Stability maps for columnar structures

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