Quantitative estimates for enhancement of the field excited by an emitter due to presence of two closely located spherical inclusions

Abstract

A field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium. In this paper precise quantitative estimates for such enhancement are derived when the given field is the one excited by an emitter of a dipole type and inclusions are spheres of the same radii in three dimensions. Derived estimates reveal the difference, as well as the similarity, between enhancement of the field excited by the emitter and that of the smooth background field. In particular, an estimate shows that when the enhancement occurs, the factor of enhancement is ( √ ǫ| log ǫ|) −1 , which is different from that for the smooth background field, which is known to be (ǫ| log ǫ|) −1 (ǫ is the distance between two inclusions).

Singular Functions and Characterizations of Field Concentrations: A Survey

“…There is a long list of literature in this direction of research among which we mention [3,4,9,13,21,27,28,33,34,38]. We also mention for related works [10,12,14,[22][23][24]. If the conductivity of the inclusions is 0 (the insulating case), the two-dimensional problem is dual to the perfectly conducting case (by means of the harmonic conjugation), and hence the blow-up rate of the insulating case is also −1/2 .…”

Stress concentration factors for the Lamé system arising from composites

“…Bonnetier and Triki [13] presented the asymptotic expansions of the eigenvalues for the Poincaré variational problem in the presence of two nearly touching inclusions as the distance between two inclusions approaches to zero. Kang and Yun [27,28] gave a quantitative characterization for enhancement of the field induced by an emitter in the narrow regions between two circular and spherical inclusions, respectively. The techniques used in abovementioned works are designed to solve only the linear problem.…”