Publications on Packing, Tiling and Ground States, by Charles Radin

  1. C. Radin, Low temperature and the origin of crystalline symmetry, Intl. J. Mod. Phys., B1(1987), 1157-1191. print.pdf; (higher resolution)
  2. C. Radin, Global Order from Local Sources, Review-Expository Paper, Bull. Amer. Math. Soc. 25(1991), 335-364. print.pdf; (higher resolution)
  3. C. Radin and M. Wolff, Space tilings and local isomorphism, Geometriae Dedicata 42(1992), 355-360. print.pdf; (higher resolution)
  4. C. Radin, Z^n versus Z actions for systems of finite type, Contemporary Mathematics 135(1992), 339-342. print.pdf; (higher resolution)
  5. D. Berend and C. Radin, Are there chaotic tilings?, Comm. Math. Phys. 152(1993), 215-219. print.pdf; Original, longer version: preprint.pdf
  6. C. Radin, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. 29(1993), 213-217. print.pdf
  7. C. Radin, The pinwheel tilings of the plane, Annals of Math. 139(1994), 661-702. print.ps;  print.pdf
  8. C. Radin, Symmetry and tilings, Notices Amer. Math. Soc. 42(1995), 26-31. print.ps;  print.pdf
  9. C. Radin, Space tilings and substitutions, Geometriae Dedicata 55(1995), 257-264. print.pdf; (higher resolution)
  10. C. Radin, Aperiodic tilings in higher dimensions, Proc. Amer. Math. Soc. 123(1995), 3543-3548. print.ps;  print.pdf
  11. C. Radin, Quasicrystals and geometry, Notices Amer. Math. Soc. 43(1996), 416-421. print.ps;  print.pdf
  12. C. Radin, Miles of Tiles, Ergodic theory of Z^d-actions, London Math. Soc. Lecture Notes Ser. 228(1996), Cambridge Univ Press, 237-258. preprint.ps;  preprint.pdf
  13. C. Radin and L. Sadun, The isoperimetric problem for pinwheel tilings, Comm. Math. Phys. 177(1996), 255-263. print.pdf
  14. C. Radin, Aperiodic tilings, ergodic theory and rotations, The Mathematics of Long-Range Aperiodic Order, Nato Adv. Sci. Institutes Ser. 489(1997), Kluwer, 499-519. print.pdf; (higher resolution)
  15. J.H. Conway and C. Radin, Quaquaversal tilings and rotations, Inventiones math. 132(1998), 179-188. print.ps;  print.pdf
  16. C. Radin and L. Sadun, Subgroups of SO(3) associated with tilings, J. Algebra 202(1998), 611-633. print.ps;  print.pdf
  17. C. Radin, Statistical Symmetry, chapter in "Geometry at Work", MAA Notes volume 53 (Math. Assoc. Amer., Washington, DC, 2000). print.pdf; (higher resolution)
  18. C. Radin and L. Sadun, An algebraic invariant for substitution tiling systems, Geometriae Dedicata, 73(1998), 21-37. print.ps;  print.pdf
  19. C. Radin, Rashomon: pavages et rotations, Gaz. Soc. Math. de France 79(1999), 49-57. print.pdf; (higher resolution)
  20. C. Radin and L. Sadun, On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351(1999), 4469-4480. print.ps;  print.pdf
  21. J.H. Conway, C. Radin and L. Sadun, On angles whose squared trigonometric functions are rational, Discrete Comput. Geom. 22(1999), 321-332. print.ps;  print.pdf
  22. C. Radin, Symmetries of quasicrystals, J. Stat. Phys. 95(1999), 827-833. print.ps;  print.pdf
  23. J.H. Conway, C. Radin and L. Sadun, Relations in SO(3) supported by geodetic angles, Discrete Comput. Geom. 23(2000), 453-463. print.ps;  print.pdf
  24. C. Radin and L. Sadun, Isomorphism of hierarchical structures, Ergodic Theory Dynam. Systems 21(2001), 1239-1248. print.ps;  print.pdf
  25. N. Ormes, C. Radin and L. Sadun, A homeomorphism invariant for substitution tiling spaces, Geometriae Dedicata 90(2002), 153-182. print.ps;  print.pdf
  26. L. Bowen and C. Radin, Densest packing of equal spheres in hyperbolic space, Discrete Comput. Geom. 29(2003), 23-39. print.ps;  print.pdf
  27. L. Bowen and C. Radin, Optimally dense packings of hyperbolic space, Geometriae Dedicata 104(2004), 37-59. print.ps print.pdf
  28. C. Radin, The symmetry of optimally dense packings, in Non-Euclidean Geometries: János Bolyai Memorial Volume, Mathematics and Its Applications, Vol. 581, Springer, 2006, pp. 197-207. print.pdf;  (higher resolution)
  29. L. Bowen, C. Holton, C. Radin and L. Sadun, Uniqueness and symmetry in problems of optimally dense packings, Math. Phys. Electron. J. 11(2005), Paper 1, 34pp. (electronic) print.ps;  print.pdf
    C. Radin,
  30. Orbits of orbs: sphere packing meets Penrose tilings, Amer. Math. Monthly 111(2004), 137-149. print.ps;  print.pdf
  31. C. Holton, C. Radin and L. Sadun, Conjugacies for tiling dynamical systems, Comm. Math. Phys. 209(2005), 343-359. print.ps;  print.pdf
  32. C. Radin, Existence of ground state configurations, Math. Phys. Electron. J. 10(2004), Paper 6. (electronic). print.ps;  print.pdf
  33. C. Holton and C. Radin, Topological conjugacy between aperiodic tiling dynamical systems. preprint.ps;  preprint.pdf
  34. C. Radin and L. Sadun, Structure of the hard sphere solid, Phys. Rev. Lett. 94(2005), 015502. print.ps;  print.pdf
  35. C. Radin, A review of two books on sphere packing, Amer. Math. Monthly 113(2006), 87-90. print.pdf
  36. H. Koch, C. Radin and L. Sadun, Most stable structure for hard spheres, Phys. Rev. E 72(2005), 016708. print.ps;  print.pdf
  37. L. Bowen, R. Lyons, C. Radin and P. Winkler, Fluid-solid transition in a hard-core system, Phys. Rev. Lett. 96(2006), 025701. print.ps;  print.pdf
  38. L. Bowen, R. Lyons, C. Radin and P. Winkler, A solidification phenomenon in random packings, SIAM J. Math. Anal. 38(2006), 1075-1089. print.pdf
  39. M. Schröter, S. Nägle, C. Radin and H.L. Swinney, Phase transition in a static granular system, EPL 78 (2007), 44004. print.pdf
  40. C. Radin, Conference report II, Appl. Rheol. 17:3(2007), 166.
  41. C. Radin, Random close packing of granular matter, J. Stat. Phys. 131(2008), 567-573. print.pdf
  42. D. Aristoff and C. Radin, Random loose packing in granular matter, J. Stat. Phys., 135(2009), 1-23. print.pdf
  43. J. Bellissard, C. Radin and S. Shlosman, The characterization of ground states, J. Phys. A: Math. Theor. 43(2010), 305001. print.pdf
  44. D. Aristoff and C. Radin, Random close packing in a granular model, J. Math. Phys. 51(2010), 113302. print.pdf
  45. H. Koch and C. Radin, Modelling quasicrystals at positive temperature, J. Stat. Phys., 138(2010), 465-475. print.pdf
  46. D. Aristoff and C. Radin, Layering in crumpled sheets, EPL 91(2010), 56003. print.pdf
  47. D. Aristoff and C. Radin, Dilatancy Transition in a Granular Model, J. Stat. Phys. 143(2011), 215-225. print.pdf
  48. T. Argo, M. Guild, P. Wilson, M. Schröter, C. Radin and H. Swinney, Sound speed in water-saturated glass beads as a function of frequency and porosity, J. Acoust. Soc. Am. 129(2011) EL101-EL107. print.pdf
  49. J.-F. Métayer, D.J. Suntrup III, C. Radin, H.L. Swinney and M. Schröter, Shearing of frictional sphere packings, EPL 93(2011), 64003 preprint.pdf
  50. D. Aristoff and C. Radin, First order phase transition of a long polymer chain, J. Phys. A: Math. Theor. 44(2011), 065004. print.pdf
  51. D. Aristoff and C. Radin, First order phase transition in a model of quasicrystals, J. Phys. A: Math. Theor. 44(2011), 255001. print.pdf
  52. D. Aristoff and C. Radin, Rigidity in solids, J. Stat. Phys. 144(2011) 1247-1255. print.pdf
  53. C. Radin and M. Yin, Phase transitions in exponential random graphs, Ann. Appl. Probab. 23(2013) 2458-2471. eprint.pdf
  54. D. Aristoff and C. Radin, Emergent structures in large networks, J. Appl. Probab. 50(2013) 883-888. print.pdf
  55. C. Radin, A revolutionary material, Notices Amer. Math. Soc. 60(2013) 310-315. print.pdf
  56. C. Radin and L. Sadun, Phase transitions in a complex network, J. Phys. A: Math. Theor. 46 (2013) 305002 preprint.pdf;    The previous version, with title `A mean field analysis of the fluid/solid phase transition', is here
  57. C. Radin and L. Sadun, Singularities in the entropy of asymptotically large simple graphs. J. Stat. Phys. 158 (2015) 853-865 print.pdf
  58. C. Radin, K. Ren and L. Sadun, The asymptotics of large constrained graphs, J. Phys. A: Math. Theor. 47 (2014) 175001 print-color.pdf    print-grayscale.pdf
  59. R. Kenyon, C. Radin, K. Ren and L. Sadun, Multipodal structure and phase transitions in large constrained graphs, J. Stat. Phys. (2017) 233-258 doi:10.1007/s10955-017-1804-0 print
  60. R. Kenyon, D. Král’, C. Radin and P. Winkler, Permutations with fixed pattern densities, Random Structures Algorithms 56(2020) 220-250. DOI: 10.1002/rsa.20882, print.
  61. R. Kenyon, C. Radin, K. Ren and L. Sadun, Bipodal structure in oversaturated random graphs, Int. Math. Res. Notices 2018(2016) 1009-1044 print
  62. C. Radin, Phases in large combinatorial systems, Ann. Inst. H. Poincaré D 5 (2018) 287-308 print.
  63. C. Radin, K. Ren and L. Sadun, A symmetry breaking transition in the edge/triangle network model, Ann. Inst. H. Poincaré D 5 (2018) 251-286 print.
  64. C. Radin, The open mathematics of crystallization, Notices Amer. Math. Soc. 64(2017) 551-556. print. There is a more technical version: `Wulff shape for equilibrium phases', arXiv:1610.08564v2 , here
  65. R. Kenyon, C. Radin, K. Ren and L. Sadun, The phases of large networks with edge and triangle constraints, J. Phys. A: Math. Theor. 50(2017) 435001. print
  66. F. Rietz, C. Radin, H. Swinney and M. Schröter, Nucleation in sheared granular matter, Phys. Rev. Lett. 120(2018) 055701. print.    Supplemental Material.    Movie from Supplementary Material.
  67. C. Radin, K. Ren and L. Sadun, Surface effects in dense random graphs with sharp edge constraint, arXiv:1709.01036v2 preprint
  68. C. Radin and H. Swinney, Phases of granular matter, J. Stat. Phys. 175(2019) 542-553 doi.org/10.10/s10955-018-2144-4 print
  69. J. Neeman, C. Radin and L. Sadun, Phase transitions in finite random networks, J Stat Phys 181 (2020) 305-328, print.    Title of previous version: `Nucleation during phase transitions in random networks'.    Supplementary movies at https://www.youtube.com/playlist?list=PLZcI2rZdDGQqx3WEY6BXoJXcxqQXF5ZzQ
  70. W. Jin, C. O'Hern, C. Radin, M. Shattuck and H.L. Swinney, Homogeneous crystallization in cyclically sheared frictionless grains, Phys. Rev. Lett. 125 (2020) 258003. print.    Supplemental Material.
  71. C. Radin, Conway and aperiodic tilings, Math. Intell. 43 (2021) 15-20, print.
  72. J. Neeman, C. Radin and L. Sadun, Moderate deviations in cycle count, Random Struct. Alg. 63 (2023) 779-820, %https://doi.org/10.1002/rsa.21147, %arxiv:2101.08249, print.
  73. C. Radin, Equivalence between random close packing in granular matter and freezing in the hard sphere model, arxiv:2105.09982, preprint.
  74. J. Neeman, C. Radin and L. Sadun, Typical large graphs with given edge and triangle densities, Probab. Theory Relat. Fields (2023), https://doi.org/10.1007/s00440-023-01187-8. arxiv:2110.14052.
  75. J. Neeman, C. Radin and L. Sadun, Existence of a symmetric bipodal phase in the edge-triangle model, J. Phys. A: Math. Theor. 57 (2024) 095003. print.
  76. C. Radin and L. Sadun, Optimal graphons in the edge-2star model, arxiv:2305.00333 preprint.
  77. S. Su, J. Zhang, C. Radin and H.L. Swinney, Crystalline and polycrystalline regimes in a periodically sheared 2-dimensional system of disks, arxiv:2411.03667v1 preprint.
  78. C. Radin and L. Sadun, Emergence in graphs with near-extreme constraints, arxiv:2411.14556v1 preprint.

WEB PAGES

Definitions of thermodynamic phases and phase transitions (AIM workshop, 2006; with M.E. Fisher)

Quasicrystals: solids with unusual symmetry (Scholarpedia)

Phase transitions in crumpled matter (IOP Insights)

Sphere packing and phases

Complex networks and phases
VIDEOS

Lecture to undergraduates (2010): "Water vs. ice"

Lecture at Vanderbilt conference (2010): "The Stability of Optimizers of Energy or Density"

Lecture at Newton Institute conference on random graphs, 2016: "Emergent Phases"
BOOKS

M. Bowick, D. Kinderlehrer, G. Menon and C. Radin, eds., Mathematics and Materials, IAS/Park City Mathematics Series, Vol 23, Amer. Math. Soc., Providence, 2017

C. Radin, Miles of Tiles, Student Mathematical Library, Vol 1 (Amer. Math. Soc., Providence, 1999).
ARTICLES IN THE POPULAR PRESS

Wired.com, Encyclopaedia Britannica etc.