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Alexander G Ramm

Alexander G Ramm

Kansas State University, USA

Title: Wave scattering by many small impedance particles and creating materials with a desired refraction coeffcient

Biography

Biography: Alexander G Ramm

Abstract

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: http://www.mdpi.com/journal/mathematics
[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.