Journal articles on the topic 'Linear wave scattering'
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Mi, Zhao, Long Pengzhen, Wang Piguang, Zhang Chao, and Du Xiuli. "An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders." Mathematical Problems in Engineering 2021 (October 11, 2021): 1–12. http://dx.doi.org/10.1155/2021/5710894.
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This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.
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Savotchenko, S. E. "THE LINEAR WAVE SCATTERING BY A NON-LINEAR DEFECT." Belgorod State University Scientific bulletin Mathematics Physics 50, no. 3 (September 30, 2018): 283–91. http://dx.doi.org/10.18413/2075-4639-2018-50-3-283-291.
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Porter, R. "An extended linear shallow-water equation." Journal of Fluid Mechanics 876 (August 1, 2019): 413–27. http://dx.doi.org/10.1017/jfm.2019.555.
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An extension to the classical shallow-water equation (SWE) is derived that exactly satisfies the bed condition and can be regarded as an approximation to wave scattering at the next order in the small parameter $(h/\unicode[STIX]{x1D706})^{2}$ (depth to wavelength ratio squared). In the frequency domain, the extended SWE shares the same simple structure as the standard SWE with coefficients modified by terms relating to the bed variation. In three dimensions the governing equation demonstrates that variable topography gives rise to anisotropic effects on wave scattering not present in the standard SWE, with consequences for the design of water wave metamaterials. Numerical examples illustrate that approximations to wave scattering using the extended SWE are significantly improved in comparison with the standard SWE.
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CHEN, YONGZE, and R. T. GUZA. "Resonant scattering of edge waves by longshore periodic topography." Journal of Fluid Mechanics 369 (August 25, 1998): 91–123. http://dx.doi.org/10.1017/s0022112098001700.
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The resonant scattering of topographically trapped, low-mode progressive edge waves by longshore periodic topography is investigated using a multiple-scale expansion of the linear shallow water equations. Coupled evolution equations for the slowly varying amplitudes of incident and scattered edge waves are derived for small-amplitude, periodic depth perturbations superposed on a plane beach. In ‘single-wave scattering’, an incident edge wave is resonantly scattered into a single additional progressive edge wave having the same or different mode number (i.e. longshore wavenumber), and propagating in the same or opposite direction (forward and backward scattering, respectively), as the incident edge wave. Backscattering into the same mode number as the incident edge wave, the analogue of Bragg scattering of surface waves, is a special case. In ‘multi-wave scattering’, simultaneous forward and backward resonant scattering results in several (rather than only one) new progressive edge waves. Analytic solutions are obtained for single-wave scattering and for a special case of multi-wave scattering involving mode-0 and mode-1 edge waves, over perturbed depth regions of both finite and semi-infinite longshore extent. In single-wave backscattering with small (subcritical) detuning (i.e. departure from exact resonance), the incident and backscattered wave amplitudes both decay exponentially with propagation distance over the periodic bathymetry, whereas with large (supercritical) detuning the amplitudes oscillate with distance. In single-wave forward scattering, the wave amplitudes are oscillatory regardless of the magnitude of the detuning. Multi-wave solutions combine aspects of single-wave backward and forward scattering. In both single- and multi-wave scattering, the exponential decay rates and oscillatory wavenumbers of the edge wave amplitudes depend on the detuning. The results suggest that naturally occurring rhythmic features such as beach cusps and crescentic bars are sometimes of large enough amplitude to scatter a significant amount of incident low-mode edge wave energy in a relatively short distance (O(10) topographic wavelengths).
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Li, Hong Liang. "Far Field Solution of Circular Inclusion and Linear Crack by SH-Wave." Key Engineering Materials 462-463 (January 2011): 455–60. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.455.
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Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect composition, location and shape, so the research on the scattering far-field is important to the geological prospects, seismological investigation, non-destruction evaluation and the other fields. In the ocean acoustics, the scattering far-field of the acoustic wave is also used in the under-water survey, object distinguishing and so on. In theory, the scattering solution of elastic waves is one of the basic topics of reverse problems on elastic wave. On the basis of literature, few paper concentrates on the scattering far-field solution of SH-wave by a circular inclusion and a linear crack around the inclusion. In the paper a new model and a new method are presented in order to investigate deeply on this kind problem. The paper uses the Green’s function to study the scattering far-field of an elastic wave by a circular inclusion and a linear crack. The Green’s function should be a fundamental solution of displacement field for an elastic space possessing a circular inclusion while bearing out-of-plane harmonic line source force at any point. In terms of the solution of SH-wave’s scattering by an elastic space with a circular inclusion, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Then, the expressions of the displacement and stresses are given when the circular inclusion and linear crack exist at the same time. When the special Green’s function has been constructed and close field solution has been illustrated, the far field of scattered wave is studied. The displacement mode of scattered wave at far field and scattering cross-section are given. At last, an example is given and its numerical results are discussed.
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PETER, MALTE A., and MICHAEL H. MEYLAN. "Water-wave scattering by a semi-infinite periodic array of arbitrary bodies." Journal of Fluid Mechanics 575 (March 2007): 473–94. http://dx.doi.org/10.1017/s0022112006004319.
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We consider the scattering by a semi-infinite array of bodies of arbitrary geometry excited by an incident wave in the linear water-wave formulation (which reduces to the simpler case of Helmholtz scattering if the depth dependence can be removed). The theory presented here is extremely general, and we present example calculations for an array of floating elastic plates (a highly non-trivial scatterer). The solution method follows closely from the solution for point scatterers in a medium governed by Helmholtz's equation. We have made several extensions to this theory, considering water-wave scattering, allowing for bodies of arbitrary scattering geometry and showing how to include the effects of bound waves (called Rayleigh–Bloch waves in the water-wave context) in the formulation. We present results for scattering by arrays of cylinders that show the convergence of our methods and also some results for the case of scattering by floating elastic plates and fixed docks.
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Vakakis, A. F. "Scattering of Structural Waves by Nonlinear Elastic Joints." Journal of Vibration and Acoustics 115, no. 4 (October 1, 1993): 403–10. http://dx.doi.org/10.1115/1.2930364.
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An analytic study of the scattering of structural waves by nonlinear elastic joints is presented. Under the assumption of small nonlinearities and/or amplitudes of motion, an averaging methodology is implemented for analyzing the interaction between an incident wave and a nonlinear joint with symmetric stiffness. It is found that, contrary to the predictions of existing linear theories, a single incident wave gives rise to an infinity of reflected waves with frequencies equal to odd multiples of the frequency of the incident wave. The orders of magnitude of the amplitudes of the various reflected waves are considered, and an application of the theory is made by considering the wave scattering from a joint with cubic stiffness nonlinearity. In addition, it is shown that the wave propagation approach presented in this work can be effectively used for predicting nonlinear free oscillations (standing waves) in finite waveguides with nonlinear joints.
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Razavy, M. "Scattering of acoustic waves by an oscillating soft sphere." Canadian Journal of Physics 68, no. 2 (February 1, 1990): 184–89. http://dx.doi.org/10.1139/p90-026.
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The problem of the scattering of acoustic waves by an oscillating sphere with a perfectly reflecting surface is studied. Here, the scattering amplitude is expressible in terms of partial wave amplitudes and these depend on both the incident and the scattered wave frequencies, the difference between these two frequencies being an integral multiple of the frequency of oscillation of the sphere. The exact formulation leads to an infinite set of linear equations for the partial wave scattering amplitude of which only a finite number of terms are important. If the amplitude of oscillation of the sphere is small compared with the wavelength of the scattered wave and the radius of the sphere, a perturbation technique can be used to obtain the scattering amplitude.
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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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Chen, Cheng-Tsung, Jaw-Fang Lee, and Chun-Han Lo. "Mooring Drag Effects in Interaction Problems of Waves and Moored Underwater Floating Structures." Journal of Marine Science and Engineering 8, no. 3 (February 25, 2020): 146. http://dx.doi.org/10.3390/jmse8030146.
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In contrast to either considering structures with full degrees of freedom but with wave force on mooring lines neglected or with wave scattering and radiation neglected, in this paper, a new analytic solution is presented for wave interaction with moored structures of full degrees of freedom and with wave forces acting on mooring lines considered. The linear potential wave theory is applied to solve the wave problem. The wave fields are expressed as superposition of scattering and radiation waves. Wave forces acting on the mooring lines are calculated using the Morison equation with relative motions. A coupling formulation among water waves, underwater floating structure, and mooring lines are presented. The principle of energy conservation, as well as numerical results, are used to verify the present solution. With complete considerations of interactions among waves and moored structures, the characteristics of motions of the structure, the wave fields, and the wave forces acting on the mooring lines are investigated.
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Hamid, A.-K., I. R. Ciric, and M. Hamid. "Multiple scattering by a linear array of conducting spheres." Canadian Journal of Physics 68, no. 10 (October 1, 1990): 1157–65. http://dx.doi.org/10.1139/p90-163.
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The problem of multiple scattering of a plane electromagnetic wave incident on N closely spaced perfectly conducting spheres is solved analytically by expanding the incident and scattering fields in terms of an appropriate set of vector spherical wave functions. To impose the boundary conditions, the scattered field from one sphere is expressed in coordinate systems attached to the others by using the translation addition theorem. An approximate solution is obtained to solve for the scattering by N small spheres. Numerical results for the normalized backscattering and bistatic cross sections for systems of spheres show that the agreement between the analytic and approximate solutions is better for larger electrical distances between neighbouring spheres.
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Wang, Jingjing, Lixin Guo, Yiwen Wei, Shuirong Chai, Ke Li, and Anqi Wang. "Electromagnetic Scattering Analysis of the Sea Surface with Single Breaking Waves." International Journal of Antennas and Propagation 2021 (November 27, 2021): 1–13. http://dx.doi.org/10.1155/2021/1545031.
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A new electromagnetic (EM) scattering model of the sea surface with single breaking waves is proposed based on the high-frequency method in this paper. At first, realistic breaking wave sequences are obtained by solving the fluid equations which are simplified. Then, the rough sea surface is established using the linear filtering method. A new wave model is obtained by combining breaking waves with rough sea surface using a 3D coordinate transformation. Finally, the EM scattering features of the sea surface with breaking waves are studied by using shooting and bouncing rays and the physical theory of diffraction (SBR-PTD). It is found that the structure that is similar to a dihedral corner reflector between the breaking wave and rough sea surface exhibits multiple scattering, which leads to the sea-spike phenomenon that the scattering result of horizontal (HH) polarization is larger than that of vertical (VV) polarization, especially at low-grazing-angle (LGA) incidents with upwind. The sea-spike phenomenon is also closely related to the location of strong scattering.
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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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LINTON, C. M., and J. R. CADBY. "Scattering of oblique waves in a two-layer fluid." Journal of Fluid Mechanics 461 (June 25, 2002): 343–64. http://dx.doi.org/10.1017/s002211200200842x.
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We consider problems based on linear water wave theory concerning the interaction of oblique waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are solved using multipole expansions.
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Gautesen, A. K. "Scattering of a Rayleigh Wave by an Elastic Quarter Space." Journal of Applied Mechanics 52, no. 3 (September 1, 1985): 664–68. http://dx.doi.org/10.1115/1.3169118.
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We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic quarter space. We derive decoupled equations for the Fourier transforms of the normal and tangential displacements on the free surfaces. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner. These curves were obtained numerically.
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Wongthongsiri, Supawat, and Sohichi Hirose. "Scattering Analysis and Detection of Layered Plate Debonding Using Guided SH Waves with Boundary Element Method." Shock and Vibration 2022 (July 16, 2022): 1–10. http://dx.doi.org/10.1155/2022/8799555.
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This paper investigates the scattering behavior of guided shear horizontal (SH) waves in a two-dimensional, isotropic, and linear elastic layered plate with partially debonded interface by analyzing the reflection and transmission coefficients of scattered waves. The partial wave technique is established to form the displacement and stress of guided wave functions, and the boundary element method (BEM) is utilized to handle the numerical calculation with elastodynamic fundamental solutions in the frequency domain. After applying proper boundary conditions including continuity condition on the interface with traction-free debonding, the scattering coefficients can be obtained in terms of boundary element solutions. Two different materials (steel and aluminum) with various debonding lengths and locations in a 1 mm double-layered plate are considered. With several modes of the incident wave over a frequency range up to 4.5 MHz, the variations of scattering coefficients and scattering phenomena are numerically investigated as several parameters such as mode of the incident wave, materials, locations, and length of debonding are changed. The numerical results also suggest the potential of the suitable wave mode for the debonding detection, which can be useful for non-destructive inspection.
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Arens, T. "Linear sampling methods for 2D inverse elastic wave scattering." Inverse Problems 17, no. 5 (August 30, 2001): 1445–64. http://dx.doi.org/10.1088/0266-5611/17/5/314.
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CADBY, J. R., and C. M. LINTON. "Three-dimensional water-wave scattering in two-layer fluids." Journal of Fluid Mechanics 423 (November 3, 2000): 155–73. http://dx.doi.org/10.1017/s0022112000002007.
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We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.
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Montiel, F., and V. A. Squire. "Modelling wave-induced sea ice break-up in the marginal ice zone." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170258. http://dx.doi.org/10.1098/rspa.2017.0258.
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A model of ice floe break-up under ocean wave forcing in the marginal ice zone (MIZ) is proposed to investigate how floe size distribution (FSD) evolves under repeated wave break-up events. A three-dimensional linear model of ocean wave scattering by a finite array of compliant circular ice floes is coupled to a flexural failure model, which breaks a floe into two floes provided the two-dimensional stress field satisfies a break-up criterion. A closed-feedback loop algorithm is devised, which (i) solves the wave-scattering problem for a given FSD under time-harmonic plane wave forcing, (ii) computes the stress field in all the floes, (iii) fractures the floes satisfying the break-up criterion, and (iv) generates an updated FSD, initializing the geometry for the next iteration of the loop. The FSD after 50 break-up events is unimodal and near normal, or bimodal, suggesting waves alone do not govern the power law observed in some field studies. Multiple scattering is found to enhance break-up for long waves and thin ice, but to reduce break-up for short waves and thick ice. A break-up front marches forward in the latter regime, as wave-induced fracture weakens the ice cover, allowing waves to travel deeper into the MIZ.
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Li, Mengni. "An inverse scattering theorem for (1 + 1)-dimensional semi-linear wave equations with null conditions." Journal of Hyperbolic Differential Equations 18, no. 01 (March 2021): 143–67. http://dx.doi.org/10.1142/s021989162150003x.
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We are interested in the inverse scattering problem for semi-linear wave equations in one dimension. Assuming null conditions, we prove that small data lead to global existence of solutions to [Formula: see text]-dimensional semi-linear wave equations. This result allows us to construct the scattering fields and their corresponding weighted Sobolev spaces at the infinities. Finally, we prove that the scattering operator not only describes the scattering behavior of the solution but also uniquely determines the solution. The key ingredient of our proof is the same strategy proposed by Le Floch and LeFloch [On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry, Arch. Ration. Mech. Anal. 233 (2019) 45–86] as well as Luli et al. [On one-dimension semi-linear wave equations with null conditions, Adv. Math. 329 (2018) 174–188] to make full use of the null structure and the weighted energy estimates.
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ATASSI, O. V., and J. J. GILSON. "Acoustic mode scattering from a heat source." Journal of Fluid Mechanics 651 (April 30, 2010): 1–26. http://dx.doi.org/10.1017/s0022112010000261.
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The scattering of an incident acoustic wave by a non-uniform mean flow resulting from a heat source is investigated. The heat source produces gradients in the mean flow and the speed of sound that scatter the incident duct acoustic mode into vortical, entropic, and higher-order acoustic modes. Linear solutions utilizing the compact source limit and nonlinear solutions to the Euler equations are computed to understand how variations in the amplitude and axial extent of the heat source as well as the incident acoustic wave propagation angle and amplitude modify the scattered solution. For plane wave excitation, significant entropy waves are produced as the net heat addition increases at the expense of the transmitted acoustic energy. When the net heat addition is held constant, increasing the axial extent of the heat source results in a reduction of the entropy waves produced downstream and a corresponding increase in the downstream scattered acoustic energy. For circumferential acoustic mode excitations the incident acoustic wave angle, characterized by the cutoff ratio, significantly modifies the scattered acoustic energy. As the propagating mode cutoff ratio approaches unity, a rise in the scattered vortical disturbance and a decrease in the entropic disturbance amplitude is observed. As the cutoff ratio increases, the scattered solution approaches the plane wave results. Moreover, incident acoustic waves with different frequencies and circumferential mode orders but similar cutoff ratios yield similar scattered wave coefficients. Finally, for large amplitude incident acoustic waves the scattered solution is modified by nonlinear effects. The pressure field exhibits nonlinear steepening of the wavefront and the nonlinear interactions produce higher harmonic frequency content which distorts the sinusoidal variation of the outgoing scattered acoustic waves.
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Bao, Jiading, Jun Zhang, and Longhai Zeng. "Explicit Solutions to Single Scattering of SH Waves with a Radially Gradient Interphase Layer." Shock and Vibration 2019 (January 14, 2019): 1–7. http://dx.doi.org/10.1155/2019/6978305.
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In this work, analytical solutions to the single scattering of horizontally polarized shear waves (SH) by cylindrical fibers with two specific radially gradient interphase layers are presented. In the first case, the shear modulus μr=e2βr and the square of wave number k2 is a linear function of 1/r; in the second case μr=e−βr2 and k2 is a linear function of r2. As an example, we solve the single scattering of SH waves by a SiC fiber with the two interphase layers in an aluminum matrix. The calculated scattering cross sections are compared to values obtained by an approximate method (dividing the continuous varying layer into multiple homogeneous sublayers). The results indicate the current approach gives excellent performance.
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Marsch, E. "On resonant interactions of ions with plasma waves in a reduced quasi-linear theory." Nonlinear Processes in Geophysics 9, no. 2 (April 30, 2002): 69–74. http://dx.doi.org/10.5194/npg-9-69-2002.
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Abstract. Based on quasi-linear theory (involving pitch angle scattering), the resonant interactions between ions and waves in an anisotropic multi-component plasma are discussed. In particular, electromagnetic Alfvén and ion-cyclotron waves propagating along or obliquely to the magnetic field are considered. A set of reduced (with respect to the perpendicular velocity component) quasi-linear diffusion equations is derived, involving reduced 1-D velocity distribution functions (VDFs), as they occur in wave dispersion relations. A 2-D model VDF can be constructed when using the Gaussian approximation. Wave-particle heating and acceleration rates are calculated.
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Peerlings, Luck, Friedrich Bake, Susann Boij, and Hans Bodén. "Assessing the stochastic error of acoustic scattering matrices using linear methods." International Journal of Spray and Combustion Dynamics 10, no. 4 (July 26, 2018): 380–92. http://dx.doi.org/10.1177/1756827718789066.
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To be able to compare the measured scattering matrices with model predictions, the quality of the measurements has to be known. Uncertainty analyses are invaluable to assess and improve the quality of measurement results in terms of accuracy and precision. Linear analyses are widespread, computationally fast and give information of the contribution of each error source to the overall measurement uncertainty; however, they cannot be applied in every situation. The purpose of this study is to determine if linear methods can be used to assess the quality of acoustic scattering matrices. The uncertainty in measured scattering matrices is assessed using a linear uncertainty analysis and the results are compared against Monte-Carlo simulations. It is shown that for plane waves, a linear uncertainty analysis, applied to the wave decomposition method, gives correct results when three conditions are satisfied. For higher order mode measurements, the number of conditions that have to be satisfied increases rapidly and the linear analysis becomes an unsuitable choice to determine the uncertainty on the scattering matrix coefficients. As the linear uncertainty analysis is most suitable for the plane wave range, an alternative linear method to assess the quality of the measurements is investigated. This method, based on matrix perturbation theory, gives qualitative information in the form of partial condition numbers and the implementation is straightforward. Using the alternative method, the measurements of higher order modes are analyzed and the observed difference in the measured reflection coefficients for different excitation conditions is explained by the disparity in modal amplitudes.
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Evans, D. V., and C. M. Linton. "On step approximations for water-wave problems." Journal of Fluid Mechanics 278 (November 10, 1994): 229–49. http://dx.doi.org/10.1017/s002211209400368x.
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The scattering of water waves by a varying bottom topography is considered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform strip resulting in a variable free-surface boundary condition. This is then approximated by a finite number of sections on which the free-surface boundary condition is assumed to be constant. A transition matrix theory is developed which is used to relate the wave amplitudes at ±∞. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering problems of this type.
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LI, YILE, and CHIANG C. MEI. "Bragg scattering by a line array of small cylinders in a waveguide. Part 1. Linear aspects." Journal of Fluid Mechanics 583 (July 4, 2007): 161–87. http://dx.doi.org/10.1017/s0022112007006131.
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Motivated by potential applications for offshore airports supported on vertical piles, we report a theory of wave diffraction by a periodic array of circular cylinders. The simple case of normal incidence on a rectangular array is studied here, which is equivalent to a line array along the centre of a long channel. An asymptotic theory is developed for cylinders much smaller than the incident wavelength, which is comparable to the cylinder spacing. Focus is on Bragg resonance near which scattering is strong. A combination of the method of multiple scales and the Bloch theorem leads to simple evolution equations coupling the wave envelopes. Dispersion of transient wave envelopes is investigated. Scattering of detuned waves by a large but finite number of cylinders is investigated for frequencies in and outside the band gap. Quantitative accuracy is assessed by comparisons with numerical computations via finite elements. The analytical theory prepares the ground for nonlinear studies and may facilitate future inclusion of real-fluid effects such as vortex shedding.
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Sheikh, Rizwan, and Chris Swan. "The Interaction Between Steep Waves and a Vertical, Surface-Piercing Column." Journal of Offshore Mechanics and Arctic Engineering 127, no. 1 (February 1, 2005): 31–38. http://dx.doi.org/10.1115/1.1854701.
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This paper describes new laboratory observations concerning the interaction between a series of steep incident waves and a vertical, surface-piercing, column. The motivation for the study arose as a result of wave impact damage sustained to the undersides of several concrete gravity-based structures in the northern North Sea. Earlier work, [Swan et al. Appl. Ocean. Res. 19, pp. 309–327 (1997)], demonstrated that in the case of multiple column structures, the individual diameters of which lie outside the typical (linear) diffraction regime, there exists a new and previously unexpected mechanism leading to the scattering of high-frequency waves. Although the implications of this effect was carefully documented, not least because it explained the occurrence of wave impacts in relatively moderate seas, its physical origins remained unclear. In particular, it was uncertain whether this type of scattering would be observed in the case of a single column, or whether it results from the transmission of wave modes trapped between the legs of a multiple column structure. In the case of a single column, if the diameter, D, is such that the flow lies within the drag-inertia regime, D/λ<0.2, where λ is the corresponding wavelength, linear diffraction theory suggests there will be little or no scattered wave energy. The present laboratory observations demonstrate that this is not, in fact, the case. If the incident waves are steep, a strong and apparently localized interaction is clearly observed at the water surface. This, in turn, leads to the scattering of high-frequency waves. Although these waves are relatively small in amplitude, their subsequent interaction with other steep incident waves takes the form of a classic long-wave short-wave interaction and can produce a significant increase in the maximum crest elevation relative to those recorded in the absence of the structure. The present paper will demonstrate that the scattering of these high-frequency waves, and their subsequent nonlinear interaction with other incident waves, has significant implications for the specification of an effective air-gap and hence for the setting of deck elevations.
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Meylan, M. H., and L. G. Bennetts. "Three-dimensional time-domain scattering of waves in the marginal ice zone." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2129 (August 20, 2018): 20170334. http://dx.doi.org/10.1098/rsta.2017.0334.
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Three-dimensional scattering of ocean surface waves in the marginal ice zone (MIZ) is determined in the time domain. The solution is found using spectral analysis of the linear operator for the Boltzmann equation. The method to calculate the scattering kernel that arises in the Boltzmann model from the single-floe solution is also presented along with new identities for the far-field scattering, which can be used to validate the single-floe solution. The spectrum of the operator is computed, and it is shown to have a universal structure under a special non-dimensionalization. This universal structure implies that under a scaling wave scattering in the MIZ has similar properties for a large range of ice types and wave periods. A scattering theory solution using fast Fourier transforms is given to find the solution for directional incident wave packets. A numerical solution method is also given using the split-step method and this is used to validate the spectral solution. Numerical calculations of the evolution of a typical wave field are presented. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.
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Sugawa, Masao. "Nonlinear interaction of obliquely propagating Bernstein waves with electrons in a plasma." Journal of Plasma Physics 40, no. 1 (August 1988): 87–96. http://dx.doi.org/10.1017/s0022377800013131.
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We obtain analytical expression for the interaction of obliquely propagating Bernstein waves with electrons by using the monochromatic wave approximation for quasi-linear theory in a weakly turbulent plasma. A numerical analysis is also carried out. The waves show initially strong damping and irregular amplitude oscillation, and the electron velocity distribution shows a variation corresponding to one of the waves. These are results of the energy exchange between waves and electrons. Despite the use of the monochromatic wave approximation, strongly scattering electrons with a broad velocity spread about the resonant velocity by the wave is seen.
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Lancellotti, V., and A. G. Tijhuis. "Extended Linear Embedding via Green's Operators for Analyzing Wave Scattering from Anisotropic Bodies." International Journal of Antennas and Propagation 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/467931.
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Linear embedding via Green’s operators (LEGO) is a domain decomposition method particularly well suited for the solution of scattering and radiation problems comprised of many objects. The latter are enclosed in simple-shaped subdomains (electromagnetic bricks) which are in turn described by means of scattering operators. In this paper we outline the extension of the LEGO approach to the case of penetrable objects with dyadic permittivity or permeability. Since a volume integral equation is only required to solve the scattering problem inside a brick and the scattering operators are inherently surface operators, the LEGO procedureper secan afford a reduction of the number of unknowns in the numerical solution with the Method of Moments and subsectional basis functions. Further substantial reduction is achieved with the eigencurrents expansion method (EEM) which employs the eigenvectors of the scattering operator as local entire-domain basis functions over a brick’s surface. Through a few selected numerical examples we discuss the validation and the efficiency of the LEGO-EEM technique applied to clusters of anisotropic bodies.
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Bahrami, Mousa, and Panagiotis Vasilopoulos. "Inhomogeneous linear responses and transport in armchair graphene nanoribbons in the presence of elastic scattering." Nanotechnology 33, no. 19 (February 15, 2022): 195201. http://dx.doi.org/10.1088/1361-6528/ac4fe2.
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Abstract Within linear-response theory we derive a response function that thoroughly accounts for the influence of elastic scattering and is valid beyond the long-wavelength limit. We use the theory to evaluate the polarization function and the conductivity in metallic armchair graphene nanoribbons in the Lindhard approximation for intra-band and inter-band transitions and for a relaxation time τ that is not constant. We obtain a logarithmic behaviour in the scattering-independent polarization function not only for intra-band transitions, as is usually the case for one-dimensional systems, but also for inter-band transitions. Modifying the screening wave vector and the impurity density in the long-wavelength limit strongly influences the relaxation time. In contrast, for large wave vectors, this modification leads to a conservative value of τ . We show that the imaginary part of the impurity-dependent conductivity varies with the wave vector while its scattering-independent part exists only for a single value of the wave vector.
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Belibassakis, Kostas, and Julien Touboul. "A Nonlinear Coupled-Mode Model for Waves Propagating in Vertically Sheared Currents in Variable Bathymetry—Collinear Waves and Currents." Fluids 4, no. 2 (March 30, 2019): 61. http://dx.doi.org/10.3390/fluids4020061.
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A novel coupled-mode model is developed for the wave–current–seabed interaction problem, with application in wave scattering by non-homogeneous, sheared currents over general bottom topography. The formulation is based on a velocity representation defined by a series of local vertical modes containing the propagating and evanescent modes, able to accurately treat the continuity condition and the bottom boundary condition on sloping parts of the seabed. Using the above representation in Euler equations, a coupled system of differential equations on the horizontal plane is derived, with respect to the unknown horizontal velocity modal amplitudes. In the case of small-amplitude waves, a linearized version of the above coupled-mode system is obtained, and the dispersion characteristics are studied for various interesting cases of wave–seabed–current interaction. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system is reduced to a one-equation, non-linear model, generalizing Boussinesq models. The analytical structure of the present coupled-mode system facilitates extensions to treat non-linear effects and further applications concerning wave scattering by inhomogeneous currents in coastal regions with general 3D bottom topography.
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Lim, Raymond, and Roger H. Hackman. "Elastic wave scattering from large linear arrays of bounded obstacles." Journal of the Acoustical Society of America 88, S1 (November 1990): S16. http://dx.doi.org/10.1121/1.2028746.
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Qi, Hui, Li Ming Cai, Xiang Nan Pan, and Chun Gao. "Dynamic Stress Concentration of a Circular Cavity Subjected by Steady Plane SH Waves in an Elastic Quarter with a Semi-Circular Canyon." Applied Mechanics and Materials 644-650 (September 2014): 1581–84. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.1581.
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Steady state responses of a circular cavity and a semi-circular canyon subjected by plane SH wave in an elastic quarter are presented by using Fourier-Hankel wave function expansion method and image method with Fourier series expansion on the boundary conditions to determine linear algebraic equations of unknown wave function coefficients. Especially, displacement and stress component expressions are formulated for incident, reflected, scattering waves, respectively. This method can provide an analytical ideas and methods for further studies of elastodynamic interface problems.
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Cai, Li Ming, Hui Qi, and Xiang Nan Pan. "The Scattering of Circular Cylindrical Cavity with Time-Harmonic SH Waves in Infinite Strip Region." Applied Mechanics and Materials 580-583 (July 2014): 3083–88. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3083.
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The scattering of time harmonic SH waves by arbitrary positions of circular cylindrical cavity is studied in continuous, homogeneous, isotropic, elastic strip region. In this paper, the completely analytical expression of total wave field is explicitly presented and the dynamic stress distribution is symbolically visualized in the strip region. The total wave field is divided into four sub wave fields, incident wave field and scattering wave field by the upper bound, the lower bound and the cylindrical bound, on big arc supposition. Specific wave functions are employed for each wave field expansion in series, such as circular cylindrical functions, respectively. Corresponding infinite linear algebraic equations are constructed by means of solving coefficients of Fourier series expansion on each sub wave field. Coefficients of cylindrical function expansion of each sub wave field are determined by truncated equations, which are reduced number of coefficients on pre-given computational accuracy. Numerical results graphically describe the dynamic stress concentration factor around the circumference of the cavity and the normalized dynamic stress along the cross section directly above the cavity.
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Baltenkov, Arkadiy S., and Igor Woiciechowski. "Interference Phenomenon in Electron-Molecule Collisions." Atoms 10, no. 4 (October 1, 2022): 105. http://dx.doi.org/10.3390/atoms10040105.
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This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.
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LIU, YUMING, and DICK K. P. YUE. "On generalized Bragg scattering of surface waves by bottom ripples." Journal of Fluid Mechanics 356 (February 10, 1998): 297–326. http://dx.doi.org/10.1017/s0022112097007969.
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We study the generalized Bragg scattering of surface waves over a wavy bottom. We consider the problem in the general context of nonlinear wave–wave interactions, and write down and provide geometric constructions for the Bragg resonance conditions for second-order triad (class I) and third-order quartet (class II and class III) wave– bottom interactions. Class I resonance involving one bottom and two surface wave components is classical. Class II resonance manifests bottom nonlinearity (it involves two bottom and two surface wave components), and has been studied in the laboratory. Class III Bragg resonance is new and is a result of free-surface nonlinearity involving resonant interaction among one bottom and three surface wave components. The amplitude of the resonant wave is quadratic in the surface wave slope and linear in the bottom steepness, and, unlike the former two cases, the resonant wave may be either reflected or transmitted (relative to the incident waves) depending on the wave–bottom geometry. To predict the initial spatial/temporal growth of the Bragg resonant wave for these resonances, we also provide the regular perturbation solution up to third order. To confirm these predictions and to obtain an efficient computational tool for general wave–bottom problems with resonant interactions, we extend and develop a powerful high-order spectral method originally developed for nonlinear wave–wave and wave–body interactions. The efficacy of the method is illustrated in high-order Bragg resonance computations in two and three dimensions. These results compare well with existing experiments and perturbation theory for the known class I and class II Bragg resonance cases, and obtain and elucidate the new class III resonance. It is shown that under realistic conditions with moderate to small surface and bottom steepnesses, the amplitudes of third-order class II and class III Bragg resonant waves can be comparable in magnitude to those resulting from class I interactions and appreciable relative to the incident wave.
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Chan, I.-Chi. "Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed." Mathematics 10, no. 16 (August 9, 2022): 2838. http://dx.doi.org/10.3390/math10162838.
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We present an analytical solution for the scattering of linear progressive waves by a surface rectangular obstacle above a muddy seabed. The bottom cohesive mud is assumed to act as a Newtonian fluid, and the thickness of the mud layer is considered to be comparable to the Stokes boundary layer thickness. Our analytical results based on the matched eigenfunction expansions incorporate the combined effects of obstacles and a fluid mud bottom. By reducing the mud layer thickness or the dimensions of the obstacle to zero, the present study recovers the classical solution for wave scattering by a surface obstacle above a solid bed or wave propagation over a layer of fluid mud. Our analytical predictions of wave amplitudes and wave forces acting on the bottom of the obstacle agree satisfactorily with the available numerical results. The most prominent effect of a muddy seabed is a strong damping of wave amplitude. Parameter study reveals that the obstacle submerged depth, mud layer thickness, and wave frequency can have significant impacts on the attenuation of wave amplitude due to the presence of a muddy seabed.
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Geilen, Moritz, Alexandra Nicoloiu, Daniele Narducci, Morteza Mohseni, Moritz Bechberger, Milan Ender, Florin Ciubotaru, et al. "Fully resonant magneto-elastic spin-wave excitation by surface acoustic waves under conservation of energy and linear momentum." Applied Physics Letters 120, no. 24 (June 13, 2022): 242404. http://dx.doi.org/10.1063/5.0088924.
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We report on the resonant excitation of spin waves in micro-structured magnetic thin films by short-wavelength surface acoustic waves (SAWs). The spin waves as well as the acoustic waves are studied by micro-focused Brillouin light scattering spectroscopy. At low magnetic bias fields, a resonant phonon–magnon conversion is possible, which results in the excitation of short-wavelength spin waves. Using micromagnetic simulations, we verify that during this excitation both energy and linear momentum are conserved and fully transferred from the SAW to the spin wave. This conversion can already be detected after an interaction length of a few micrometers. Thus, our findings pave the way for miniaturized magneto-elastic spin-wave emitters for magnon computing.
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Shih, P. J., T. J. Teng, and C. S. Yeh. "Fourier Expansion to Elastic Vector Wave Functions and Applications of Wave Bases to Scattering in Half-Space." Journal of Mechanics 28, no. 1 (March 2012): 19–39. http://dx.doi.org/10.1017/jmech.2012.3.
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ABSTRACTThis paper proposes a complete basis set for analyzing elastic wave scattering in half-space. The half-space is an isotropic, linear, and homogeneous medium except for a finite inhomogeneity. The wave bases are obtained by combining buried source functions and their reflected counter-waves generated from the infinite-plane boundary. The source functions are the vector wave functions of infinite-space. Based on the source functions expressed in the Fourier expansion form, the reflected counter-waves are easily obtained by solving the infinite-plane boundary conditions. Few representations adopt Wely's integration, but the Fourier expansion is developed from it and applied to decouple the angular-differential terms of the vector wave functions. In addition to the scattering of the finite inhomogeneity, the transition matrix method is extended to express the surface boundary conditions. For the numerical application in this paper, the P- and the SV- waves are assumed as the incoming fields. As an example, this paper computes stress concentrations around a cavity. The steepest-descent path method yielding the optimum integral paths is used to ensure the numerical convergence of the wave bases in the Fourier expansion. The resultant patterns from these approaches are compared with those obtained from numerical simulations.
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Los, E. E., and D. J. Strozzi. "Magnetized laser–plasma interactions in high-energy-density systems: Parallel propagation." Physics of Plasmas 29, no. 4 (April 2022): 042113. http://dx.doi.org/10.1063/5.0079547.
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We investigate parametric processes in magnetized plasmas, driven by a large-amplitude pump light wave. Our focus is on laser–plasma interactions relevant to high-energy-density (HED) systems, such as the National Ignition Facility and the Sandia MagLIF concept. We present a self-contained derivation of a “parametric” dispersion relation for magnetized three-wave interactions, meaning the pump wave is included in the equilibrium, similar to the unmagnetized work of Drake et al., Phys. Fluids 17, 778 (1974). For this, we use a multi-species plasma fluid model and Maxwell's equations. The application of an external B field causes right- and left-polarized light waves to propagate with differing phase velocities. This leads to Faraday rotation of the polarization, which can be significant in HED conditions. Phase-matching and linear wave dispersion relations show that Raman and Brillouin scattering have modified spectra due to the background B field, though this effect is usually small in systems of current practical interest. We study a scattering process we call stimulated whistler scattering, where a light wave decays to an electromagnetic whistler wave ([Formula: see text]) and a Langmuir wave. This only occurs in the presence of an external B field, which is required for the whistler wave to exist.
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Wang, G., L. Dai, and D. Liu. "A study on the scattering field of SH-waves in a topographical area consisting of a semi-cylindrical hill and a subsurface horizontal hole." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221, no. 3 (September 1, 2007): 451–65. http://dx.doi.org/10.1243/14644193jmbd52.
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This research intends to investigate the scattering field of SH-wave in a half-space containing a semicylindrical hill and a subsurface horizontal hole. A mathematical model is established in a two-dimensional plane on the basis of the characteristics of SH-waves, the ‘division-conjunction’ concept, the complex function, and moving-coordinate methods. The whole domain considered is divided into two subdomains, and the wave expressions are assumed in each subdomain. In the cylindrical subdomain, the wave function is constructed with the satisfaction of the zero-stress condition on the hill's surface automatically. In the other subdomain, the solution of the scattering waves is postulated under the stress-free condition on the horizontal surface. The analytical solutions of themodel established are obtained through a series of infinite linear algebraic equations, under the conditions that both the stress and displacement across the conjunction interface of the two subdomains are continuous. The numerical solutions are developed by truncating the infinite linear algebraic equations. The numerical simulations are performed for quantifying the displacements of the horizontal and semicylindrical hill surfaces subjected to incident SH waves, and the numerical results are verified with a comparison to the existing results of a case without subsurface hole.
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JOUDIOUX, JÉRÉMIE. "CONFORMAL SCATTERING FOR A NONLINEAR WAVE EQUATION." Journal of Hyperbolic Differential Equations 09, no. 01 (March 2012): 1–65. http://dx.doi.org/10.1142/s0219891612500014.
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We establish a geometric scattering theory for a conformally invariant nonlinear wave equation on an asymptotically simple space-time. The scattering operator is defined via some trace operators at null infinity, and the proof is decomposed into three steps. A priori linear estimates are obtained via an adaptation of the Morawetz vector field to the Schwarzschild space-time and a method introduced by Hörmander for the Goursat problem. A well-posedness theorem for the characteristic Cauchy problem on a light cone at infinity is then obtained. Its proof requires a control of the nonlinearity that is uniform in time and follows from, both, an estimate of the Sobolev constant and a decay assumption on the nonlinearity of the equation. Finally, the trace operators on conformal infinity are introduced and allow us to define the conformal scattering operator of interest.
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TAMINE, M. "SCATTERING OF ELASTIC WAVES BY THE ISOLATED LINEAR CHAIN OF PHYSISORBED ATOMS ON THE SURFACE IN A TWO-DIMENSIONAL WAVEGUIDE." Surface Review and Letters 09, no. 03n04 (June 2002): 1465–74. http://dx.doi.org/10.1142/s0218625x02003871.
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The scattering and transmission properties of vibrational waves in a perturbed two-dimensional wave-guide in the harmonic approximation are presented. The perturbation is characterized by an isolated adatom defect boundary separating two planar waveguide crystalline lattices, illustrated by a linear chain of defect masses. The theoretical approach using the matching procedure for calculating phonon scattering at their domain boundaries is also presented. The reflection and transmission probabilities in the scattering region are calculated and illustrated for heavy and light defect masses. The conductance properties, in full accordance with the Landauer–Büttiker description of electron transport, are also calculated in these two cases. It is shown that the influence of defect masses can be explained by the strong decreases of conductance values caused by the asymmetric Fano resonance type. The realistic example presented here is instructive and may constitute a precursor model for analyzing the scattering of vibrational waves by an isolated defect in the two-dimensional crystalline lattice formed by atoms adsorbed on the surface of crystal substrates such as physisorbed noble gas films on close-packed atomic planes of the metal surface. A detailed discussion on the vibrational waves in the scattering region is given.
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Grimshaw, R., L. A. Ostrovsky, A. S. Topolnikov, and K. R. Khusnutdinova. "Influence of Internal Wave on the Sound Propagation in the Subsurface Bubble Layer." Proceedings of the Mavlyutov Institute of Mechanics 8, no. 1 (2011): 54–64. http://dx.doi.org/10.21662/uim2011.1.005.
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In the paper the influence of non-linear internal wave on the propagation of acoustic signal in the subsurface ocean layer containing gas bubbles is considered. During interaction with surface waves the internal wave causes its collapse and influences the structure of bubble layer. Inhomogeneous structure of the layer promotes the local speed of sound and intensity of scattering near the ocean surface to modulate by internal wave with slight shift in phase in the direction of its propagation, which agree with recent experimental observations made on the shelf of Japan Sea.
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Linton, C. M., and M. McIver. "The interaction of waves with horizontal cylinders in two-layer fluids." Journal of Fluid Mechanics 304 (December 10, 1995): 213–29. http://dx.doi.org/10.1017/s002211209500440x.
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We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise. These relations are systematically extended to the two-fluid case. It is shown that for symmetric bodies the solutions to scattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are then solved using multipole expansions.
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Chen, Dong Ni, Hui Qi, and Yong Shi. "The Effect on Scattering of SH-Wave in a Layered Half-Space with the Subsurface Circular Cavities." Advanced Materials Research 194-196 (February 2011): 1908–11. http://dx.doi.org/10.4028/www.scientific.net/amr.194-196.1908.
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The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method and wave functions expansion method. The solution of scattering of SH-wave was given by using circular boundary of large radius to approximate straight boundary of surface elastic layer. According to boundary conditions, we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around circular cavities were discussed in numerical examples.
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Zimmerman, W. B., and G. W. Haarlemmer. "Internal gravity waves: Analysis using the periodic, inverse scattering transform." Nonlinear Processes in Geophysics 6, no. 1 (March 31, 1999): 11–26. http://dx.doi.org/10.5194/npg-6-11-1999.
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Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.
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Looi, Shi-Zhuo, and Mihai Tohaneanu. "Scattering for critical wave equations with variable coefficients." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (April 30, 2021): 298–316. http://dx.doi.org/10.1017/s0013091521000158.
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AbstractWe prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$.
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Finette, S. "Synthetic B-Scan Images by Numerical Solution of a Wave Equation." Ultrasonic Imaging 10, no. 3 (July 1988): 220–28. http://dx.doi.org/10.1177/016173468801000305.
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We describe an efficient method for obtaining model sector-scan images by direct solution of a linear wave equation characterizing pulse scattering from spatially varying bulk modulus and density distributions. Using a pseudospectral approach, the wave equation is solved numerically for each transducer orientation to obtain a set of A-line signals. After preprocessing the raw data, sector-scan images are constructed and displayed. Examples are given for several scattering object configurations, illustrating both specular and diffractive scattering in inhomogeneous media and demonstrating the utility of the model.