Andriychuk, M.I. and Ramm, A.G. (2010) Scattering by Many Small Particles and Creating Materials with a Desired Refraction Coefficient. International Journal of Computing Science and Mathematics, 3, 102-121.
https://doi.org/10.1504/IJCSM.2010.033929

has been cited by the following article:

• TITLE: Asymptotic Solution to Scattering Problem on a Set of Small Particles and Application to Creating the Materials with a Peculiar Refractive Index

  AUTHORS: Mykhaylo I. Andriychuk

  KEYWORDS: Set of Small Particles, Scattering Problem, Asymptotic Solution, Peculiar Refractive Index, Computational Modeling

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.3, February 27, 2020

  ABSTRACT: The asymptotic solution to the scattering problem on a set of small particles, supplemented into homogeneous material, is used for modeling the materials with the desired refractive index. The consideration concerns the case of acoustic scalar scattering and the solution to initial scattering problem is built using an asymptotic approach. The closed form solution is reduced for the scattering problem. This is significant advantage of approach because there is no need to solve the respective system of boundary integral equations. High accuracy of solving the scattering problem is achieved by choosing the optimal parameters of the domain with small particles. The approach allows obtaining an explicit formula for the refractive index of the resulting inhomogeneous material. The numerical calculations show the possibility to get the specific values of refractive index including its negative values.