volume | PIER Journals

2010-08-16

Electromagnetic Wave Scattering by Many Small Bodies and Creating Materials with a Desired Refraction Coefficient

Alexander G. Ramm

Professor Alexander G. Ramm

Mathematics Department

Kansas State University

USA

Homepage

Progress In Electromagnetics Research M, Vol. 13, 203-215, 2010

doi:10.2528/PIERM10072307

Abstract

Electromagnetic wave scattering by many small particles is studied. An integral equation is derived for the self-consistent field E in a medium, obtained by embedding many small particles into a given region D. The derivation of this integral equation uses a lemma about convergence of certain sums. These sums are similar to Riemannian sums for the integral equation for E. Convergence of these sums is essentially equivalent to convergence of a collocation method for solving this integral equation. By choosing the distribution law for embedding the small particles and their physical properties one can create a medium with a desired refraction coefficient. This coefficient can be a tensor. It may have a desired absorption properties.

Citation

Copy Export

Alexander G. Ramm, "Electromagnetic Wave Scattering by Many Small Bodies and Creating Materials with a Desired Refraction Coefficient," Progress In Electromagnetics Research M, Vol. 13, 203-215, 2010.
doi:10.2528/PIERM10072307

References

1. Marchenko, V. and E. Khruslov, "Homogenization of partial Differential Equations," Birkhauser, Basel, 2006.

2. Mikhlin, S. and S. Prossdorf, Singular Integral Operators, Springer-Verlag, Berlin, 1986.

3. Milton, G., "The Theory of Composites," Cambridge University Press, Cambridge, 2002.

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., Vol. 48, No. 10, 103511, 2007.
doi:10.1063/1.2799258

6. Ramm, A. G., "Distribution of particles which produces a ``smart" material," J. Stat. Phys., Vol. 127, No. 5, 915-934, 2007.
doi:10.1007/s10955-007-9303-3

7. Ramm, A. G., "Electromagnetic wave scattering by small bodies," Phys. Lett. A, Vol. 372, No. 23, 4298-4306, 2008.
doi:10.1016/j.physleta.2008.03.010

8. 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

9. Ramm, A. G., "A collocation method for solving integral equations," International Journ. of Comput. Sci. and Math. (IJCSM), Vol. 3, No. 2, 222-228, 2009.
doi:10.1504/IJCSM.2009.027874

10. Ramm, A. G., "A singular integral equation for electromagnetic wave scattering," Internat. Journ. Pure and Appl. Math., Vol. 55, No. 4, 7-11, 2009.

11. Ramm, A. G., "Creating desired potentials by embedding small inhomogeneities," J. Math. Phys., Vol. 50, No. 12, 123525, 2009.
doi:10.1063/1.3267887

12. Stromberg, K., An Introduction to Classical Real Analysis, Wadsworth Int. Group, Belmont California, 1981.