Abstract
Local structural arrest in random packings of colloidal or granular spheres is quantified by a caging number, defined as the average minimum number of randomly placed spheres on a single sphere that immobilize all its translations. We present an analytic solution for the caging number for two-dimensional hard disks immobilized by neighbor disks which are placed at random positions under the constraint of a nonoverlap condition. Immobilization of a disk with radius r = 1 by arbitrary larger neighbor disks with radius r > or = 1 is solved analytically, whereas for contacting neighbors with radius 0 < r < 1, the caging number can be evaluated accurately with an approximate excluded volume model that also applies to spheres in higher Euclidean dimension. Comparison of our exact two-dimensional caging number with studies on random disk packing indicates that it relates to the average coordination number of random loose packing, whereas the parking number is more indicative for coordination in random dense packing of disks.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.