Wave Propagation and Diffraction

Wave propagation and diffraction through non-persistent rock joints: An analytical and numerical study

Numerical modeling of wave propagation into a harbor using improved characteristic scheme

Article Maslov canonical operator in problems of numerical simulation of diffraction and propagation of waves in inhomogeneous media was published on January 1, 1990 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 5, issue 6).

Application of the method of generalized potentials to the solution of certain problems in the theory of the diffraction and propagation of waves

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A finite element model for wave refraction, diffraction, reflection and dissipation

Various formulations of problems in the statistical theory of diffraction and wave propagation are discussed: excitation of fields by random sources, diffraction of partially coherent waves, diffraction of waves by bodies having random shapes or positions, and diffraction and propagation of waves in a randomly inhomogeneous medium. For each of these types of problem, physical problems from acoustics, radio astronomy, radiophysics, optics, and other branches of physics are given as examples, and the methods (mostly approximate ones) most widely used for solving them are indicated. Among the problems discussed are those of the diffraction content of the radiation transport equation and the back scattering enhancement effect observed in the diffraction of waves by small bodies immersed in a randomly irregular medium. Examples of statistical problems of mixed type are also given.

This introductory chapter presents some of the methods that are useful for solving the problems of wave diffraction theory: method of separation of variables, method of power series, method of spline functions, and method of an auxiliary boundary. We also consider some algorithms for the numerical inversion of the Laplace transform, which is often used to solve the wave diffraction problems. Finally, we give a brief account of the method of multiple scales that is often used to study the propagation of transient waves.

This chapter deals with some aspects of the initial-boundary-value problems of the initiation, generation and propagation of tsunami waves. The generation of tsunami waves by bottom movements is considered. We formulate an appropriate initial-boundary-value problem and analyse the effect of the sharpness of vertical axisymmetric bottom disturbance and the disturbance duration on the generation of tsunami waves. The propagation of nonlinear waves on water and their evolution over a nonrigid elastic bottom are investigated. Some aspects and indeterminacy of the formulation of the initial-boundary-value problems dealing with the initiation and generation of tsunami waves are considered. We consider some typical types of tsunami waves that demonstrate the indeterminacy of their initiation in time because of the indeterminacy in the physical trigger mechanism of underwater earthquakes. Based on the three-dimensional formulation, evolution equations describing the propagation of nonlinear dispersive surface waves on water over a spatially inhomogeneous bottom are obtained with allowance for the bottom disturbances in time. We use the Laplace transform with respect to the time coordinate and the power series method with respect to the spatial coordinate to find a solution to the nonstationary problem of the diffraction of surface gravity waves by a radial bottom inhomogeneity that deviates from its initial position. The propagation and stability of nonlinear waves in a two-layer fluid with allowance for surface tension are analysed by the asymptotic method of multiscale expansions.

In connection with its Industrial Associates program, the California Institute of Technology sponsors four or five conferences or symposia each year on scientific subject matter of topical interest. In May 1961 the Division of Engineering at Caltech was host to a conference on ‘Developments in Wave Propagation’ in this continuing program. With wave propagation as a common theme, the conference program drew on recognized authorities from a broad variety of physical fields for modern accounts of the knowledge, existing problems, and techniques for dealing with them. Specifically, the 3-day meeting had twelve 1-hour lectures, given in sessions on Methods in Wave Problems, Diffraction and Scattering of Elastic Waves, Waves in Dispersive Elastic and Anelastic Media, Hydrodynamic and Magnetohydrodynamic Waves, Electromagnetic Waves, and Nuclear Burst Wave Problems.

3D modeling of the influence of a splay fault on controlling the propagation of nonlinear stress waves induced by blast loading

PACS number: 41.20.Jb Purpose: The E-polarized wave diffraction by an infinite periodic strip grating without a single strip is considered. Design/methodology/approach: The total field is found as a sum of field of infinite periodical grating and field induced by the removal of a single strip. The problem is reduced to the singular integral equations with additional conditions. Findings: The directional patterns and field distribution in the domain above the grating are represented. Conclusions: The effective algorithm for study of the field which appeared as a result of absence of a single strip is suggested. Key words: infinite periodic grating, integral equation, diffraction Manuscript submitted 30.05.2016 Radio phys. radio astron. 2016, 21(3): 189-197 REFERENCES 1. SHESTOPALOV, V. P., 1971. The method of the Riemann-Hilbert problem in the theory of electromagnetic wave diffraction and propagation . Kharkiv: Kharkiv State University Press (in Russian). 2. SHESTOPALOV, V. P., LYTVYNENKO, L. M., MASALOV, S. A. and SOLOGUB, V. G., 1973. Wave diffraction by gratings . Kharkiv: Kharkiv State University Press,(in Russian). 3. SOLOGUB, V. G., 1975. On some method for studying the problem of diffraction by a finite number of strips in the same plane. Dokl. AN USSR . Ser. A . no. 6, pp. 549–552 (in Russian). 4. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2012. Wave diffraction by periodic multilayer structures . Cambridge: Cambridge Scientific Publishers. 5. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY,S. A., 2013. Wave diffraction by semi-infinite venetian blind type grating. IEEE Trans. Antennas Propag . vol. 61, no. 12, pp. 6120–6127. DOI: https://doi.org/10.1109/TAP.2013.2281510 6. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY,S. A., 2015. Diffraction of H-polarized electromagnetic waves by a multi-element planar semi-infinitegrating. Telecommunications and Radio Engineering . vol. 74, no. 9, pp. 753–767. DOI: https://doi.org/10.1615/TelecomRadEng.v74.i9.10 7. NEPA, P., MANARA, G. and ARMOGIDA, A., 2005. EM scattering from the edge of a semi-infinite planar strip grating using approximate boundary conditions. IEEE Trans.Antennas Propag . vol. 53, no. 1, pp. 82–90. DOI: https://doi.org/10.1109/TAP.2004.840523 8. GANDEL, YU. V., 1986. The method of discrete singularities in problems of electrodynamics. Voprosy Kibernetiki . no. 124, pp. 166–183 (in Russian) 9. GANDEL, YU. V., 2010. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J. Math. Sci. vol. 171, no. 1, pp. 74–88. DOI: https://doi.org/10.1007/s10958-010-0127-3 10. ZAGINAYLOV, G. I., GANDEL, Y. V., KAMYSHAN, O. P.,KAMYSHAN, V. V., HIRATA, A., THUMVONGSKUL, T. and SHIOZAWA, T., 2002. Full-wave analysis of the field distribution of natural modes in the rectangular waveguide grating based on singular integral equation method. IEEE Trans. Plasma Sci . vol. 30, no. 3. pp. 1151–1159. DOI: https://doi.org/10.1109/TPS.2002.801613 11. ZAMYATIN, YE. V. and PROSVIRNIN, S. L., 1986. Diffraction of electromagnetic waves by an array with small random fluctuations of the dimensions. Sov. J. Commun. Technol. Electron . vol. 31, no. 3, pp. 43–50. 12. ABRAMOWITZ, M. and STEGUN, I. A., eds., 1964. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables . Numder 55 in National Bureau of Standards Applied Mathematics Series. U. S. Government Printing Office, Washington, D. C. 13. FELSEN, L. B. and MARCUVITS, N., 1973. Radiation and Scattering of Waves . Englewood Cliffs, N.J.: Prentice-Hall.

A higher-order boundary element method (HOBEM) for simulating the fully nonlinear regular wave propagation and diffraction around a fixed vertical circular cylinder is investigated. The domain decomposition method with continuity conditions enforced on the interfaces between the adjacent sub-domains is implemented for reducing the computational cost. By adjusting the algorithm of iterative procedure on the interfaces, four types of coupling strategies are established, that is, Dirchlet/Dirchlet-Neumman/Neumman (D/D-N/N), Dirchlet-Neumman (D-N), Neumman-Dirchlet (N-D) and Mixed Dirchlet-Neumman/Neumman-Dirchlet (Mixed D-N/N-D). Numerical simulations indicate that the domain decomposition methods can provide accurate results compared with that of the single domain method. According to the comparisons of computational efficiency, the D/D-N/N coupling strategy is recommended for the wave propagation problem. As for the wave-body interaction problem, the Mixed D-N/N-D coupling strategy can obtain the highest computational efficiency.

Thermo-mechanical analysis and application to depressurization and wave propagation

With the demand of high accuracy of defection and sizing in ultrasonic testing, numerical modeling of wave propagation needs to consider the scattering of waves among the boundaries of crystal grains. In this paper, a method is developed for automatically generating grain boundaries in finite element models. The properties of received signals in intensity and frequency spectrum by simulations are compared with those by experiments. They are in excellent agreement. This model is also applied to the numerical analysis of the wave propagation under longitudinal angle beam testing for solids with various average grain diameters. Numerical results show that a diffracted longitudinal wave can be easily measured in the case where the average grain diameter is smaller than 80 μm but it is diffcult to identify the diffracted longitudinal wave when the average grain diameter is larger than 150 μm because the diffracted waves are probably masked by the scattering waves on the grain boundaries. Moreover, numerical results also show that the crystal grain model developed in this paper provides an effective way to model wave propagation quantitatively.