# zbMATH — the first resource for mathematics

Disks vs. spheres: Contrasting properties of random packings. (English) Zbl 0935.82521
Summary: Collections of random packings of rigid disks and spheres have been generated by computer using a previously described concurrent algorithm. Particles begin as infinitesimal moving points, grow in size at a uniform rate, undergo energy-nonconserving collisions, and eventually jam up. Periodic boundary conditions apply, and various numbers of particles have been considered ($$N\leq 2000$$ for disks, $$N\leq 8000$$ for spheres). The irregular disk packings thus formed are clearly polycrystalline with mean grain size dependent upon particle growth rate. By contrast, the sphere packings show a homogeneously amorphous texture substantially devoid of crystalline grains. This distinction strongly intluences the respective results for packing pair correlation functions and for the distributions of particles by contact number. Rapidly grown disk packings display occasional vacancies within the crystalline grains; no comparable voids of such distinctive size have been found in the random sphere packings. “Rattler” particles free to move locally but imprisoned by jammed neighbors occur in both the disk and sphere packings.

##### MSC:
 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 52C17 Packing and covering in $$n$$ dimensions (aspects of discrete geometry) 82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
Full Text:
##### References:
 [1] B. D. Lubachevsky and F. H. Stillinger,J. Stat. Phys. 60:561 (1990). · Zbl 1086.82569 · doi:10.1007/BF01025983 [2] C. H. Bennett,J. Appl. Phys. 43:2727 (1972). · doi:10.1063/1.1661585 [3] D. J. Adams and A. J. Matheson,J. Chem. Phys. 56:1989 (1972). · doi:10.1063/1.1677488 [4] W. M. Visscher and M. Bolsterli,Nature 239:504 (1972). · doi:10.1038/239504a0 [5] A. J. Matheson,J. Phys. C 7:2569 (1974). · doi:10.1088/0022-3719/7/15/007 [6] P. Mrafko and P. Duhaj,Phys. Stat. Sol. (a) 23:583 (1974). · doi:10.1002/pssa.2210230230 [7] T. Ichikawa,Phys. Stat. Sol. (a) 29:293 (1975). · doi:10.1002/pssa.2210290132 [8] F. Delyon and Y. E. Lévy,J. Phys. A 23:4471 (1990). · doi:10.1088/0305-4470/23/20/009 [9] G. Mason,Disc. Faraday Soc. 43:75 (1967). · doi:10.1039/df9674300075 [10] J. L. Finney,Mater. Sci. Eng. 23:199 (1976). · doi:10.1016/0025-5416(76)90194-4 [11] E. L. Hinrichsen, J. Feder, and T. Jossang,Phys. Rev. A 41:4199 (1990). · doi:10.1103/PhysRevA.41.4199 [12] B. D. Lubachevsky,J. Comp. Phys. 94:255 (1991). · Zbl 0716.68094 · doi:10.1016/0021-9991(91)90222-7 [13] H. L. Frisch,Adv. Chem. Phys. 6:229 (1964). · doi:10.1002/9780470143520.ch5 [14] F. H. Stillinger and Z. W. Salsburg,J. Stat. Phys. 1:179 (1969). · doi:10.1007/BF01007250 [15] D. Ruelle and Ya. G. Sinai,Physica 140A:1 (1986). [16] J. L. Finney,Nature 266:309 (1977). · doi:10.1038/266309a0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.