Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder

Abstract

Abstract Phyllotaxis is a botanical classification scheme that can describe regular lattice-like structures on cylinders, often as a set of helical chains. In this letter, we study the general properties of repulsive particles on cylindrical geometries and demonstrate that this leads to a model which allows one to predict the minimum energy configuration for any given combination of system parameters. We are able to predict a sequence of transitions between phyllotactic ground states at zero temperature. Our results are understood in terms of a newly identified global scale invariant, \(\alpha\), dependent on circumference and density, which \emph{alone} determines the ground state structure. This representation provides a framework within which to understand and create lattice structures on more complex curved surfaces, which occur in both biological and nanoscale experimental settings.