Is creating materials with a desired refraction coeﬃcient practically possible?

Alexander G. Ramm

doi:10.24294/can.v6i1.1953

Is creating materials with a desired refraction coeﬃcient practically possible?

Alexander G. Ramm

Article ID: 1953
Vol 6, Issue 1, 2023

VIEWS - 174 (Abstract) 184 (PDF)

Abstract

A theory of many-body wave scattering is developed under the assumption a << d << λ, where a is the characteristic size of the small body, d is the distance between neighboring bodies and λ is the wave-length in the medium in which the bodies are embedded. The multiple scattering is essential under these assumptions. The author’s theory is used for creating materials with a desired refraction coeﬃcient. This theory can be used in practice. A recipe for creating materials with a desired refraction coeﬃcient is formulated. Materials with a desired radiation pattern, for example, wave-focusing materials, can be created.

Keywords

Wave Scattering by Many Small Bodies; Smart Materials

Full Text:

PDF

References

1. Rayleigh J. Scientiﬁc papers. Cambridge: Cambridge University Press; 1992.

2. Van de Hulst HC. Light scattering by small particles. New York: Dover Publications; 1961.

3. Landau L, Lifschitz L. Electrodynamics of continuous media. Oxford: Pergamon Press; 1984.

4. Ramm AG. Wave scattering by small bodies of arbitrary shapes. Singapore: World Scientific Publishing Co. Pte. Ltd.; 2005.

5. Martin P. Multiple scattering. Cambridge: Cambridge University Press; 2006.

6. Ramm AG. Scattering by obstacles. Dordrecht: D. Reidel; 1986.

7. Ramm AG. Scattering by many small bodies and applications to condensed matter physics. Europhysics Letters 2007; 80(4): 44001. doi: 10.1209/0295-5075/80/44001.

8. Ramm AG. Many-body wave scattering by small bodies and applications. Journal of Mathematical Physics 2007; 48: 103511. doi: 10.1063/1.2799258.

9. Ramm AG. Wave scattering by small particles in a medium. Physics Letters A 2007; 367(1-2): 156–161. doi: 10.1016/j.physleta.2007.02.076.

10. Ramm AG. Wave scattering by small impedance particles in a medium. Physics Letters A 2007; 368(1-2): 164–172. doi: 10.1016/j.physleta.2007.04.061.

11. Ramm AG. Distribution of particles which produces a desired radiation pattern. Communications in Nonlinear Science and Numerical Simulation 2007; 12(7): 1115–1119. doi: 10.1016/j.cnsns.2005.11.001.

12. Ramm AG. Distribution of particles which produces a “smart” material. Journal of Statistical Physics 2007; 127: 915–934. doi: 10.1007/s10955-007-9303-3.

13. Ramm AG. Distribution of particles which produces a desired radiation pattern. Physica B: Condensed Matter 2007; 394(2): 253–255. doi: 10.1016/j.physb.2006.12.019.

14. Ramm AG. Creating wave-focusing materials. Latin American Journal of Solids and Structures 2008; 5(2): 119–127.

15. Ramm AG. Electromagnetic wave scattering by small bodies. Physics Letters A 2008; 372(23): 4298–4306. doi: 10.1016/j.physleta.2008.03.010.

16. Ramm AG. Wave scattering by many small particles embedded in a medium. Physics Letters A 2008; 372(17): 3064–3070. doi: 10.1016/j.physleta.2008.01.006.

17. Ramm AG. Preparing materials with a desired refraction coeﬃcient and applications. In: Skiadas C, Dimotikalis I, Skiadas C (editors). Topics on chaotic systems: Selected papers from Chaos 2008 International Conference. Singapore: World Scientific Publishing Co. Pte. Ltd.; 2009. p. 265–273.

18. Ramm AG. Preparing materials with a desired refraction coeﬃcient. Nonlinear Analysis: Theory, Methods & Applications 2009; 71(12): e186–e190. doi: 10.1016/j.na.2008.10.011.

19. Ramm AG. Creating desired potentials by embedding small inhomogeneities. Journal of Mathematical Physics 2009; 50: 123525. doi: 10.1063/1.3267887.

20. Ramm AG. A method for creating materials with a desired refraction coeﬃcient. International Journal of Modern Physics B 2010; 24(27): 5261–5268. doi: 10.1142/S0217979210056074.

21. Ramm AG. Materials with a desired refraction coeﬃcient can be created by embedding small particles into a given material. International Journal of Structural Changes in Solids 2010; 2(2): 17–23.

22. Ramm AG. Wave scattering by many small bodies and creating materials with a desired refraction coeﬃcient. Afrika Matematika 2011; 22: 33–55. doi: 10.1007/s13370-011-0004-3.

23. Ramm AG. Scattering by many small inhomogeneities and applications. In: Skiadas C, Dimotikalis I, Skiadas C (editors). Topics on chaotic systems: Selected papers from Chaos 2010 International Conference. Singapore: World Scientific Publishing Co. Pte. Ltd.; 2011. p. 41–52.

24. Ramm AG. Collocation method for solving some integral equations of estimation theory. International Journal of Pure and Applied Mathematics 2010; 62(1): 57–65. doi: 10.1504/IJCSM.2009.027874.

25. Ramm AG. Electromagnetic wave scattering by a small impedance particle of arbitrary shape. Optics Communications 2011; 284(16-17): 3872–3877. doi: 10.1016/j.optcom.2011.04.035.

26. Ramm AG. Scattering of scalar waves by many small particles. AIP Advances 2011; 1(2): 022135. doi: 10.1063/1.3600704.

27. Ramm AG. Scattering of electromagnetic waves by many thin cylinders. Results in Physics 2011; 1(1): 13–16. doi: 10.1016/j.rinp.2011.05.002.

28. Ramm AG. Electromagnetic wave scattering by many small perfectly conducting particles of an arbitrary shape. Optics Communications 2012; 285(18): 3679–3683. doi: 10.1016/j.optcom.2012.05.010.

29. Ramm AG. Electromagnetic wave scattering by small impedance particles of an arbitrary shape. Journal of Applied Mathematics and Computing 2013; 43(1): 427–444. doi: 10.1007/s12190-013-0671-3.

30. Ramm AG. Many-body wave scattering problems in the case of small scatterers. Journal of Applied Mathematics and Computing 2013; 41(1): 473–500. doi: 10.1007/s12190-012-0609-1

31. Ramm AG. Scattering of acoustic and electromagnetic waves by small bodies of arbitrary shapes. Applications to creating new engineered materials. New York: Momentum Press; 2013. p. 260.

32. Ramm AG. Creating materials with a desired refraction coeﬃcient. doi: 10.1088/978-1-6817-4708-8. San Rafael, California: IOP Concise Physics, Morgan & Claypool Publishers; 2017.

33. Ramm AG. Creating materials with a desired refraction coeﬃcient. 2nd ed. Bristol, UK: IOP Publishing; 2020. doi: 10.1088/978-0-7503-3391-7.

34. Ramm AG. How can one create a material with a prescribed refraction coeﬃcient? Sun Text Review of Material Science 2020; 1(1): 102. doi: 10.51737/2766-5100.2020.002.

35. Ramm AG. Scattering by obstacles and potentials, Singapore: World Scientific Publishing Co. Pte. Ltd.; 2017. p. 620. doi: 10.1142/10473.

36. Ramm AG, Tran N. A fast algorithm for solving scalar wave scattering problem by billions of particles. Journal of Algorithms and Optimization 2015; 3(1): 1–13.

37. Andriychuk MI, Ramm AG. Numerical solution of many-body wave scattering problem for small particles and creating materials with desired refraction coeﬃcient. In: Awrejcewicz J (editor). Numerical simulations of physical and engineering processes. London: IntechOpen; 2011. p. 1–28. doi: 10.5772/24495.

38. Andriychuk M, Ramm AG. Scattering of electromagnetic waves by many thin cylinders: Theory and computational modeling, Optics Communications 2012; 285(20): 4019–4026. doi: 10.1016/j.optcom.2012.06.017.

DOI: https://doi.org/10.24294/can.v6i1.1953