Vol. 13
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2010-08-16
Electromagnetic Wave Scattering by Many Small Bodies and Creating Materials with a Desired Refraction Coefficient
By
Progress In Electromagnetics Research M, Vol. 13, 203-215, 2010
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
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
http://www.jpier.org/PIERM/pier.php?paper=10072307
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.