to ≤2 km. We examine observations from three unique case study flights in detail. One case study shows observations that are consistent with Rayleigh isotopic distillation theory coinciding with clear skies, dry adiabatic lapse rates within the boundary layer, and relatively constant vertical profiles of wind speed and wind direction. This suggests that the air mass retained the isotopic fingerprint of dehydration during moist adiabatic processes upwind of the study area. Also, observed d-excess values in the free troposphere were sometimes larger than Rayleigh theory predicts, which may indicate mixing of extremely dehydrated air from higher altitudes. The two remaining case studies show isotopic anomalies in the d-excess signature relative to Rayleigh theory and indicate cloud processes and complex boundary layer development. The most notable case study with stratocumulus clouds present had extremely low (negative) d-excess values at the interface of the inversion layer and the free troposphere, which is possibly indicative of cloud or rain droplet evaporation. We discuss how in situ H2Ov stable isotope measurements, and d excess in particular, could be useful for improving our understanding of water phase changes, transport, and mixing that occurs between the BL, INV, and FT.

Calculating fissility without Legendre polynomials: A walk in the woods

The original estimate of the fissility of very heavy nuclei made by Meitner and Frisch can be derived without resorting to Rayleigh's theory of vibrating liquid drops and Legendre polynomials. A simple expression, familiar from the theory of the Wilson cloud chamber, suffices.

Direct Observations of Surface‐Wave Eigenfunctions at the Homestake 3D Array

AbstractDespite the theory for both Rayleigh and Love waves being well accepted and the theoretical predictions accurately matching observations, the direct observation of their quantifiable decay with depth has never been measured in the Earth’s crust. In this work, we present observations of the quantifiable decay with depth of surface‐wave eigenfunctions. This is done by making direct observations of both Rayleigh‐wave and Love‐wave eigenfunction amplitudes over a range of depths using data collected at the 3D Homestake array for a suite of nearby mine blasts. Observations of amplitudes over a range of frequencies from 0.4 to 1.2 Hz are consistent with theoretical eigenfunction predictions. They show a clear exponential decay of amplitudes with increasing depth and a reversal in sign of the radial‐component Rayleigh‐wave eigenfunction at large depths, as predicted for fundamental‐mode Rayleigh waves. Minor discrepancies between the observed eigenfunctions and those predicted using estimates of the local velocity structure suggest that the observed eigenfunctions could be used to improve the velocity model. Our results confirm that both Rayleigh and Love waves have the depth dependence that they have long been assumed to have. This is an important direct validation of a classic theoretical result in geophysics and provides new observational evidence that classical seismological surface‐wave theory can be used to accurately infer properties of Earth structure and earthquake sources.

Dynamics of fluid conveying pipes using Rayleigh theory under non-classical boundary conditions

Abstract The dynamic behavior of fluid conveying pipe has been investigated by using Rayleigh theory to present the effect of non-classical boundary conditions on natural frequencies. The assumption of ideal fluid is used for acquiring the equation of motion for a uniform Rayleigh pipe. The ideal fluid moves in the vertical direction with pipe and the pipe makes small oscillations by Hamilton’s variation principle. Euler equation is adopted for the modeling of the flow behavior in the pipe. Accordingly, the dimensionless partial differential equations of motion are converted into matrix equations and solved for two different set of non-classical boundary conditions. The natural frequencies are obtained depending on fluid velocity and stiffnesses of boundary conditions by using Rayleigh Theory. The effect of mass ratio and slenderness ratio on vibration frequency is examined for the first three modes. The one-way FSI (Fluid–Structure Interaction) technique is used by ANSYS software to determine natural frequencies of pipe. The results of first natural frequency based on the numerical solution performed by using ANSYS-FSI are compared with the results of analytical solution for Rayleigh pipe.