2016/12/26 by Kazunori Ando, Hyeonbae Kang, Ando, Kazunori +5 · 1 citation
Computer Science · Physics and Astronomy · Engineering · #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #Composite Material Mechanics
paper · pdf · doi:10.48550/arxiv.1612.08384
We investigate anomalous localized resonance on the circular coated structure and cloaking related to it in the context of elasto-static systems. The structure consists of the circular core with constant Lamé parameters and the circular shell of negative Lamé parameters proportional to those of the core. We show that the eigenvalues of the Neumann-Poincaré operator corresponding to the structure converges to certain non-zero numbers determined by Lamé parameters and derive precise asymptotics of the convergence. We then show with estimates that cloaking by anomalous localized resonance takes place if and only if the dipole type source lies inside critical radii determined by the radii of the core and the shell.