Existence of isostatic, maximally random jammed monodisperse hard-disk packings

Existence of isostatic, maximally random jammed monodisperse hard-disk packings. Atkinson, S., Stillinger, F., H., & Torquato, S. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 111(52):18436-18441, NATL ACAD SCIENCES, 12, 2014.
abstract bibtex

We generate jammed packings of monodisperse circular hard-disks in two dimensions using the Torquato-Jiao sequential linear programming algorithm. The packings display a wide diversity of packing fractions, average coordination numbers, and order as measured by standard scalar order metrics. This geometric-structure approach enables us to show the existence of relatively large maximally random jammed (MRJ) packings with exactly isostatic jammed backbones and a packing fraction (including rattlers) of phi = 0.826. By contrast, the concept of random close packing (RCP) that identifies the most probable packings as the most disordered misleadingly identifies highly ordered disk packings as RCP in 2D. Fundamental structural descriptors such as the pair correlation function, structure factor, and Voronoi statistics show a strong contrast between the MRJ state and the typical hyperstatic, polycrystalline packings with phi approximate to 0.88 that are more commonly obtained using standard packing protocols. Establishing that the MRJ state for monodisperse hard disks is isostatic and qualitatively distinct from commonly observed polycrystalline packings contradicts conventional wisdom that such a disordered, isostatic packing does not exist due to a lack of geometrical frustration and sheds light on the nature of disorder. This prompts the question of whether an algorithm may be designed that is strongly biased toward generating the monodisperse disk MRJ state.

@article{
 title = {Existence of isostatic, maximally random jammed monodisperse hard-disk packings},
 type = {article},
 year = {2014},
 identifiers = {[object Object]},
 keywords = {packing; jamming; randomness},
 pages = {18436-18441},
 volume = {111},
 month = {12},
 publisher = {NATL ACAD SCIENCES},
 city = {2101 CONSTITUTION AVE NW, WASHINGTON, DC 20418 USA},
 id = {1595360e-d8fb-3743-aaee-65559cb4aa94},
 created = {2015-12-14T19:51:25.000Z},
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 last_modified = {2017-03-14T12:30:08.401Z},
 read = {false},
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 abstract = {We generate jammed packings of monodisperse circular hard-disks in two
dimensions using the Torquato-Jiao sequential linear programming
algorithm. The packings display a wide diversity of packing fractions,
average coordination numbers, and order as measured by standard scalar
order metrics. This geometric-structure approach enables us to show the
existence of relatively large maximally random jammed (MRJ) packings
with exactly isostatic jammed backbones and a packing fraction
(including rattlers) of phi = 0.826. By contrast, the concept of random
close packing (RCP) that identifies the most probable packings as the
most disordered misleadingly identifies highly ordered disk packings as
RCP in 2D. Fundamental structural descriptors such as the pair
correlation function, structure factor, and Voronoi statistics show a
strong contrast between the MRJ state and the typical hyperstatic,
polycrystalline packings with phi approximate to 0.88 that are more
commonly obtained using standard packing protocols. Establishing that
the MRJ state for monodisperse hard disks is isostatic and qualitatively
distinct from commonly observed polycrystalline packings contradicts
conventional wisdom that such a disordered, isostatic packing does not
exist due to a lack of geometrical frustration and sheds light on the
nature of disorder. This prompts the question of whether an algorithm
may be designed that is strongly biased toward generating the
monodisperse disk MRJ state.},
 bibtype = {article},
 author = {Atkinson, Steven and Stillinger, Frank H and Torquato, Salvatore},
 journal = {PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA},
 number = {52}
}

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The packings display a wide diversity of packing fractions,\naverage coordination numbers, and order as measured by standard scalar\norder metrics. This geometric-structure approach enables us to show the\nexistence of relatively large maximally random jammed (MRJ) packings\nwith exactly isostatic jammed backbones and a packing fraction\n(including rattlers) of phi = 0.826. By contrast, the concept of random\nclose packing (RCP) that identifies the most probable packings as the\nmost disordered misleadingly identifies highly ordered disk packings as\nRCP in 2D. Fundamental structural descriptors such as the pair\ncorrelation function, structure factor, and Voronoi statistics show a\nstrong contrast between the MRJ state and the typical hyperstatic,\npolycrystalline packings with phi approximate to 0.88 that are more\ncommonly obtained using standard packing protocols. 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This prompts the question of whether an algorithm\nmay be designed that is strongly biased toward generating the\nmonodisperse disk MRJ state.","bibtype":"article","author":"Atkinson, Steven and Stillinger, Frank H and Torquato, Salvatore","journal":"PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA","number":"52","bibtex":"@article{\n title = {Existence of isostatic, maximally random jammed monodisperse hard-disk packings},\n type = {article},\n year = {2014},\n identifiers = {[object Object]},\n keywords = {packing; jamming; randomness},\n pages = {18436-18441},\n volume = {111},\n month = {12},\n publisher = {NATL ACAD SCIENCES},\n city = {2101 CONSTITUTION AVE NW, WASHINGTON, DC 20418 USA},\n id = {1595360e-d8fb-3743-aaee-65559cb4aa94},\n created = {2015-12-14T19:51:25.000Z},\n file_attached = {false},\n profile_id = {3187ec9d-0fcc-3ba2-91e0-3075df9b18c3},\n group_id = {d75e47fd-ff52-3a4b-bf1e-6ebc7e454352},\n last_modified = {2017-03-14T12:30:08.401Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {true},\n hidden = {false},\n citation_key = {ISI:000347444400025},\n source_type = {article},\n user_context = {Article},\n private_publication = {false},\n abstract = {We generate jammed packings of monodisperse circular hard-disks in two\ndimensions using the Torquato-Jiao sequential linear programming\nalgorithm. 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