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1
ZHONG, WEI-PING. "ROGUE WAVE SOLUTIONS OF THE GENERALIZED ONE-DIMENSIONAL GROSS–PITAEVSKII EQUATION." Journal of Nonlinear Optical Physics & Materials 21, no. 02 (June 2012): 1250026. http://dx.doi.org/10.1142/s0218863512500269.
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By considering a simple one-dimensional Gross–Pitaevskii equation with variable coefficient, we study various rogue waves by the choice of different trapping potential coefficient. The trapping potential coefficient is used as an independent parameter function; a simple procedure is established to obtain different chasses of the scattering length and rogue wave solutions by using similarity transformation. A few properties of rogue wave solutions are also discussed. Our results demonstrate that the rogue waves can be controlled by selecting appropriate trapping potential coefficients.
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Sugaya, R. "Momentum-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma." Journal of Plasma Physics 56, no. 2 (October 1996): 193–207. http://dx.doi.org/10.1017/s0022377800019206.
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The momentum-space diffusion equation and the kinetic wave equation for resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov–Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave—wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation, and are expressed in terms of the nonlinear wave—wave coupling coefficient in the kinetic wave equation. The conservation laws for the total energy and momentum densities of waves and particles are verified from the kinetic wave equation and the transport equations. These equations are very useful for the theoretical analysis of transport phenomena or the acceleration and generation of high-energy or relativistic particles caused by quasi-linear and resonant wave—wave scattering processes.
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Kumar, Uma Vinod. "Scattering of Gravity Waves by a Rectangular Floating Flexible Porous Plate." Journal of Advanced Research in Applied Mathematics and Statistics 06, no. 1&2 (May 7, 2021): 4–11. http://dx.doi.org/10.24321/2455.7021.202102.
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Scattering of oblique surface gravity waves by a finite, floating porous-elastic plate is investigated, with assumptions of linear water wave theory and plate response. A boundary value problem is set up, wherein the thin plate equation together with a porosity parameter is used to formulate the condition on the floating plate. A matched eigenfunction approach is adopted for the solution of this problem, with roots of the dispersion relation being located with the aid of contour plots, and various hydrodynamic scattering quantities are computed. Energy dissipation due to plate porosity is seen to have a significant impact on both reflection and transmission of waves, while flexibility of plate only alters the extent of wave reflection by porous elastic plates. An oscillatory trend is shown by reflection coefficient for smaller values of relative plate width, and there is no variation in reflection or transmission coefficients when the plate width is increased beyond a certain cut-off value. Comparison of scattering properties of four different types of plates highlights the effects of porosity and flexibility and establishes the superiority of a flexible porous plate as a wave attenuating device, with moderate reflection, high energy dissipation and low transmission.
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Kar, Prakash, Harekrushna Behera, and Trilochan Sahoo. "Oblique Long Wave Scattering by an Array of Bottom-Standing Non-Smooth Breakwaters." Fluids 7, no. 11 (November 15, 2022): 352. http://dx.doi.org/10.3390/fluids7110352.
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Bragg scattering of surface gravity waves by an array of submerged bottom-standing non-smooth breakwaters is studied under the assumption of linearized long wave theory. The closed-form long-wave analytical solutions are derived and validated by comparing them with the results available in the literature. The role of various physical parameters such as breakwaters friction coefficient, depth, width and gap between the adjacent breakwaters are investigated by analyzing the reflection and transmission coefficients. Further, the time-domain simulation for the scattering of long gravity waves over multiple breakwaters is analysed for different values of parameters of breakwaters. The results reveal that the rough surface of the breakwater plays a vital role in reducing wave reflection and transmission. Moreover, it is observed that the transmitted wave dissipates completely for larger values of friction parameters. For certain critical angles, change in wave dissipation becomes maximum due to the variation of phase of the incident wave. Various findings can be considered as benchmark results for the design of the non-smooth structures to attenuate the waves based on the Bragg reflection.
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Guo, Yinjing, Yuanyuan Ju, Zhen Liu, and Jianhua Zhang. "A Propagation Loss Coefficient Model of Low-Frequency Elastic Wave in Coal Strata Set." Mathematical Problems in Engineering 2020 (March 9, 2020): 1–7. http://dx.doi.org/10.1155/2020/6832362.
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Elastic waves cause energy loss during the transmission of coal measures. These losses include propagation loss, dielectric absorption loss, scattering loss, and frequency migration loss. The absorption loss is mainly caused by the inelastic absorption. The scattering loss is caused by the uneven heat absorption in the formation. The frequency shift loss is caused by the piezoelectric effect of coal-bearing formations and the intermodulation of different frequency signals. After considering the influence factors of the coal seam structure, this paper presents a model of low-frequency elastic waves loss coefficient. The paper proposed the loss coefficient of the elastic wave in the coal measure strata by considering two main attenuation mechanisms: intrinsic absorption and scattering. This paper theoretically studied the effects of the model parameters such as density, porosity, particle size, and wave frequency on the loss of wave energy using COMSOL simulation. Besides, the comparison of MATLAB simulation results shows that the simulation results produced by the model proposed in this paper are similar to the models embedded in COMSOL. This work can be applied to coal, oil, and gas exploration and is also helpful to study the mechanisms of wave attention on the low-frequency band.
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Zhao, Ye, Wen-Tao Guan, and Peng-Ju Yang. "The Mono/Bistatic SAR Imaging Simulation of Sea Surface with Breaking Waves Based on a Refined Facet Scattering Field Model." International Journal of Antennas and Propagation 2021 (July 12, 2021): 1–9. http://dx.doi.org/10.1155/2021/9915688.
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In order to analyze the scattering characteristics of sea surface under high sea state, a complete scattering model of sea surface considering breaking wave is established in this study based on the refined facet scattering field model (RFSFM) and the scattering theory of breaking wave. On the basis of this model, the influence of breaking waves on the mono/bistatic SAR imaging of sea surface at HH and VV polarization is studied. The results show that with the increase in wind speed, the coverage of breaking wave increases obviously and the consideration of breaking wave has a good correction for the scattering coefficient at HH polarization under grazing incidence; however, for VV polarization, the effect of breaking wave is very small.
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Mudaliar, S. "Acoustic wave scattering from a randomly rough surface." Canadian Journal of Physics 74, no. 9-10 (September 1, 1996): 641–50. http://dx.doi.org/10.1139/p96-093.
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Acoustic wave scattering from a randomly rough surface is studied using a multiple scattering analysis. Assuming the surface asperities to be small, approximate boundary conditions are used to derive a pair of coupled integral equations for the velocity potentials. The Dyson equation is next derived on introducing symbolic operators. Using the bilocal approximation the Dyson equation is solved, thereby obtaining explicit expressions for the coherent reflection and transmission coefficients. The analysis is similarly carried on further to compute the incoherent intensity by using the ladder approximation, and hence an expression for the scattering coefficient is obtained.
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Angel, Y. C. "Scattering of Love Waves by a Surface-Breaking Crack." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 587–92. http://dx.doi.org/10.1115/1.3171815.
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The interaction of Love waves with a surface-breaking crack normal to the free surface is investigated. By the use of Fourier transform techniques, the mixed-boundary value problem is reduced to a singular integral equation which is solved numerically. It is shown that the reflected and transmitted displacement fields at some distance from the crack are the superposition of a finite number of Love-wave modes. The reflection coefficients for the first three modes and the transmission coefficient are plotted versus the frequency. Several sharp resonances are observed. Each resonance corresponds to the vanishing of the amplitude of a particular Love-wave mode.
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Kohout, Alison L., Michael H. Meylan, and David R. Plew. "Wave attenuation in a marginal ice zone due to the bottom roughness of ice floes." Annals of Glaciology 52, no. 57 (2011): 118–22. http://dx.doi.org/10.3189/172756411795931525.
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AbstractWave attenuation in a diffuse marginal ice zone (MIZ) is thought to be mainly a result of wave scattering. In a compact MIZ, additional physical factors are thought to be relevant. In this paper, we propose that viscous drag, form drag and energy lost to internal waves under the ice play a role in attenuating wave energy. We derive a relation for the wave attenuation due to drag. We combine the drag attenuation coefficient with the scattering attenuation coefficient and compare the result to experimental results for compact MIZs. We find that the combined scatter and drag (CSD) model improves the rate of decay of wave attenuation in compact ice fields, but fails to predict the ‘rollover’ seen at short periods.
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Sato, Haruo. "Isotropic scattering coefficient of the solid earth." Geophysical Journal International 218, no. 3 (June 6, 2019): 2079–88. http://dx.doi.org/10.1093/gji/ggz266.
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SUMMARY The isotropic scattering model is a simple mathematical model of the radiative transfer theory (RTT) for the propagation of the wave energy density in random media. There have been many measurements of the isotropic scattering coefficient of the heterogeneous solid earth medium, where the target region varies from the lower and upper mantle, the crust, sediments, volcanoes, mines, rock samples and also the crust and the upper mantle of the moon. Reported isotropic scattering coefficients increase according to some power of frequency with some scatter. We know that the RTT is well approximated by the diffusion equation in the multiple scattering regime, where the equipartition is established. Then, the transport scattering coefficient effectively functions as an isotropic scattering coefficient even if the scattering coefficient derived by the Born approximation for the random velocity fluctuation is anisotropic. Recent review of the power spectral density functions of random velocity fluctuations in the solid earth revealed from various kinds of measurements shows that their spectral envelope is well approximated by the inverse cube of wavenumber for a wide range of wavenumbers (Sato, 2019). The transport scattering coefficient derived from the spectral envelope linearly increases with frequency, which well explains the observed isotropic scattering coefficients for a wide range of frequencies. However, some reported isotropic scattering coefficients show unusual behaviour: the isotropic scattering coefficient increases as depth decreases in the crust and the upper mantle of the earth and the moon, those beneath volcanoes are larger than those in the lithosphere, and that in a sandstone sample with a large porosity is larger than that in a gabbro sample with little porosity. Those differences may suggest possible scattering contribution of pores and cracks widely distributed in addition to the scattering by random velocity fluctuations.
11
Zhou, Chuanping, Jiayou Weng, Zhiwen Wang, Wanrong Pei, Ning Hu, Rougang Zhou, and Youping Gong. "SH Wave Scattering and Dynamic Stress Concentration in Piezomagnetic Materials with Non-Circular Openings." Applied Sciences 13, no. 12 (June 9, 2023): 6972. http://dx.doi.org/10.3390/app13126972.
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The study uses complex variable functions and conformal mapping to investigate the scattering and dynamic stress concentration phenomena of SH waves in non-circular opening magnetic–elastic materials. Elastic dynamics and piezomagnetic equations are employed to derive expressions for the scattered wave intensity and dynamic stress concentration coefficient around non-circular openings. Special attention is devoted to elliptical openings, where different incident angles and dimensionless wave numbers exhibit varying effects on the dynamic stress concentration coefficients. The numerical results indicate a positive correlation between the dynamic stress concentration coefficient and the illumination region of elliptical openings, with low wave numbers exerting a more significant influence. These findings provide a valuable theoretical foundation for studying fatigue mechanics in piezomagnetic materials. Therefore, to enhance the performance and reliability of piezomagnetic materials, it is imperative to conduct elastic dynamic analysis of non-circular defects in low-frequency environments.
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Kneib, Guido, and Serge A. Shapiro. "Viscoacoustic wave propagation in 2-D random media and separation of absorption and scattering attenuation." GEOPHYSICS 60, no. 2 (March 1995): 459–67. http://dx.doi.org/10.1190/1.1443783.
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Wave theoretical analysis of scalar, time‐harmonic waves propagating in a constant density medium with isotropic, random velocity fluctuations and being scattered mainly in the forward direction yields a simple and robust procedure that combines the logarithm of the mean wave amplitude with the mean logarithm of the wave amplitude to perform a separation of scattering attenuation and absorption effects. Finite‐difference simulations of wave propagation in 2-D random media with a Voigt‐body rheology illustrate the evolution of wave field fluctuations and demonstrate that the separation procedure works for a wide range of seismic albedos. In the case of no absorption, the logarithms of seismic amplitudes will have a nonlinear dependence on the travel distance if the wavefield fluctuations are small compared to the amplitude of the coherent field. If these fluctuations are large, the logarithms of seismic amplitudes will tend to constant levels independent of the travel distance. In the case of random viscoacoustic media and at propagation distances larger than the inverse of the scattering coefficient of the coherent field, and apart from geometrical spreading, the overall amplitude decrease will be predominated by absorption, even if the absorption coefficient is one order smaller than the scattering coefficient of the coherent field.
13
Lacombe, C., J. L. Steinberg, C. C. Harvey, D. Hubert, A. Mangeney, and M. Moncuquet. "Density fluctuations measured by ISEE 1-2 in the Earth's magnetosheath and the resultant scattering of radio waves." Annales Geophysicae 15, no. 4 (April 30, 1997): 387–96. http://dx.doi.org/10.1007/s00585-997-0387-5.
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Abstract. Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earth's magnetosheath, the ISEE 1-2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2fp) ≃ 0.5 – 4 × 10–9 rad2/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to1RE) just downstream of the shock ramp, and close to the magnetopause.
14
Mandal, B. N., and Soumen De. "Water wave scattering by two submerged nearly vertical barriers." ANZIAM Journal 48, no. 1 (July 2006): 107–17. http://dx.doi.org/10.1017/s1446181100003448.
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AbstractThe problem of surface water wave scattering by two thin nearly vertical barriers submerged in deep water from the same depth below the mean free surface and extending infinitely downwards is investigated here assuming linear theory, where configurations of the two barriers are described by the same shape function. By employing a simplified perturbational analysis together with appropriate applications of Green's integral theorem, first-order corrections to the reflection and transmission coefficients are obtained. As in the case of a single nearly vertical barrier, the first-order correction to the transmission coefficient is found to vanish identically, while the correction for the reflection coefficient is obtained in terms of a number of definite integrals involving the shape function describing the two barriers. The result for a single barrier is recovered when two barriers are merged into a single barrier.
15
Mandal, B. N., and Sudeshna Banerjea. "Scattering of water waves by a submerged nearly circular cylinder." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 36, no. 3 (January 1995): 372–80. http://dx.doi.org/10.1017/s0334270000010481.
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AbstractThe problem of scattering of surface water waves by a horizontal circular cylinder totally submerged in deep water is well studied in the literature within the framework of linearised theory with the remarkable conclusion that a normally incident wave train experiences no reflection. However, if the cross-section of the cylinder is not circular then it experiences reflection in general. The present paper studies the case when the cylinder is not quite circular and derives expressions for reflection and transmission coefficients correct to order ∈, where ∈ is a measure of small departure of the cylinder cross-section from circularity. A simplified perturbation analysis is employed to derive two independent boundary value problems (BVP) up to first order in ∈. The first BVP corresponds to the problem of water wave scattering by a submerged circular cylinder. The reflection coefficient up to first order and the first order correction to the transmission coefficient arise in the second BVP in a natural way and are obtained by a suitable use of Green' integral theorem without solving the second BVP. Assuming a Fourier expansion of the shape function, these are evaluated approximately. It is noticed that for some particular shapes of the cylinder, these vanish. Also, the numerical results for the transmission coefficients up to first order for a nearly circular cylinder for which the reflection coefficients up to first order vanish, are given in tabular form. It is observed that for many other smooth cylinders, the result for a circular cylinder that the reflection coefficient vanishes, is also approximately valid.
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Sugaya, Reiji. "Velocity-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a plasma." Journal of Plasma Physics 45, no. 1 (February 1991): 103–13. http://dx.doi.org/10.1017/s002237780001552x.
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The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation.
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Liu, Xiling, Feng Xiong, Qin Xie, Xiukun Yang, Daolong Chen, and Shaofeng Wang. "Research on the Attenuation Characteristics of High-Frequency Elastic Waves in Rock-Like Material." Materials 15, no. 19 (September 23, 2022): 6604. http://dx.doi.org/10.3390/ma15196604.
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In order to study the frequency-dependent attenuation characteristics of high-frequency elastic waves in rock-like materials, we conducted high-frequency elastic wave attenuation experiments on marble, granite, and red sandstone rods, and investigated the frequency dependence of the attenuation coefficient of high-frequency elastic waves and the frequency dependence of the attenuation of specific frequency components in elastic waves. The results show that, for the whole waveform packet of the elastic wave signal, the attenuation coefficient and the elastic wave frequency have an approximate power relationship, with the exponents of this power function being 0.408, 0.420, and 0.384 for marble, granite, and red sandstone, respectively, which are close to 1/2 the exponent value obtained theoretically by the Kelvin–Voigt viscoelastic model. However, when the specific frequency components are tracked during the elastic wave propagation, the exponents of the power relationship between the attenuation coefficient and frequency are 0.982, 1.523, and 0.860 for marble, granite, and red sandstone, respectively, which indicate that the relationship between the attenuation coefficient and frequency is rock-type dependent. Through the analysis of rock microstructure, we demonstrate that this rock-type-dependent relationship is mainly caused by the scattering attenuation component due to the small wavelength of the high-frequency elastic wave. Therefore, the scattering attenuation component may need to be considered when the Kelvin–Voigt model is used to describe high-frequency elastic wave attenuation in rock-like materials. The results of this research are of good help for further understanding the attenuation characteristics of high-frequency elastic waves in rock-like materials.
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Liu, Yu, Chao Li, Huai-Yu Wang, and Yun-Song Zhou. "The generalized scattering coefficient method for plane wave scattering in layered structures." American Journal of Physics 85, no. 2 (February 2017): 146–54. http://dx.doi.org/10.1119/1.4965884.
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Ye, Shubing, Guobin Feng, Zhejun Feng, Zhenbao Wang, Dahui Wang, and Changqing Cao. "Properties of Scattering Fields from Gaussian Beam Incident on Rough Cylinders." Photonics 10, no. 6 (June 20, 2023): 699. http://dx.doi.org/10.3390/photonics10060699.
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At present, most researchers focus on plane wave incident on targets, but in practical applications, most of the beams are Gaussian beam. We study the scattering fields of Gaussian beam incident on rough cylinders. Coherent and incoherent scattering coefficients are obtained based on the angular spectrum expansion and physical optics approximation, and the effects of cylinder roughness, beam radius, cylinder radius and angle of incidence on scattering coefficients are analyzed. The results show that, for a constant wavelength, when the root mean square height is greater than or equal to 1/5 of the wavelength, the coherent scattering coefficient curve undergoes a change in its distribution, with the peak transforming into a trough. Furthermore, when the root mean square height is greater than or equal to 1/3 of the wavelength, the incoherent scattering coefficient experiences a decline as the root mean square height increases. The correlation length only affects the incoherent scattering coefficient. Both the coherent and incoherent scattering coefficients decrease with the increase in the incident angle. Finally, when the roughness and incident angle are constant, with the increase in the ratio of the cylinder radius to the beam waist radius, the scattered light field is more concentrated. Our results provide the theoretical basis for the measurement of the cylindrical scattering field.
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Hassanabadi, Hassan, Hadi Sobhani, and Won Sang Chung. "Scattering Study of Fermions due to Double Dirac Delta Potential in Quaternionic Relativistic Quantum Mechanics." Advances in High Energy Physics 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/8124073.
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We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.
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MAUREL, AGNES, VINCENT PAGNEUX, FELIPE BARRA, and FERNANDO LUND. "ULTRASOUND AS A PROBE OF PLASTICITY? THE INTERACTION OF ELASTIC WAVES WITH DISLOCATIONS." International Journal of Bifurcation and Chaos 19, no. 08 (August 2009): 2765–81. http://dx.doi.org/10.1142/s0218127409024475.
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An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO 3, and the ratio of longitudinal to transverse wave attenuation in a number of materials. Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.
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Dolai, P. "Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap." International Journal of Applied Mechanics and Engineering 21, no. 2 (May 1, 2016): 303–22. http://dx.doi.org/10.1515/ijame-2016-0019.
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AbstractIn this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.
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Bennetts, Luke G., and Vernon A. Squire. "On the calculation of an attenuation coefficient for transects of ice-covered ocean." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2137 (August 24, 2011): 136–62. http://dx.doi.org/10.1098/rspa.2011.0155.
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Exponential attenuation of ocean surface waves in ice-covered regions of the polar seas is modelled in a two-dimensional, linear setting, assuming that the sea ice behaves as a thin-elastic plate. Attenuation is produced by natural features in the ice cover, with three types considered: floes, cracks and pressure ridges. An inelastic damping parameterization is also incorporated. Efficient methods for obtaining an attenuation coefficient for each class of feature, involving an investigation of wave interaction theory and averaging methods, are sought. It is found that (i) the attenuation produced by long floes can be obtained from the scattering properties of a single ice edge; and (ii) wave interaction theory in ice-covered regions requires evanescent and damped-propagating motions to be included when scattering sources are relatively nearby. Implications for the integration of this model into an oceanic general circulation model are also discussed.
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FEDOROV, A. V., N. D. MALMUTH, and V. G. SOUDAKOV. "Supersonic scattering of a wing-induced incident shock by a slender body of revolution." Journal of Fluid Mechanics 585 (August 7, 2007): 305–22. http://dx.doi.org/10.1017/s0022112007006714.
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The lift force acting on a slender body of revolution that separates from a thin wing in supersonic flow is analysed using Prandtl–Glauert linearized theory, scattering theory and asymptotic methods. It is shown that this lift is associated with multi-scattering of the wing-induced shock wave by the body surface. The local and global lift coefficients are obtained in simple analytical forms. It is shown that the total lift is mainly induced by the first scattering. Contributions from second, third and higher scatterings are zero in the leading-order approximation. This greatly simplifies calculations of the lift force. The theoretical solution for the flow field is compared with numerical solutions of three-dimensional Euler equations and experimental data at free-stream Mach number 2. There is agreement between the theory and the computations for a wide range of shock-wave strength, demonstrating high elasticity of the leading-order asymptotic approximation. Theoretical and experimental distributions of the cross-sectional normal force coefficient agree satisfactorily, showing robustness of the analytical solution. This solution can be applied to the moderate supersonic (Mach numbers from 1.2 to 3) multi-body interaction problem for crosschecking with other computational or engineering methods.
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Wei, Yiwen, Lixin Guo, and Xiao Meng. "The Fast Simulation of Scattering Characteristics from a Simplified Time Varying Sea Surface." International Journal of Antennas and Propagation 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/815913.
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This paper aims at applying a simplified sea surface model into the physical optics (PO) method to accelerate the scattering calculation from 1D time varying sea surface. To reduce the number of the segments and make further improvement on the efficiency of PO method, a simplified sea surface is proposed. In this simplified sea surface, the geometry of long waves is locally approximated by tilted facets that are much longer than the electromagnetic wavelength. The capillary waves are considered to be sinusoidal line superimposing on the long waves. The wavenumber of the sinusoidal waves is supposed to satisfy the resonant condition of Bragg waves which is dominant in all the scattered short wave components. Since the capillary wave is periodical within one facet, an analytical integration of the PO term can be performed. The backscattering coefficient obtained from a simplified sea surface model agrees well with that obtained from a realistic sea surface. The Doppler shifts and width also agree well with the realistic model since the capillary waves are taken into consideration. The good agreements indicate that the simplified model is reasonable and valid in predicting both the scattering coefficients and the Doppler spectra.
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Hamid, A., and F. Cooray. "Scattering from a Buried PEMC Cylinder Illuminated by a Normally Incident Plane Wave Propagating in Free Space." Advanced Electromagnetics 8, no. 1 (December 30, 2018): 1–7. http://dx.doi.org/10.7716/aem.v8i1.873.
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A rigorous solution is presented to the problem of scattering by a perfect electromagnetic conducting (PEMC) circular cylinder buried inside a dielectric half-space that is excited by a normally incident transverse magnetic (TM) plane wave propagating in free space. The plane wave incident on the planar interface separating the two media creates fields transmitting into the dielectric half- space becoming the known primary incident fields for the buried cylinder. When the fields scattered by the cylinder, in response to those fields incident on it, are incident at the interface, they generate fields reflected into the dielectric half-space and fields transmitted into free space. These fields, and the fields scattered by the cylinder are expressed in terms of appropriate cylindrical waves consisting of unknown expansion coefficients which are to be determined. Imposing boundary conditions at the surface of the cylinder and at a point on the planar interface, enables the evaluation of the unknown coefficients. This procedure is then replicated, by considering multiple reflections and transmissions at the planar interface, and multiple scattering by the cylinder, till a preset accuracy is obtained for the reflection coefficient at the particular point on the interface. The refection coefficient at this point is then computed for cylinders of different sizes, to show how it varies with the PEMC admittance of the cylinder, its burial depth, and the permittivity of the dielectric half-space.
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Wu, Wen, Sergio Cantero-Chinchilla, Wang-ji Yan, Manuel Chiachio Ruano, Rasa Remenyte-Prescott, and Dimitrios Chronopoulos. "Damage Quantification and Identification in Structural Joints through Ultrasonic Guided Wave-Based Features and an Inverse Bayesian Scheme." Sensors 23, no. 8 (April 21, 2023): 4160. http://dx.doi.org/10.3390/s23084160.
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In this paper, defect detection and identification in aluminium joints is investigated based on guided wave monitoring. Guided wave testing is first performed on the selected damage feature from experiments, namely, the scattering coefficient, to prove the feasibility of damage identification. A Bayesian framework based on the selected damage feature for damage identification of three-dimensional joints of arbitrary shape and finite size is then presented. This framework accounts for both modelling and experimental uncertainties. A hybrid wave and finite element approach (WFE) is adopted to predict the scattering coefficients numerically corresponding to different size defects in joints. Moreover, the proposed approach leverages a kriging surrogate model in combination with WFE to formulate a prediction equation that links scattering coefficients to defect size. This equation replaces WFE as the forward model in probabilistic inference, resulting in a significant enhancement in computational efficiency. Finally, numerical and experimental case studies are used to validate the damage identification scheme. An investigation into how the location of sensors can impact the identified results is provided as well.
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Tobita, Miwa, and Yoshiharu Omura. "Scattering of energetic electrons through nonlinear cyclotron resonance with coherent whistler-mode hiss emissions." Physics of Plasmas 29, no. 11 (November 2022): 112901. http://dx.doi.org/10.1063/5.0106004.
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Recent observations have revealed that plasmaspheric hiss consists of many discrete waves called “hiss elements.” However, the interaction of energetic electrons (10 keV to several MeV) with the plasmaspheric hiss has only been simulated by the quasilinear (QL) diffusion theory, which does not take the fine wave structure into account. The QL theory cannot address nonlinear particle motions determined by the inhomogeneity factor, which influences the scattering of electrons in pitch angle and energy. This study aims to identify differences between the nonlinear wave–particle interaction and QL theory for plasmaspheric hiss emissions. We conduct test particle simulations to demonstrate the nonlinear interactions between hiss waves and electrons. The nonlinear theory is used to model hiss elements consisting of discrete frequencies and continuous phases. Unlike the other theories, the frequency and amplitude variations in time of the hiss packet are taken into account. Frequencies of the packets are determined to satisfy the separability criterion; when the criterion is met, resonance overlapping is absent, and the electrons can generate each wave element independently. The realistic simulation model of hiss waves reproduces the scattering of electrons by both first- and second-order resonances. We also evaluate the efficiency of electron scattering by calculating nonlinear diffusion coefficients. The diffusion coefficient of equatorial pitch angle is of the same order of magnitude as those calculated by the QL diffusion theory, while we find the effective acceleration of resonant electrons by successive nonlinear trapping, which is not evaluated by the QL theory.
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KIM, JIN YOUNG, H. W. LEE, and Y. S. MYUNG. "HAWKING TEMPERATURE FROM SCATTERING OFF THE CHARGED 2-D BLACK HOLE." Modern Physics Letters A 10, no. 37 (December 7, 1995): 2853–61. http://dx.doi.org/10.1142/s0217732395002994.
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The charged 2-D black hole is visualized as presenting a potential barrier Vout(r*) to incoming tachyon wave. Since this takes the complicated form, an approximate form VAPP(r*) is used for scattering analysis. We calculate the reflection and transmission coefficients for scattering of tachyon off the charged 2-D black hole. The Hawking temperature is also derived from the reflection coefficient by Bogoliubov transformation. In the limit Q→0, we recover the Hawking temperature of the 2-D dilaton black hole.
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Ursin, Bjørn. "Parameter inversion and angle migration in anisotropic elastic media." GEOPHYSICS 69, no. 5 (September 2004): 1125–42. http://dx.doi.org/10.1190/1.1801931.
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Seismic parameter inversion using the inverse generalized Radon transform (GRT) was originally formulated as an integral over source and receiver surface coordinates, involving a Jacobian from angle to surface coordinates. By formulating the inversion directly in terms of angle coordinates at the subsurface image point, I obtain simplified inversion formulas for point scatterers and subsurface reflectors. Amplitude‐preserving angle migration based on the inverse GRT gives an estimate of the scattering coefficient in the Born integral as a function of scattering angle and azimuth. The scattering coefficient is directly related to the linearized plane‐wave reflection coefficient between two anisotropic media, which limits the result to small angles and small contrasts in the elastic parameters. I use the Kirchhoff modeling integral for anisotropic media to formulate a Kirchhoff angle‐migration integral that is valid for large angles and large parameter contrasts. It gives an estimate of the plane‐wave reflection coefficient normalized with respect to amplitude. The Kirchhoff integrals, however, are non reciprocal, so I propose to use new reciprocal integrals for modeling and angle migration. The new migration integral, which is much simpler than the Kirchhoff integral, gives an estimate of the plane‐wave reflection coefficient normalized with respect to the energy flux normal to the reflector. A restricted inverse GRT has been proposed for migration‐velocity analysis. By simplifying this, I derive an expression for amplitude‐compensated migration that is the estimated reflection coefficient divided by the norm of the radiation pattern vector. This partly removes the effects of amplitude variations with scattering angle and azimuth.
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Zhang, Likun, and David B. Thiessen. "Capillary-wave scattering from an infinitesimal barrier and dissipation at dynamic contact lines." Journal of Fluid Mechanics 719 (February 19, 2013): 295–313. http://dx.doi.org/10.1017/jfm.2013.5.
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AbstractThe interaction of pure capillary waves with boundaries that constrain the contact line are of interest for problems involving liquids contained by minimal solid contact for applications in low gravity and at small scales in normal gravity. Time-harmonic capillary waves on a liquid cylinder axially incident on and scattered by an infinitesimal concentric barrier are considered theoretically in the inviscid limit. The barrier is taken to be infinitesimally small in the sense that its immersed depth is of the order of the amplitude of contact-line motion. Edge conditions on the barrier that are investigated include a pinned contact line and a moving contact line by an effective-slip model, assuming that contact-line velocity is proportional to the deviation of the contact angle from equilibrium multiplied by a slip coefficient. The incident waves are taken to be those with wavelengths short enough to be stable on the liquid cylinder. Scattering and dissipation by the contact line are determined as a function of wavenumber and slip coefficient. Zero transmission is approached in the long-wave limit. The short-wave limit agrees with established results for the scattering of planar gravity–capillary waves on a deep liquid by a surface-piercing vertical barrier in the limit of zero barrier depth and zero gravity. We find that contact-line dissipation at the barrier is a maximum for incident waves whose phase speed is of the order of the slip coefficient, which is interpreted as an effect of impedance matching. Transmission past an infinitesimal barrier is found to be low over all parameter space, illustrating the importance of contact-line constraints.
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Kariotou, Foteini, Dimitris E. Sinikis, and Maria Hadjinicolaou. "On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers." Mathematics 10, no. 23 (November 28, 2022): 4487. http://dx.doi.org/10.3390/math10234487.
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The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework of a new algorithmic procedure for deriving the scattering coefficients of the total pressure field, produced by a plane wave excitation of an arbitrary, convex impenetrable scatterer. The proposed semi-analytical procedure reduces the demands for computation time and errors significantly since it includes mainly algebraic and linear integral operators. Based on the Atkinson–Wilcox theorem, any order low frequency scattering coefficient can be calculated, in finite steps, through algebraic operators at all steps, except for the last one, where a regular Fredholm integral equation with a continuous and separable integral kernel is needed to be solved. Explicit, ready to use formulae are provided for the first three low frequency scattering coefficients, demonstrating the applicability of the algorithm. The validation of the obtained formulae is demonstrated through recovering of the well-known analytical results for the case of a radially symmetric scatterer.
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Chen, Jiabao, Bangjun Lv, Likun Peng, and Bin Huang. "Study on resistance characteristics of submarine near water surface." MATEC Web of Conferences 355 (2022): 01002. http://dx.doi.org/10.1051/matecconf/202235501002.
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The submarine is usually affected by free surface and the navigation resistance increases when sailing near the surface. In order to study the specific resistance characteristics of submarine sailing near the surface, the SUBOFF with appendages was taken as the research object, and the calculation model was built based on Star CCM+ fluid simulation software, and the resistance coefficients under different submarine depths and speeds were calculated. Through comparative analysis, the influence of the depth and speed of the submarine on the resistance components was obtained, and the cause of the formation was analyzed. The results show that the influence of the depth of submarine on friction resistance coefficient is small in general. With the increase of the depth of the submarine, the pressure resistance coefficient decreases, and the wave amplitude decreases. The shear wave of Kelvin wave system is more obvious and the effect of scattering is weakened, which is of great significance for the study of submarine concealment. With the increase of speed, friction resistance coefficient decreases, the overall change trend of pressure resistance coefficient is first increased and then decreases. The interference effect between free surface and hull increases first and then decreases at each depth. The wave shape changes and resistance results mutually confirm. The free surface mainly generates waves by interacting with the hull, which affects the resistance characteristics of the submarine. The interference effect is greatly affected by the depth and speed of the submarine.
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MANAM, S. R., and R. B. KALIGATLA. "MEMBRANE-COUPLED GRAVITY WAVE SCATTERING BY A VERTICAL BARRIER WITH A GAP." ANZIAM Journal 55, no. 3 (January 2014): 267–88. http://dx.doi.org/10.1017/s1446181114000078.
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AbstractWe study the reflection of membrane-coupled gravity waves in deep water against a vertical barrier with a gap. A floating membrane is attached on both sides of the barrier. The associated mixed boundary value problem, which is not particularly well posed, is analysed. We utilize an orthogonal mode-coupling relation to reduce the problem to solving a set of dual integral equations with trigonometric kernel. We solve these by using a weakly singular integral equation. The reflection coefficient is determined explicitly, while having freedom to clamp the membrane with a spring of a certain stiffness on only one side of the vertical barrier. The physical problem is of capillary–gravity wave scattering by a vertical barrier with a gap, when the membrane density is neglected. In this case, the reflection coefficient is known up to an undetermined edge slope on either side of the barrier. The scattering quantity is computed and presented graphically against a wave parameter for different values of nondimensional parameters pertaining to the structures involved in the problem.
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GANOULIS, N., and M. HATZIS. "LIGHT SCATTERING BY AN AXIONIC DOMAIN WALL." Modern Physics Letters A 01, no. 06 (September 1986): 409–14. http://dx.doi.org/10.1142/s0217732386000518.
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We discuss the electromagnetic scattering of a plane wave by an axionic domain wall, under an arbitrary incident angle. We estimate the reflection coefficient which depends on the plane wave frequency and angle and take always a very small value. The two independent circular polarizations propagate with different velocities through the wall.
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Yu, Li-Ping, Jheng-Syong Wu, Sheng-Yi Chang, and Chien Chou. "Glucose detection in a highly scattering medium with diffuse photon-pair density wave." Journal of Innovative Optical Health Sciences 10, no. 01 (January 2017): 1650032. http://dx.doi.org/10.1142/s1793545816500322.
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We propose a novel optical method for glucose measurement based on diffuse photon-pair density wave (DPPDW) in a multiple scattering medium (MSM) where the light scattering of photon-pair is induced by refractive index mismatch between scatters and phantom solution. Experimentally, the DPPDW propagates in MSM via a two-frequency laser (TFL) beam wherein highly correlated pairs of linear polarized photons are generated. The reduced scattering coefficient [Formula: see text] and absorption coefficient [Formula: see text] of DPPDW are measured simultaneously in terms of the amplitude and phase measurements of the detected heterodyne signal under arrangement at different distances between the source and detection fibers in MSM. The results show that the sensitivity of glucose detection via glucose-induced change of reduced scattering coefficient ([Formula: see text]) is 0.049%[Formula: see text]mM[Formula: see text] in a 1% intralipid solution. In addition, the linear range of [Formula: see text] vs glucose concentration implies that this DPPDW method can be used to monitor glucose concentration continuously and noninvasively subcutaneously.
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Kuznetsova, I. A., D. N. Romanov, and A. A. Yushkanov. "Interaction of an electromagnetic E-wave with a thin conducting film between two dielectric media in the case of an anisotropic isoenergetic surface and impurity scattering." Journal of Physics: Conference Series 2103, no. 1 (November 1, 2021): 012156. http://dx.doi.org/10.1088/1742-6596/2103/1/012156.
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Abstract The coefficients of reflection, transmission and absorption are calculated in the framework of the kinetic approach, when an electromagnetic E-wave interacts with a thin conducting film located between two dielectric media. To account for the surface scattering of charge carriers is used a model of mirror-diffuse boundary conditions, assuming that the specularity coefficients of the upper and lower surfaces of the film differ from each other. The electromagnetic wave falls on the upper surface of the film at an arbitrary angle. The case of an anisotropic isoenergetic surface of a conductor having the form of a three-axis ellipsoid, one of the main axes of which is parallel to the magnetic field strength of the wave, and the other is perpendicular to the film surfaces, is considered. The impurity scattering of electrons (holes) is dominated in the volume of the conductor. The dependence of the absorption coefficient on the parameters of the isoenergetic surface of the conductor is analyzed.
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Yi, D., and C. R. Bentley. "Analysis of satellite radar-altimeter return wave forms over the East Antarctic ice Sheet." Annals of Glaciology 20 (1994): 137–42. http://dx.doi.org/10.3189/1994aog20-1-137-142.
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The precision of satellite-radar altimetry over the Antarctic ice sheet can be improved by using a physically based retracking algorithm on the altimeter returns ("wave forms"). Ridley and Partington (1988) have shown that both surface and volume-scattering affect the shape of the return. Here, we develop a model that is based on a variable combination of surface- and volume-scattering and determine the model parameters through least-square fitting to the observed wave forms. The model parameters include surface roughness, proportion of volume-scattering, extinction coefficient and an amplitude coefficient. Geosat data collected over a test sector of the East Antarctic ice sheet have been analyzed to find quantitative estimates of seasonal and geographic variations of the several parameters. Our results show that the effect of volume-scattering can change the elevation measurement over the inland part of the East Antarctic ice sheet by more than I m and that there are both spatial and temporal variations; temporal variations are less significant than spatial variations.
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Yi, D., and C. R. Bentley. "Analysis of satellite radar-altimeter return wave forms over the East Antarctic ice Sheet." Annals of Glaciology 20 (1994): 137–42. http://dx.doi.org/10.1017/s0260305500016359.
Full textAbstract:
The precision of satellite-radar altimetry over the Antarctic ice sheet can be improved by using a physically based retracking algorithm on the altimeter returns ("wave forms"). Ridley and Partington (1988) have shown that both surface and volume-scattering affect the shape of the return. Here, we develop a model that is based on a variable combination of surface- and volume-scattering and determine the model parameters through least-square fitting to the observed wave forms. The model parameters include surface roughness, proportion of volume-scattering, extinction coefficient and an amplitude coefficient. Geosat data collected over a test sector of the East Antarctic ice sheet have been analyzed to find quantitative estimates of seasonal and geographic variations of the several parameters. Our results show that the effect of volume-scattering can change the elevation measurement over the inland part of the East Antarctic ice sheet by more than I m and that there are both spatial and temporal variations; temporal variations are less significant than spatial variations.
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D'Antonio, Peter, Luiz Augusto T. Ferraz Alvim, and Rinaldi P. Petrolli. "Boundary element method virtual goniometer to predict the diffusion and scattering coefficients." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A144. http://dx.doi.org/10.1121/10.0010917.
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The experimental measurement of the diffusion coefficient according to ISO 17497-2 is very time consuming and requires several sample periods to evaluate the effect of diffraction lobes, an anechoic or large reflection-free volume and far-field conditions. Wave-based BEM methods have predicted diffusion and correlation scattering coefficients very accurately [Hargreaves et al., J. Acoust. Soc. Am. 108 (4), 1710–1720 (2000)]. This presentation will describe a new Python Virtual Goniometer program, called VIRGO, which predicts the free-field and surface-mounted diffusion and correlation scattering coefficients for any shaped surface that can be successfully meshed from a three-dimensional file. The program accurately predicts the periodic diffraction grating lobes of a reference one-dimensional hemicylinder and a two-dimensional hemisphere, both in the free-field and surface mounted on a boundary. The diffusion coefficient and three-dimensional polar responses of additional number-theoretic and optimized profiled and curvilinear shapes will also be compared with scale model boundary-plane goniometer measurements. The results will verify that it is possible to precisely predict the diffusion and correlation scattering coefficients, without having to fabricate or 3D print scale models or full-scale samples.
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Mandal, B. N., and Mridula Kanoria. "Oblique Wave-Scattering by Thick Horizontal Barriers." Journal of Offshore Mechanics and Arctic Engineering 122, no. 2 (January 8, 1999): 100–108. http://dx.doi.org/10.1115/1.533731.
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This paper is concerned with scattering of an obliquely incident surface water wave train by an obstacle in the form of a thick horizontal barrier of rectangular cross section present in finite depth water. Four different geometrical configurations of the obstacle are considered. It may be surface-piercing or bottom-standing, or in the form of a submerged block not extending down to the bottom, or in the form of a thick wall with a submerged gap. Multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving first-kind integral equations are utilized in the mathematical analysis to obtain very accurate numerical estimates for the reflection coefficient, which are depicted graphically against the wave number for each configurations of the thick barrier. [S0892-7219(00)00701-9]
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Wang, Zhiwen, Chuanping Zhou, Xueting Zhang, Xiao Han, Junqi Bao, Lingkun Chen, Maofa Wang, Yongping Gong, and Weihua Zhou. "Magnetoacoustic Wave Scattering and Dynamic Stress Concentration around the Elliptical Opening in Exponential-Gradient Piezomagnetic Materials." Materials 15, no. 13 (June 29, 2022): 4564. http://dx.doi.org/10.3390/ma15134564.
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Based on the theory of magnetoacoustic coupled dynamics, the purpose of this paper is to evaluate the dynamic stress concentration near an elliptical opening in exponential-gradient piezomagnetic materials under the action of antiplane shear waves. By the wave function expansion, the solutions for the acoustic wave fields and magnetic fields can be obtained. Stress analysis is performed by the complex function method and the conformal mapping method, which are used to solve the boundary conditions problem, and is used to express the dynamic stress concentration coefficient (DSCC) theoretically. As cases, numerical results of DSCCs are plotted and discussed with different incident wave numbers and material parameters by numerical simulation. Compared with circular openings, elliptical openings are widely used in material processing techniques and are more difficult to solve. Numerical results show that the dynamic stress concentration coefficient at the elliptical opening is strongly dependent on various parameters, which indicates that the elliptical opening is more likely to cause crack and damage to exponential-gradient piezomagnetic materials.
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Ng, Ching Tai, and Martin Veidt. "Prediction and Measurement of Lamb Wave from Debondings at Structural Features in Composite Laminates." Key Engineering Materials 558 (June 2013): 139–48. http://dx.doi.org/10.4028/www.scientific.net/kem.558.139.
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The interaction of the fundamental anti-symmetric Lamb wave (A0) with debondings at structural features is investigated using experimental data and finite element (FE) simulations. In this study explicit three-dimensional (3D) FE simulations are employed, which allows the study of the scattered wave along different propagation directions. Good agreement between the FE predictions and the measurements are obtained that demonstrates that the 3D FE scattering model is able to accurately predict the Lamb wave scattering characteristics at debondings. The study show that the characteristics of Lamb wave reflected from the debondings at the structure feature is much more complicated than that from defects in flat composite laminates. Parameter studies show that the backward and forward scattering coefficient of Lamb wave is a function of debonding size to wavelength ratio and debonding location. This shows the potential of employing Lamb wave to identify the size and monitor the growth of the debondings. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques for complex structures made by composite laminates.
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Vaughan, Gareth L., Luke G. Bennetts, and Vernon A. Squire. "The decay of flexural-gravity waves in long sea ice transects." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2109 (June 24, 2009): 2785–812. http://dx.doi.org/10.1098/rspa.2009.0187.
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Flexural oscillations of floating sea ice sheets induced by ocean waves travelling at the boundary between the ice and the water below can propagate great distances. But, by virtue of scattering, changes of ice thickness and other properties encountered during the journey affect their passage, notwithstanding attenuation arising from several other naturally occurring agencies. We describe here a two-dimensional model that can simulate wave scattering by long (approx. 50 km) stretches of inelastic sea ice, the goal being to replicate heterogeneity accurately while also assimilating supplementary processes that lead to energy loss in sea ice at scales that are amenable to experimental validation. In work concerned with scattering from solitary or juxtaposed stylized features in the sea ice canopy, reflection and transmission coefficients are commonly used to quantify scattering, but on this occasion, we use the attenuation coefficient as we consider that it provides a more helpful description when dealing with long sequences of adjoining scatterers. Results show that scattering and viscosity both induce exponential decay and we observe three distinct regimes: (i) low period, where scattering dominates, (ii) high period, where viscosity dominates, and (iii) a transition regime. Each regime’s period range depends on the sea ice properties including viscosity, which must be included for the correct identification of decay rate.
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Gayen, Rupanwita, Sourav Gupta, and Aloknath Chakrabarti. "WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE." Mathematical Modelling and Analysis 26, no. 2 (May 26, 2021): 223–35. http://dx.doi.org/10.3846/mma.2021.13207.
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An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.
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Wang, Xiao Qin, Qing Zhou, Jun Ying Zeng, Xiao Yun Pu, and Xing Zhu. "The Calculation of the Evanescent Wave and the Coupling Coefficient of the Whispering-Gallery-Mode Disk Microcavity." Solid State Phenomena 121-123 (March 2007): 1375–78. http://dx.doi.org/10.4028/www.scientific.net/ssp.121-123.1375.
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Ultrahigh-Quality microcavity with whispering-gallery-mode (WGM) is a new kind of resonator with high quality. The evanescent wave of WGM plays an important role in surface enhanced Raman scattering (SERS). In this paper we study the relationship between coupling coefficient and evanescent wave of the WGM and the coupling character difference between the microsphere and the microstadium. Based on the finite-difference time-domain (FDTD), we calculate the coupling coefficient of different substances (water, C2H5OH, CHCL3, olive oil, C6H6 and CS2) with different dielectric constant and the mode volume ratio of the evanescent wave in microsphere and microstadium of the above substances in near field. The results show that (1) the mode volume ratio of evanescent wave will decrease with the increasing of the coupling coefficient; (2) the microstadium has a higher coupling coefficient than the sphere one.
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Mandal, B. N., and P. K. Kundu. "A note on the reflection coefficient in a water wave scattering Problem." Applied Mathematics Letters 3, no. 4 (1990): 5–7. http://dx.doi.org/10.1016/0893-9659(90)90035-a.
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MILES, JOHN. "On gravity-wave scattering by non-secular changes in depth." Journal of Fluid Mechanics 376 (December 10, 1998): 53–60. http://dx.doi.org/10.1017/s0022112098002900.
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The reflection of a straight-crested gravity wave by a non-secular perturbation h1(x) in depth relative to an otherwise flat bottom of depth h0 is calculated through an expansion in ε∝h1/h0. Explicit results are developed up to second order for the sinusoidal patch h1=−bsin(mπx/l), 0<x<l, and reduced for Bragg resonance. Trapped modes are absent at first order but appear at second order and contribute O(ε2)/O(ε3) to the maximum (Bragg-resonant) reflection coefficient for odd/even m. A third-order approximation that includes the dominant contributions of the third-order components of the resonant peak of the reflection coefficient for large m, but neglects the trapped modes, predicts resonant peaks that agree with the values measured by Davies & Heathershaw (1984).
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ESPAÑOL, PEP, and IGNACIO ZÚÑIGA. "SCALING OF THE TIME-DEPENDENT SELF-DIFFUSION COEFFICIENT." International Journal of Modern Physics B 09, no. 04n05 (February 28, 1995): 469–94. http://dx.doi.org/10.1142/s0217979295000173.
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The advent of the new light scattering technique of Diffusing Wave Spectroscopy has aroused great interest on the very short time scale dynamics of colloidal particles in suspension. Here we review some advances in the experimental, computer simulation and theoretical fronts on the problem of the dynamics of Brownian particles at time scales where hydrodynamic transient effects become very important. We also present some open questions regarding the scaling of the time-dependent self-diffusion coefficient and propose possible ways of attacking them.
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Tsinopoulos, S. V., J. T. Verbis, and D. Polyzos. "An Iterative Effective Medium Approximation for Wave Dispersion and Attenuation Predictions in Particulate Composites." Advanced Composites Letters 9, no. 3 (May 2000): 096369350000900. http://dx.doi.org/10.1177/096369350000900303.
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This work deals with the dispersion and attenuation of elastic waves propagating in a random particle-reinforced composite. A new iterative effective medium approximation based on the single scattering consideration, for the quantitative estimation of wave dispersion and attenuation is proposed. The iterations are carried out via the classical dispersion relation of Foldy while the convergence of the iterative procedure is accomplished through a self-consistent condition proposed by Kim et al. [ 6 ]. The methodology is quite general and it works for any type of particles. The single scattering problem is solved numerically by means of an advanced boundary element code. Numerical results concerning the frequency dependent behaviour of the wave velocity and attenuation coefficient for three particular types of composites are presented. The results obtained are compared to those taken either experimentally or numerically by other investigators.