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Journal articles on the topic 'Rayleigh analysis'

Author: Grafiati

Published: 6 September 2023

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1

Hubral, P., and M. Tygel. "Analysis of the Rayleigh pulse." GEOPHYSICS 54, no. 5 (May 1989): 654–58. http://dx.doi.org/10.1190/1.1442692.

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Seismologists make frequent use of wavelets (also referred to as signals, signatures, or pulses), particularly in such fields as seismic filtering, wavelet processing, wave‐propagation modeling, and trace inversion. Whenever possible, the actual seismic wavelet of the real source should be considered (Hosken, 1988). However, frequently, particularly in wave‐propagation modeling, one must consider a synthetic source wavelet. This should, if possible, be given by a simple mathematical formula and possess an easy description for its most important spectral properties (e.g., amplitude and phase spectrum, main frequency, Hilbert transform, etc.). Moreover, the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained.

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2

Cardoso, Fernando, Partially supported by CNP, q. sub, esub Brazil, Fernando Cardoso, Partially supported by CNP, q. sub, and esub Brazil. "Rayleigh Quasimodes In Linear Elasticity." Communications in Partial Differential Equations 17, no. 7 (1992): 87–100. http://dx.doi.org/10.1080/03605309208820888.

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3

Gupta, J. R., and M. B. Kaushal. "Generalized hydromagnetic Rayleigh-Taylor instability." Journal of Mathematical Analysis and Applications 134, no. 1 (August 1988): 51–63. http://dx.doi.org/10.1016/0022-247x(88)90006-6.

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4

Qingling, Du, Liu Zhengping, and Liu Shijie. "Analysis of Influencing Factors and Numerical Simulation of Horizontal-to-Vertical Spectral Ratio Method." Journal of Earthquake and Tsunami 14, no. 01 (September 18, 2019): 2050004. http://dx.doi.org/10.1142/s1793431120500049.

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To improve the calculation accuracy of the horizontal-to-vertical spectral ratio (HVSR) method, this study theoretically analyzed the influencing factors of Rayleigh wave polarizability. The phase difference of the horizontal component and the phase difference of the vertical component are found to play a key role in calculating the polarizability. The influence mechanism of the superposition of body waves and different Rayleigh waves on the polarizability of the Rayleigh wave is derived. The effects of the body wave, amplitude, frequency and Rayleigh wave superposition of different sources on the polarizability are verified by numerical simulation. The results show that the body wave significantly interferes with the polarizability of the Rayleigh wave. When a signal contains more than one set of Rayleigh waves, the superposition of the same-source Rayleigh waves does not affect the ratio. However, the superposition of Rayleigh waves from different sources significantly interferes with the calculation of the polarizability. This provides a technical method and a theoretical basis for accurately extracting the Rayleigh wave polarizability dispersion curve from a seismic record signal. This would help improve the detection accuracy of the HVSR method for ground pulse signals.

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5

Bosner, Nela, and Zlatko Drmač. "Subspace Gap Residuals for Rayleigh–Ritz Approximations." SIAM Journal on Matrix Analysis and Applications 31, no. 1 (January 2009): 54–67. http://dx.doi.org/10.1137/070689425.

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6

Tang, Ping Tak Peter. "Dynamic Condition Estimation and Rayleigh–Ritz Approximation." SIAM Journal on Matrix Analysis and Applications 15, no. 1 (January 1994): 331–46. http://dx.doi.org/10.1137/s0895479892226603.

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7

Batterson, Steve, and John Smillie. "The Dynamics of Rayleigh Quotient Iteration." SIAM Journal on Numerical Analysis 26, no. 3 (June 1989): 624–36. http://dx.doi.org/10.1137/0726037.

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8

Kaminski, Allison, and James McDaniel. "Analysis of modified structures by Rayleigh quotient." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A344. http://dx.doi.org/10.1121/10.0008528.

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In structural vibrations, the Rayleigh quotient may be used to calculate the natural frequency (or eigenvalue) of a structure given the corresponding mode shape (or eigenvector). Previous works have shown that the eigenvalue may be calculated relatively accurately using the Rayleigh quotient as long as an appropriate guess is made for the eigenvector. Typically, the Rayleigh quotient is used to predict the eigenvalues when the structure does not change. However, in this work the structure will be modified and the change in the eigenvalue will be predicted using the Rayleigh quotient. In order to use the Rayleigh quotient a guess for the eigenvector must be made. Here, the displacement vector of the nominal structure forced near a resonance will be used as the guess. Analysis and computations will be done for an undamped beam that is harmonically forced. To modify the structure, the stiffness elements will be scaled. Using this approach, it will be demonstrated that changes in the natural frequencies can be predicted relatively quickly for a modified structure. In addition, this method provides insight into which elements should be scaled to get the greatest frequency change. [Work supported by ONR under Grant N00014-19-1-2100.]

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9

Jimenez, Javier, and Juan A. Zufiria. "A boundary-layer analysis of Rayleigh-Bénard convection at large Rayleigh number." Journal of Fluid Mechanics 178 (May 1987): 53–71. http://dx.doi.org/10.1017/s0022112087001113.

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A boundary-layer analysis is presented for the two-dimensional nonlinear convection of an infinite-Prandtl-number fluid in a rectangular enclosure, in the limit of large Rayleigh numbers. Particular emphasis is given to the analysis of the periodic boundary layers, and on the removal of the singularities that appear near the corners of the cell. It is argued that this later step is necessary to ensure the correctness of the boundary-layer assumptions. Numerical values are obtained for the heat transfer and stress characteristics of the flow.

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10

FASANA, A., and S. MARCHESIELLO. "RAYLEIGH-RITZ ANALYSIS OF SANDWICH BEAMS." Journal of Sound and Vibration 241, no. 4 (April 2001): 643–52. http://dx.doi.org/10.1006/jsvi.2000.3311.

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11

Beattie, Christopher, and David W. Fox. "Localization Criteria and Containment for Rayleigh Quotient Iteration." SIAM Journal on Matrix Analysis and Applications 10, no. 1 (January 1989): 80–93. http://dx.doi.org/10.1137/0610006.

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12

Adnan, Mian Arif Shams, and Humayun Kiser. "A class of rayleigh mixtured distributions." Journal of Interdisciplinary Mathematics 14, no. 5-6 (October 2011): 507–22. http://dx.doi.org/10.1080/09720502.2011.10700769.

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13

Cheung, Wing-Sum, and Jingli Ren. "Periodic solutions for -Laplacian Rayleigh equations." Nonlinear Analysis: Theory, Methods & Applications 65, no. 10 (November 2006): 2003–12. http://dx.doi.org/10.1016/j.na.2005.11.002.

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14

Aich, Walid, Imen Hajri, and Ahmed Omri. "Numerical analysis of natural convection in a prismatic enclosure." Thermal Science 15, no. 2 (2011): 437–46. http://dx.doi.org/10.2298/tsci1102437a.

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Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

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15

Diwan, Sourabh S. "Necessary conditions for spatial inviscid instability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140607. http://dx.doi.org/10.1098/rspa.2014.0607.

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Rayleigh’s inflection point theorem and Fjortoft’s theorem provide necessary conditions for inviscid temporal instability of a plane parallel flow. Although these theorems have been assumed to hold in the spatial framework also, a rigorous theoretical basis for such an application is not available in the literature. In this paper, we provide such a basis by carrying out a formal analysis of the Rayleigh equation. We prove that, under certain conditions satisfied by a wide class of flows, the Rayleigh and Fjortoft theorems are applicable to the spatial stability problem also. This work thus fills the lacuna in the spatial stability theory with regard to these classical theorems.

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16

Zhang, Lei-Hong, Jungong Xue, and Ren-Cang Li. "Rayleigh--Ritz Approximation For the Linear Response Eigenvalue Problem." SIAM Journal on Matrix Analysis and Applications 35, no. 2 (January 2014): 765–82. http://dx.doi.org/10.1137/130946563.

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17

Knyazev, Andrew V., and Merico E. Argentati. "Rayleigh–Ritz Majorization Error Bounds with Applications to FEM." SIAM Journal on Matrix Analysis and Applications 31, no. 3 (January 2010): 1521–37. http://dx.doi.org/10.1137/08072574x.

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18

Ramm, Alexander G., and Semion Gutman. "Modified Rayleigh conjecture method and its applications." Nonlinear Analysis: Theory, Methods & Applications 68, no. 12 (June 2008): 3884–908. http://dx.doi.org/10.1016/j.na.2007.04.028.

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19

Palymskii, I. B. "Simulation of complex regimes of Rayleigh-Benard convection." Numerical Analysis and Applications 4, no. 2 (April 2011): 145–66. http://dx.doi.org/10.1134/s1995423911020066.

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20

Szyld, Daniel B. "Criteria for Combining Inverse and Rayleigh Quotient Iteration." SIAM Journal on Numerical Analysis 25, no. 6 (December 1988): 1369–75. http://dx.doi.org/10.1137/0725078.

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21

Chen, Xiao Ming, Jin Duan, Hu Qi, and Yun Gui Li. "Rayleigh Damping in Abaqus/Explicit Dynamic Analysis." Applied Mechanics and Materials 627 (September 2014): 288–94. http://dx.doi.org/10.4028/www.scientific.net/amm.627.288.

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In the nonlinear time-history analysis for high-rise building, different damping models may lead to results with great difference. Limited by the stable time increment, the stiffness proportional damping is usually neglected in Abaqus/Explicit, and only a simplified mass proportional damping is used, which can be derived from the fundamental frequency and the critical damping factor. In this paper, the influence on the results of this method has been researched by numerical examples, the numerical results also show that the stiffness proportional damping cannot be neglected. Based on these comparisons, a more reasonable damping model is presented for improving the results of high frequencies.

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22

Prakash, Gyan. "Bayesian Analysis Under Progressively Censored Rayleigh Data." Journal of Modern Applied Statistical Methods 14, no. 2 (November 1, 2015): 110–22. http://dx.doi.org/10.22237/jmasm/1446351000.

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23

VENTURI, DANIELE, XIAOLIANG WAN, and GEORGE EM KARNIADAKIS. "Stochastic bifurcation analysis of Rayleigh–Bénard convection." Journal of Fluid Mechanics 650 (April 6, 2010): 391–413. http://dx.doi.org/10.1017/s0022112009993685.

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Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by different stochastic modelling approaches. Deterministic stability analysis is carried out first to obtain steady-state solutions and primary bifurcations. It is found that multiple stable steady states coexist, in agreement with recent results, within specific ranges of Rayleigh number. Stochastic simulations are then conducted around bifurcation points and transitional regimes. The influence of random initial flow states on the development of supercritical convection patterns is also investigated. It is found that a multi-element polynomial chaos method captures accurately the onset of convective instability as well as multiple convection patterns corresponding to random initial flow states.

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24

Dalziel, Stuart B. "Rayleigh-Taylor instability: experiments with image analysis." Dynamics of Atmospheres and Oceans 20, no. 1-2 (November 1993): 127–53. http://dx.doi.org/10.1016/0377-0265(93)90051-8.

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25

Sheu, G. J., and S. M. Yang. "Dynamic analysis of a spinning Rayleigh beam." International Journal of Mechanical Sciences 47, no. 2 (February 2005): 157–69. http://dx.doi.org/10.1016/j.ijmecsci.2005.01.007.

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26

To, W. M., and D. J. Ewins. "Structural modification analysis using Rayleigh quotient iteration." International Journal of Mechanical Sciences 32, no. 3 (January 1990): 169–79. http://dx.doi.org/10.1016/0020-7403(90)90013-9.

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27

Notay, Yvan. "Convergence Analysis of Inexact Rayleigh Quotient Iteration." SIAM Journal on Matrix Analysis and Applications 24, no. 3 (January 2003): 627–44. http://dx.doi.org/10.1137/s0895479801399596.

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28

Tan, Lin, Wen Du, Yan Zhang, Li-Juan Tang, Jian-Hui Jiang, and Ru-Qin Yu. "Rayleigh scattering correction for fluorescence spectroscopy analysis." Chemometrics and Intelligent Laboratory Systems 203 (August 2020): 104028. http://dx.doi.org/10.1016/j.chemolab.2020.104028.

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29

Kent, E. F. "Numerical analysis of laminar natural convection in isosceles triangular enclosures." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 5 (February 4, 2009): 1157–69. http://dx.doi.org/10.1243/09544062jmes1122.

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In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

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30

Oluyede, Broderick, Boikanyo Makubate, Adeniyi Fagbamigbe, and Precious Mdlongwa. "A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications." Stats 1, no. 1 (June 9, 2018): 77–91. http://dx.doi.org/10.3390/stats1010006.

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A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

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31

Tagawa, Toshio. "Numerical Analysis of Linear Traveling Wave in Rotating Rayleigh–Bénard Convection with an Adiabatic Sidewall." Fluids 8, no. 3 (March 8, 2023): 96. http://dx.doi.org/10.3390/fluids8030096.

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In rotating Rayleigh–Bénard problems, convection with traveling waves may occur near the sidewalls. The Rayleigh number, Taylor number and Prandtl number are involved in this phenomenon, and the convection mode is determined depending on their values. We focused on the onset of this convection with traveling waves under the assumption that centrifugal force is neglected. By conducting two-dimensional linear stability analyses assuming periodicity of the flow and temperature fields along the sidewall direction, we investigated the effect of the Taylor number and the Prandtl number on the critical Rayleigh number and also attempted to understand the phenomenon qualitatively through three-dimensional visualizations. It was exhibited that as the Taylor number increases, the wave number, the Rayleigh number and the phase speed are found to increase. On the other hand, as the Prandtl number decreases, the wavenumber and the Rayleigh number decrease, but the phase velocity increases. The present analyses suggest that convection modes localized near the sidewalls are unlikely to emerge for low Prandtl number cases, which are comparable to those of liquid metals.

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32

Ikeda, Tatsunori, Toshifumi Matsuoka, Takeshi Tsuji, and Toru Nakayama. "Characteristics of the horizontal component of Rayleigh waves in multimode analysis of surface waves." GEOPHYSICS 80, no. 1 (January 1, 2015): EN1—EN11. http://dx.doi.org/10.1190/geo2014-0018.1.

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In surface-wave analysis, S-wave velocity estimations can be improved by the use of higher modes of the surface waves. The vertical component of P-SV waves is commonly used to estimate multimode Rayleigh waves, although Rayleigh waves are also included in horizontal components of P-SV waves. To demonstrate the advantages of using the horizontal components of multimode Rayleigh waves, we investigated the characteristics of the horizontal and vertical components of Rayleigh waves. We conducted numerical modeling and field data analyses rather than a theoretical study for both components of Rayleigh waves. As a result of a simulation study, we found that the estimated higher modes have larger relative amplitudes in the vertical and horizontal components as the source depth increases. In particular, higher-order modes were observed in the horizontal component data for an explosive source located at a greater depth. Similar phenomena were observed in the field data acquired by using a dynamite source at 15-m depth. Sensitivity analyses of dispersion curves to S-wave velocity changes revealed that dispersion curves additionally estimated from the horizontal components can potentially improve S-wave velocity estimations. These results revealed that when the explosive source was buried at a greater depth, the horizontal components can complement Rayleigh waves estimated from the vertical components. Therefore, the combined use of the horizontal component data with the vertical component data would contribute to improving S-wave velocity estimations, especially in the case of buried explosive source signal.

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33

Liu, Bin, Shi Yun Dong, Bin Shi Xu, and Peng He. "Study on Surface Stress Measurement of Laser Cladding Fe-Based Alloy Coating Based on Rayleigh Wave Signal Analysis." Advanced Materials Research 399-401 (November 2011): 2177–80. http://dx.doi.org/10.4028/www.scientific.net/amr.399-401.2177.

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Experimental study on surface stress measurement of laser cladding Fe-based alloy coating based on Rayleigh wave acoustoelastic theory was introduced. Two Rayleigh wave transducers with 5MHz frequency, the distance between which was fixed, were employed to measure the difference in time of flight along the surface of laser cladding Fe-based alloy coating. Rayleigh wave signal responding to different tensile stress was collected and the difference in time of flight between unstressed and each stressed Rayleigh wave signal was calculated with normalized cross correlation function. Results show that the propagation velocity of Rayleigh wave linearly increases with tensile stress increasing, and the maximum difference in time of flight is obtained at tensile stress level of 492MPa, while the relation between tensile stress and the difference in time of flight is obscure with tensile stress further increasing. Furthermore, the thickness of laser cladding Fe-based alloy coating and the deformation of coating surface may result in errors in experiment. Finally the surface stress of laser cladding Fe-based alloy coating is evaluated by Rayleigh wave acoustoelastic technique and the experimental result is well compared with the theoretical value.

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34

Nasiru, Suleman, Peter N. Mwita, and Oscar Ngesa. "Discussion on Generalized Modified Inverse Rayleigh." Applied Mathematics & Information Sciences 12, no. 1 (January 1, 2018): 113–24. http://dx.doi.org/10.18576/amis/120110.

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35

Venegas, Iriarte, Astorga, G ´ omez, Osvaldo, Yuri A. ,. Juan M. ,. Hector W. "Lomax-Rayleigh Distribution with an Application." Applied Mathematics & Information Sciences 13, no. 5 (September 1, 2019): 741–48. http://dx.doi.org/10.18576/amis/130506.

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36

Yu, Ling Ling. "Damping Value for Seismic Response Analysis of Long-Span Bridges." Applied Mechanics and Materials 90-93 (September 2011): 1522–25. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.1522.

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The current problems on damping in seismic response analysis of bridges is presented. The Rayleigh damping theory is simply introduced in this paper. Taking the Longtan River Bridge for instance, the finite element model of Longtan River Bridge (left line) is established. Then, the dynamic properties of the bridge is analyzed. Based on this, the Rayleigh damping constants and in an ANSYS dynamic analysis are obtained.

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37

Dostanić, Milutin R. "Fourier Expansions with Respect to the Rayleigh System." Journal of Approximation Theory 104, no. 1 (May 2000): 1–20. http://dx.doi.org/10.1006/jath.1999.3443.

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38

Xie, Xuming. "Existence and uniqueness of analytic solution for Rayleigh–Taylor problem." Journal of Differential Equations 237, no. 1 (June 2007): 116–32. http://dx.doi.org/10.1016/j.jde.2007.03.004.

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39

Beck, Thomas, Philippe Sosoe, and Percy Wong. "Duchon–Robert solutions for the Rayleigh–Taylor and Muskat problems." Journal of Differential Equations 256, no. 1 (January 2014): 206–22. http://dx.doi.org/10.1016/j.jde.2013.09.001.

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40

Rommes, Joost, and Gerard L. G. Sleijpen. "Convergence of the Dominant Pole Algorithm and Rayleigh Quotient Iteration." SIAM Journal on Matrix Analysis and Applications 30, no. 1 (January 2008): 346–63. http://dx.doi.org/10.1137/060671401.

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41

Gamblin, Didier. "Construction de quasimodes de Rayleigh à grande durée de vie." Journal of Functional Analysis 236, no. 1 (July 2006): 201–43. http://dx.doi.org/10.1016/j.jfa.2006.02.021.

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42

Zhou, Guo Liang, and Xiao Jun Li. "Improved Large Mass Method for Structural Base Excitation Analysis." Applied Mechanics and Materials 29-32 (August 2010): 1588–93. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1588.

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To verify the precision and possible applicability of the large mass method (LMM) widely used in multiple-supported structures subjected to non-uniform base excitations, numerical simulations of a two-degrees-of-freedom (2-DOF) finite element model using the Rayleigh damping assumption are performed respectively according to the LMM and the relative motion method (RMM). Through comparisons with the RMM, the error origins and the applicability of the LMM are discussed. Then the improved LMM is presented herein based on the modification of ground motions considering the influences of Rayleigh damping coefficient α. It indicates that the LMM is not applicable to multi-support excitation analysis in the case of Rayleigh damping, which can cause significant errors. And the errors depend on the damping coefficient α. It’s also proved that the improved LMM is able to yield results that are identical to those of the RMM.

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43

Yang, Li Ming, Jia Guo, Hong Wei Ding, Yong Wang, and Yi Fan Zhao. "Simulation Implementation and Analysis of the OFDM Modulated by MPSK and M-QAM." Applied Mechanics and Materials 543-547 (March 2014): 2221–24. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2221.

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Simulated for OFDM system modulated by 16PSK, 16QAM and 64QAM, and then we compared and analyzed their performance in the Rayleigh channel and 2 paths Rayleigh channel. Simulation results show that under the same conditions, Bit Error Rate (BER) of MQAM modulation system is lower than the same order MPSKs

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44

Vancoppenolle, M., D. Notz, F. Vivier, J. Tison, B. Delille, G. Carnat, J. Zhou, et al. "Technical Note: On the use of the mushy-layer Rayleigh number for the interpretation of sea-ice-core data." Cryosphere Discussions 7, no. 4 (July 1, 2013): 3209–30. http://dx.doi.org/10.5194/tcd-7-3209-2013.

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Abstract. We examine some practical aspects of using a mushy-layer Rayleigh number for the interpretation of sea-ice-core data. In principle, such analysis should allow one to determine convectively active regions within the ice core by identifying those regions in which the mush-Rayleigh number is super-critical. In practice, however, a quantitative analysis is complicated by uncertainties regarding the specific formulation of both the mush-Rayleigh number itself and of the sea-ice permeability that is crucial for quantifying the Rayleigh number. Additionally, brine loss from highly permeable sections of the ice core, in particular close to the ice–ocean interface, and typically weekly ice core sampling, limit the practical applicability of the Rayleigh number for ice-core interpretation. We here quantify these uncertainties, suggest a standard method for the computation of the Rayleigh number for sea ice and discuss possibilities and limitations of ice-core interpretation based on the Rayleigh number.

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45

Rashidi, Saeede, S. Reza Hejazi, and Elham Dastranj. "Approximate symmetry analysis of nonlinear Rayleigh-wave equation." International Journal of Geometric Methods in Modern Physics 15, no. 04 (March 13, 2018): 1850055. http://dx.doi.org/10.1142/s021988781850055x.

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In this paper, the Lie approximate symmetry analysis is applied to investigate the new exact solutions of the Rayleigh-wave equation. The power series method is employed to solve some of the obtained reduced ordinary differential equations with a small parameter. We yield the new analytical solutions with small parameter which is effectively obtained by the proposed method. The concept of nonlinear self-adjointness is used to construct the conservation laws for Rayleigh-wave equation. It is shown that this equation is approximately nonlinearly self-adjoint and therefore desired conservation laws can be found using appropriate formal Lagrangians.

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46

Kakar, Rajneesh. "Analysis of the effect of gravity and nonhomogeneity on Rayleigh waves in higher-order elastic-viscoelastic half-space." Journal of the Mechanical Behavior of Materials 23, no. 3-4 (August 1, 2014): 87–93. http://dx.doi.org/10.1515/jmbm-2014-0010.

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AbstractIn this study, the coupled effects of gravity and nonhomogeneity on Rayleigh waves in an anisotropic layer placed over an isotropic viscoelastic half-space of higher order are discussed. The dispersion properties of waves are derived. The numerical solutions are also discussed for the Rayleigh waves. It is observed that the phase velocity of Rayleigh waves is influenced quite remarkably by the presence of inhomogeneity, gravity, and strain rates of the strain parameters in the half-space.

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47

Yue, D., Xudong Wang, and Feng Xu. "Performance analysis for optimum combining of Rayleigh fading signals with correlated Rayleigh interferers and noise." IEEE Signal Processing Letters 13, no. 5 (May 2006): 269–72. http://dx.doi.org/10.1109/lsp.2006.870372.

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48

Limaye, B. V., and M. T. Nair. "On the accuracy of the Rayleigh-Schrödinger approximations." Journal of Mathematical Analysis and Applications 139, no. 2 (May 1989): 413–31. http://dx.doi.org/10.1016/0022-247x(89)90118-2.

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49

Amori, Karima E., and Qasim Kadhim Hunehen. "Computational Analysis of Turbulent Natural Convection in Water Filled Tall Enclosure." Journal of Engineering 19, no. 11 (June 5, 2023): 1467–82. http://dx.doi.org/10.31026/j.eng.2013.11.08.

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Abstract:

In this study, the turbulent buoyancy driven fluid flow and heat transfer in a differentially heated rectangular enclosure filled with water is quantified numerically. The two dimensional governing differential equations are discretized using the finite volume method. SIMPLE algorithm is employed to obtain stabilized solution for high Rayleigh numbers by a computational code written in FORTRAN language. A parametric study is undertaken and the effect of Rayleigh numbers (1010 to 1014), the aspect ratio (30, 40 and 50), and the tilt angle (10o to 170o ) on fluid flow and heat transfer are investigated. The results of the adopted model in the present work is compared with previously published results and a qualitative agreement and a good validation is obtained. Results show that the fluid circulation and temperature fields are strongly affected by the enclosure tilt angle and Rayleigh Number.

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50

Tamim, S. I., and J. B. Bostwick. "The elastic Rayleigh drop." Soft Matter 15, no. 45 (2019): 9244–52. http://dx.doi.org/10.1039/c9sm01753d.

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Abstract:

Soft gel drops exhibit shape oscillations which obey a dispersion relationship that depends upon elastocapillary and compressibility effects, thus extending the classical analysis for the Rayleigh drop to include elasticity.

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