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. (to appear). arXiv:1108.0649 preprint.pdf
  54. D. Aristoff and C. Radin, Emergent structures in large networks, J. Appl. Probab. (to appear). arXiv:1110.1912 preprint.pdf
  55. C. Radin, A revolutionary material, Notices Amer. Math. Soc. 60(2013) 310-315. print.pdf
  56. C. Radin and L. Sadun, A mean field analysis of the fluid/solid phase transition. arXiv:1301.1256 preprint.pdf
  57. C. Radin and L. Sadun, Singularities in the entropy of asymptotically large simple graphs. arXiv:1302.3531 preprint.pdf

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)
VIDEOS

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

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

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

Encyclopaedia Britannica etc.