2010/12/13 by A. G. Ramm, А. Г. Рамм, Ramm, A. G.
Engineering · Mathematics · Physics and Astronomy · #26D10 #34G20 #37L05 #44J05 #47J35 #Classical Physics (physics.class-ph) #Electromagnetic Scattering and Analysis #FOS: Physical sciences #Numerical methods in engineering #Numerical methods in inverse problems #Optics (physics.optics) #msc:26D10 #msc:34G20 #msc:37L05 #msc:44J05 #msc:47J35 #physics.class-ph #physics.optics
paper · pdf · doi:10.48550/arxiv.1012.2761
openalex publication_date 2010/12/13 · arxiv created 2011/01/23 · arxiv updated 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scattering of electromagnetic (EM) waves by many small particles, embedded in a given medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→ 0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. An analytical formula for the permeability μ(x) of the limiting medium is given. Analysis of this formula allows one to find out the range of the values of the permeability in the material, obtained by embedding many small particles.