An analytical-numerical approach to solving the problem of scattering of acoustic waves by many small particles is investigated, based on the assumption that the distance between them is greater than their radius. It is assumed that the distances between the particles can change, and this change can be specified in different ways. Impedance boundary conditions are specified at the particle boundaries. The results of numerical simulation show that the radiation characteristics of the constructed inhomogeneous region are sensitive to the way the particles are distributed. The results obtained can be used to create materials with a given refractive index.
[1] L. L. Foldy, “The multiple scattering of waves I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev., 1945, vol. 67, pp. 107–119.
[2] G. C. Gaunaurd, H.Huang, “Acoustic scattering by a pair of spheres,” J. Acoust. Soc. Am., 1995. vol. 98. pp. 495–507.
[3] A. Charalambopoulos, G. Dassios, M. Hadjinicolaou, “Ananalytic solution for low-frequency scattering by two soft spheres,” SIAM J. Appl. Math., 1998, vol. 58, pp. 370–386.
[4] P.Gabrielli, M. Mercier-Finidori, “Acoustic scattering by two spheres: multiple scattering and symmetry considerations,” J. Sound Vibr., 2001, vol. 241. pp. 423–439.
[5] J. A. Roumeliotis, A. D. Kotsis, “Acoustic scattering from two spheres, one with a small radius,” Acoust. Phys., 2007, vol. 53, pp. 33–43.
[6] G. Kapodistrias, P. H. Dahl, “Effects of interaction between two bubble scatterers,” J. Acoust. Soc. Am., 2000, vol. 107, no. 6, pp. 3006-3017.
[7] P. A. Martin, “On the T-matrix f or scattering by small obstacles,” J. Comput. Appl. Math., 2007, vol. 204, pp. 219–230.
[8] A. G. Ramm, Wave Scattering by Small Bodies of Arbitrary Shapes. Singapore: World Scientific, 2005.
[9] A. G. Ramm, “Many Body Wave Scattering by Small Bodies and Applications,” J. Math. Phys., vol. 48, pp. 103511–103511-7, October 2007.
[10] A. G. Ramm, “Wave Scattering by Many Small Particles Embedded in a Medium,” Physics Letters A, vol. 372, pp. 3064–3070, April 2008.
[11] M. I. Andriychuk and B. Ye. Yevstyhneiev, “Asymptotic method for solving the problem of scattering of electromagnetic fields by a set of small impedance particles,” Journal of Mathematical Sciences, vol. 287, no. 2, January, 2025, pp. 186-204. https://doi.org/10.1007/s10958-025-07584-9.
[12] A. G. Ramm, “A recipe for making materials with negative refraction in acoustics,” Phys. Lett. A, 2008, vol. 372. no. 13, pp. 2319-2321.