A Solidification Phenomenon in Random Packings
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Bibliographic record
Abstract
Previous article Next article A Solidification Phenomenon in Random PackingsL. Bowen, R. Lyons, C. Radin, and P. WinklerL. Bowen, R. Lyons, C. Radin, and P. Winklerhttps://doi.org/10.1137/050647785PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe prove that uniformly random packings of copies of a certain simply connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.[1] Google Scholar[2] L. Bowen, , R. Lyons, , C. Radin and , and P. Winkler, Fluid/solid transition in a hard‐core system, Phys. Rev. Lett., 96 (2006), paper 025701. prl PRLTAO 0031-9007 Phys. Rev. Lett. CrossrefISIGoogle Scholar[3] L. Bowen, , C. Holton, , C. Radin and , and L. Sadun, Uniqueness and symmetry in problems of optimally dense packings, Math. Phys. Electron. J., 11 (2005), paper 1. 9cb MPEJFJ 1086-6655 Math. Phys. Electron. J. Google Scholar[4] A. Donev, , S. Torquato, , F. H. Stillinger and , and R. Connelly, Jamming in hard sphere and disk packings, J. Appl. Phys., 95 (2004), pp. 989–999. jap JAPIAU 0021-8979 J. Appl. Phys. CrossrefISIGoogle Scholar[5] Google Scholar[6] Google Scholar[7] Google Scholar[8] Google Scholar[9] H. Koch, , L. Sadun and , and C. Radin, Most stable structure for hard spheres, Phys. Rev. E, 72 (2005), paper 016708. pre PLEEE8 1063-651X Phys. Rev. E CrossrefISIGoogle Scholar[10] C. Radin, Orbits of orbs: Sphere packing meets Penrose tilings, Amer. Math. Monthly, 111 (2004), pp. 137–149. aml AMMYAE Am. Math. Monthly CrossrefISIGoogle Scholar[11] Google ScholarKeywordssphere packingsolidification Previous article Next article FiguresRelatedReferencesCited ByDetails On Percolation of Two-Dimensional Hard DisksCommunications in Mathematical Physics, Vol. 364, No. 1 | 6 July 2018 Cross Ref Percolation of Hard DisksJournal of Applied Probability, Vol. 51, No. 01 | 19 February 2016 Cross Ref Percolation of Hard DisksJournal of Applied Probability, Vol. 51, No. 1 | 30 January 2018 Cross Ref Spontaneous breaking of continuous rotational symmetry in two dimensionsElectronic Journal of Probability, Vol. 14, No. none | 1 Jan 2009 Cross Ref Random Close Packing of Granular MatterJournal of Statistical Physics, Vol. 131, No. 4 | 22 March 2008 Cross Ref Volume 38, Issue 4| 2006SIAM Journal on Mathematical Analysis1035-1370 History Submitted:16 December 2005Accepted:19 July 2006Published online:20 November 2006 InformationCopyright © 2006 Society for Industrial and Applied MathematicsKeywordssphere packingsolidificationMSC codes52C2552C17PDF Download Article & Publication DataArticle DOI:10.1137/050647785Article page range:pp. 1075-1089ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it