The problem of scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium is studied in order to create medium with desired permeability. Physical properties of the particles are described by their boundary impedance. The limiting integral equation is obtained for the effective EM field in the limiting medium, at a → 0 , where a is the characteristic size of a particle and M ( ) a is the number of particles. The proposed approach allows one to create a medium with a desirable spatially inhomogeneous permeability. The results of computational modeling are presented.
1. Andriychuk M. I. and Ramm A. G. Scattering by many small particles and creating materials with a desired refraction coefficient, Int. J. Computing Science and Mathematics. Vol. 3, № ½, pp. 102–121, January 2010. 2. Cioranescu D., Donate P. An introduction to homogenization, Oxford Univ. Press, New York, 1999. 3. Marchenko V., Khruslov E. Homogenization of partial differential equations, Birkhauser, Boston, 2006. 4. Muller C. Foundations of the mathematical theory of electromagnetic waves, Springer-Verlag, Berlin, 1969. 5. Ramm A. G. Many-body wave scattering by small bodies and applications, J. Math. Phys., 48, N 10, (2007). 6. Ramm A. G. Wave scattering by many small particles embedded in a medium, Phys. Lett. A, 372/17, (2008), pp. 3064-3070. 7. Ramm A. G. Electromagnetic wave scattering by many small particles and creating materials with a desired permeability, Progress in Electromagnetic Research, M (PIER M), 14, (2010), pp. 193–206.