Ramm, A. G. Electromagnetic wave scattering by small bodies. (English) Zbl 1221.78020 Phys. Lett., A 372, No. 23, 4298-4306 (2008). Summary: A reduction of the Maxwell’s system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the characteristic size of the bodies tends to zero. The technique developed is used for solving the many-body EM wave scattering problem by rigorously reducing it to solving linear algebraic systems, completely bypassing the usage of integral equations. An equation is derived for the effective field in the medium, in which many small particles are embedded. A method for creating a desired refraction coefficient is outlined. Cited in 8 Documents MSC: 78A40 Waves and radiation in optics and electromagnetic theory 78A45 Diffraction, scattering 35J10 Schrödinger operator, Schrödinger equation 70F10 \(n\)-body problems 81U40 Inverse scattering problems in quantum theory 81U05 \(2\)-body potential quantum scattering theory Keywords:electromagnetic waves; wave scattering by small bodies; many-body scattering; “smart” materials PDFBibTeX XMLCite \textit{A. G. Ramm}, Phys. Lett., A 372, No. 23, 4298--4306 (2008; Zbl 1221.78020) Full Text: DOI arXiv References: [1] Chew, W. C., Waves and Fields in Inhomogeneous Medium (1995), IEEE Press: IEEE Press Piscataway [2] Landau, L.; Lifschitz, E.; Pitaevsky, L., Electrodynamics of Continuous Medium (1984), Pergamon Press: Pergamon Press Oxford [3] (Mishchenko, M.; Hovenier, J.; Travis, L., Light Scattering by Nonspherical Particles (2002), Academic Press: Academic Press New York) [4] Müller, C., Grundprobleme der mathematischen Theorie electromagnetischer Schwingungen (1957), Springer-Verlag: Springer-Verlag Berlin · Zbl 0087.21305 [5] Ramm, A. G., Wave Scattering by Small Bodies of Arbitrary Shapes (2005), World Sci. Publisher: World Sci. Publisher Singapore · Zbl 1081.78001 [6] Ramm, A. G., Electromagnetic wave scattering by small bodies of arbitrary shapes, (Varadan, V., Acoustic, Electromagnetic and Elastic Scattering-Focus on T-matrix Approach (1980), Pergamon Press: Pergamon Press NY), 537-546 [7] Ramm, A. G., Scattering by Obstacles (1986), D. Reidel: D. Reidel Dordrecht, pp. 1-442 · Zbl 0607.35006 [8] Ramm, A. G., J. Math. Phys., 48, N10, 103511 (2007) [9] Ramm, A. G., Eur. Phys. Lett., 80, 44001 (2007) [10] Ramm, A. G., Phys. Lett. A, 370, 5-6, 522 (2007) · Zbl 1209.35138 [11] Ramm, A. G., J. Stat. Phys., 127, 5, 915 (2007) [12] Ramm, A. G., Physica B, 394, 2, 253 (2007) [13] Ramm, A. G., Phys. Lett. A, 372, 13, 2319 (2008) · Zbl 1220.35024 [14] Ramm, A. G., Phys. Lett. A, 372, 17, 3064 (2008) · Zbl 1220.35025 [15] A.G. Ramm, Creating materials with desired properties, Math. Forschungsinst. Oberwolfach, report 58/2007, pp. 10-13. “Material Theories” 16-22 December 2007; A.G. Ramm, Creating materials with desired properties, Math. Forschungsinst. Oberwolfach, report 58/2007, pp. 10-13. “Material Theories” 16-22 December 2007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.