Selective renormalization in real space: A simple approach to intermediate-wavelength properties of granular structures

Abstract

A new real-space renormalization technique is introduced, aimed at simplifying the computation of dynamical properties of granular structures at wavelengths of order a typical grain size. The technique consists in replacing the large number of atoms within a grain by a small number of rigid masses and choosing the couplings between the masses to reproduce the low-lying properties of the isolated grains. The transformation is shown to yield results that converge rapidly to the exact solution for the dynamical properties at intermediate wavelengths.