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RRJOMS | Volume 5 | Issue 7 | November, 2017
November 13-15, 2017 | Las Vegas, USA
14th International Conference and Exhibition on
Materials Science and Engineering
Wave scattering by many small impedance particles and creating materials with a desired refraction coeffcient
The theory of acoustic and electromagnetic (EM) wave scattering by one and many small impedance particles of arbitrary
shapes is developed. The basic assumptions are: a << d <<λ, where ‘a’ is the characteristic size of particles, ‘d’ is the smallest
distance between the neighboring particles, ‘λ’ is the wavelength. This theory allows one to give a recipe for creating materials
with a desired refraction coefficient.One can create material with negative refraction: the group velocity in this material is
directed opposite to the phase velocity.
• One can create a material with a desired permeability.
• Equation is derived for the EM field in the medium in which many small impedance particles are embedded.
• Similar results are obtained in [6] for heat transfer in the media in which many small particles are distributed.
• The theory presented in this talk is developed in [1]-[6].
REFERENCES:
1. A.G.Ramm, Scattering of acoustic and electromagnetic waves by small bodies of arbitrary shapes. Applications to creating
new engineered materials, Momentum Press, New York, 2013.
2. A.G.Ramm, Many-body wave scattering problems in the case of small scatterers, J. of Appl. Math and Comput., (JAMC), 41,
N1, (2013),473-500.
3. A.G.Ramm, Scattering of electromagnetic waves by many nano-wires, Mathematics, 1, (2013), 89-99. Open access Journal:
4. A.G.Ramm, Wave scattering by many small bodies: transmission boundary conditions, Reports on Math. Physics, 71, N3,
(2013), 279-290.
5. A.G.Ramm, Scattering of EM waves by many small perfectly conducting or impedance bodies, J. Math. Phys. (JMP), 56, N9,
091901, (2015).
6. A.G.Ramm, Heat transfer in complex medium, In the book "The foundation of chaos revisited: from Poincare to recent
advances", Editor C. Skiadas, Springer, 2016, pp. 119-136.
Biography
A.G.Ramm was born in USSR and emigrated to USA in 1979. he is a US citizen, professor of mathematics at KSU, an author of more than 660 papers in math-
ematical and physical Journals, of 15 monographs, and an editor of 3 books. His scientific interests include differential and integral equations, operator theory,
mathematical physics, especially scattering theory and inverse problems, numerical analysis, especially methods for solving ill-posed problems, various problems
of applied mathematics and theoretical engineering. Professor A.G.Ramm was awarded many honors, including Fulbright Research Professorships in Israel and
Ukraine, Mercator Professorship, NATO and DAAD professorships and grants, Khwarizmi international award, distinguished professorships in some countries and
distinguished lectureships of London Mathematical Society and Hong Kong Mechanical society, and many other honors and awards. He gave invited plenary talks
at many conferences throughout the world.
Alexander G Ramm
Kansas State University, USA
Alexander G Ramm, Res. Rev. J Mat. Sci. 2017, 5:7
DOI: 10.4172/2321-6212-C1-011