Modeling of materials with specific properties based on asymptotic solutions of acoustic and electromagnetic scattering problems
Transcript of scientific report at the meeting of the Presidium of NAS of Ukraine, December 3, 2025
DOI:
https://doi.org/10.15407/visn2026.02.039Abstract
The report presents new significant results obtained at the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine in the field of analytical and numerical research into the properties of inhomogeneous materials based on solving problems of acoustic and electromagnetic scattering on a set of small-sized scatterers. The proposed approach allows creating materials with a given spatial dispersion, which is important for many engineering applications, in particular for the development of metamaterials.
Cite this article:
Andriychuk M.I. Modeling of materials with specific properties based on asymptotic solutions of acoustic and electromagnetic scattering problems (transcript of scientific report at the meeting of the Presidium of NAS of Ukraine, December 3, 2025). Visn. Nac. Akad. Nauk Ukr. 2026. (2): 39—43. https://doi.org/10.15407/visn2026.02.039
References
Katsenelenbaum B.Z., Voitovich N.N. Reducing the backscattering via complex impedance coating. IEEE Transactions on Antennas and Propagation. 2009. 57(7): 2123—2129. https://doi.org/10.1109/TAP.2009.2021874
Khodapanah E. Calculation of electromagnetic scattering from an inhomogeneous sphere. IEEE Transactions on Antennas and Propagation. 2019. 67(3): 1772—1778. https://doi.org/10.1109/TAP.2018.2883695
Li S., He Z., Ding D., Gu P., Liu J., Ai X. Efficient EM scattering analysis of uncertain inhomogeneous medium. IEEE Antennas and Wireless Propagation Letters. 2022. 21(6): 1178—1182. https://doi.org/10.1109/LAWP.2022.3161031
Tsalamengas J.L. Nyström-type technique for electromagnetic wave scattering in inhomogeneous material, plasma and metamaterial slabs. IEEE Open Journal of Antennas and Propagation. 2024. 5(2): 297—315. https://doi.org/10.1109/OJAP.2023.3347704
Ramm A.G. Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes. New York: Momentum Press, 2013.
Cuesta F.S., Asadchy V.S., Mirmoosa M.S., Ma X., Tretyakov S.A. Embedding fields into invisible metasurface-bound volumes. In: Proc. 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials). Espoo, Finland, 2018. P. 87—89. https://doi.org/10.1109/MetaMaterials.2018.8534065
Yatsenko V.V., Maslovski S.I., Tretyakov S.A., Prosvirnin S.L., Zouhdi S. Plane-wave reflection from double arrays of small magnetoelectric scatterers. IEEE Transactions on Antennas and Propagation. 2003. 51(1): 2—11. https://doi.org/10.1109/TAP.2003.808569
Caloz C., Sihvola A. Electromagnetic chirality. Part 1. The microscopic perspective [electromagnetic perspectives]. IEEE Antennas and Propagation Magazine. 2020. 62(1): 58—71. https://doi.org/10.1109/MAP.2019.2955698
Caloz C., Sihvola A. Electromagnetic chirality. Part 2. The macroscopic perspective [electromagnetic perspectives]. IEEE Antennas and Propagation Magazine. 2020. 62(2): 82—98. https://doi.org/10.1109/MAP.2020.2969265
Sohl C., Gustafsson M., Kristensson G. Bounds on metamaterials in scattering and antenna problems. In: 2nd European Conference on Antennas and Propagation (EuCAP 2007). Edinburgh, 2007. P. 1—4. https://doi.org/10.1049/ic.2007.1413
Chiba H., Notomi M. Graphene-induced on-demand nanocavity based on Si photonic crystal. In: Proc. 21st OptoElectronics and Communications Conference (OECC) held jointly with 2016 International Conference on Photonics in Switching (PS). Niigata, Japan, 2016. P. 1—3.
Ramm A.G. Wave Scattering by Small Bodies of Arbitrary Shapes. Singapore: World Scientific Publishing Company, 2005. https://doi.org/10.1142/5765
Ramm A.G. A collocation method for solving integral equations. International Journal of Computing Science and Mathematics. 2009. 2(3): 202—208. https://doi.org/10.1504/IJCSM.2009.027874
Andriychuk M. Asymptotic regularisation of the solution to the problem of electromagnetic field scattering from a set of small impedance particles. IET Microwaves, Antennas & Propagation. 2021. 15(10): 1330—1346. https://doi.org/10.1049/mia2.12171
Ramm A.G., Andriychuk M.I. Scattering of electromagnetic waves by many thin cylinders: theory and computational modeling. Optics Communications. 2012. 285(20): 4019—4026. https://doi.org/10.1016/j.optcom.2012.06.017
Andriychuk M.I., Yevstyhneiev B.Ye. Asymptotic method for solving the problem of scattering of electromagnetic fields by a set of small impedance particles. Journal of Mathematical Sciences. 2025. 287(2): 186—204. https://doi.org/10.1007/s10958-025-07584-9
