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2010-10-22
Electromagnetic Wave Scattering by Many Small Particles and Creating Materials with a Desired Permeability
By
Progress In Electromagnetics Research M, Vol. 14, 193-206, 2010
Abstract
Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a → 0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium. While the initial medium has a constant permeability μ0, the limiting medium, obtained as a result of embedding many small particles with prescribed boundary impedances, has a non-homogeneous permeability which is expressed analytically in terms of the density of the distribution of the small particles and their boundary impedances. Therefore, a new physical phenomenon is predicted theoretically, namely, appearance of a spatially inhomogeneous permeability as a result of embedding of many small particles whose physical properties are described by their boundary impedances.
Citation
Alexander G. Ramm, "Electromagnetic Wave Scattering by Many Small Particles and Creating Materials with a Desired Permeability," Progress In Electromagnetics Research M, Vol. 14, 193-206, 2010.
doi:10.2528/PIERM10091603
References

1. Cioranescu, D. and P. Donato, An Introduction to Homogenization, Oxford Univ. Press, New York, 1999.

2. Marchenko, V. and E. Khruslov, Homogenization of Partial Differential Equations, BirkhÄauser, Boston, 2006.

3. Müller, C., Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, Berlin, 1969.

4. Ramm, A. G., "Many-body wave scattering by small bodies and applications," J. Math. Phys., Vol. 48, No. 10, 103511, 2007.
doi:10.1063/1.2799258

5. Ramm, A. G., "Wave scattering by many small particles embedded in a medium," Phys. Lett. A, Vol. 372, No. 17, 3064-3070, 2008.
doi:10.1016/j.physleta.2008.01.006

6. Ramm, A. G., "A collocation method for solving integral equations," Internat. Journ. Comp. Sci. Math (IJCSM), Vol. 3, No. 2, 222-228, 2009.
doi:10.1504/IJCSM.2009.027874

7. Ramm, A. G., "Electromagnetic wave scattering by many small bodies and creating materials with a desired refraction coefficient," Progress In Electromagnetic Research M, Vol. 13, 203-215, 2010.
doi:10.2528/PIERM10072307