Thin fractal fibers

We study how the inclusion of a fractal array of conductive thin fibers affects, and interacts with, the dynamical properties of the surrounding medium. Our approach is variational and is based on singular homogenization. We introduce the energy forms that describe the composite media formed by a two-dimensional Euclidean domain reinforced by an increasing number of thin conductive fibers developing fractal geometry. We study the convergence of the energy, under suitable assumptions for the relative strength of the fibers in relation to the embedding medium. Our results establish convergence of energy and of the spectral measures of the singular elliptic operators describing the composite medium. Copyright (c) 2012 John Wiley & Sons, Ltd.