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, α, dependent on circumference and density, which 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.
Bibliographical noteFunding Information:
The authors would like to thank J. M. F. G unn , J. S. W atkins , J. G artlan , R. S tanyon , H. A nsell , and C. W ilkin for their valuable insight and discussions. This work was originally presented in  and all figures are adapted from the same work. All results presented were calculated and visualised using Wolfram Mathematica. This research is funded by the EPSRC, award reference 1366111.
Copyright © 2022 The author(s).
ASJC Scopus subject areas
- Physics and Astronomy(all)