Mechanical equilibrium of conformal crystals

Abstract

The relation between a conformal mapping and the geometrical features of the conformal lattice it defines is analyzed. The field created by particles interacting via inverse power law forces and located in the vortices of the conformal lattice is determined. The field of inertial forces within a rotating disk is shown to fulfill the requirements, allowing the formation of a strictly conformal crystal. Elastic properties of the conformal crystals are analyzed: their elasticity is shown to be described by a unique elastic modulus. The distortion of a strictly conformal crystal that is induced by a small deformation of the external field is calculated. \textcopyright{} 1996 The American Physical Society.