Stability maps for columnar structures

We have previously explored the hysteresis and reversibility of transitions between ordered packings soft spheres diameter d in cylindrical channels D [A. Mughal, J. Winkelmann, D. Weaire, S. Hutzler, Phys. Rev. E 98, 043303 (2018)]. Here we extend these initial results to include all columnar structures without inner (i.e. which are contact with boundary). These can be represented by a directed network showing permissible structures. From hard sphere limit deduce that there two different types transitions, reversible irreversible. explore nature for as function pressure due changes ratio D/d. illustrated use schematic diagrams, indicating topological features each transition. Specific cases tabulated understood reference appropriate diagram.