Publications of Charles Radin

  1. C. Radin, Approach to equilibrium in a simple model, J. Math. Phys., 11(1970), 2945-2955. print.pdf
  2. C. Radin, Noncommutative mean ergodic theory, Comm. Math. Phys., 21(1971), 291-302. print.pdf
  3. C. Radin, Gentle perturbations, Comm. Math. Phys., 23(1971), 189-198. print.pdf
  4. G. Emch and C. Radin, Relaxation of local thermal deviations from equilibrium, J. Math. Phys., 12(1971), 2043-2046. print.pdf
  5. C. Radin, Ergodicity in von Neumann algebras, Pac. J. Math., 48(1973), 235-239. print.pdf
  6. C. Radin, Automorphisms of von Neumann algebras as point transformations, Proc. Amer. Math. Soc., 39(1973), 343-346. print.pdf
  7. C. Radin, Dynamics of limit models, Comm. Math. Phys., 33(1973), 283-292. print.pdf
  8. C. Radin, A noncommutative L_1-mean ergodic theorem, Advances in Math., 21(1976), 110-111. print.pdf
  9. C. Radin, Some remarks on the evolution of a Schrödinger particle in an attractive 1/r^2 potential, J. Math. Phys., 16(1975), 544-547. print.pdf
  10. C. Radin, Particle lattice models and the dynamical instability of many-body systems, Comm. Math. Phys., 44(1975), 165-168. print.pdf
  11. R.T. Powers and C. Radin, Average boundary conditions in Cauchy problems, J. Functional Analysis, 23(1976), 23-32. print.pdf
  12. C. Radin, The dynamical instability of nonrelativistic many-body systems, Comm. Math. Phys., 54(1977), 69-80. print.pdf
  13. C. Radin, Pointwise ergodic theory and operator algebras, J. Math. Phys. 19(1978), 1983-1985. print.pdf
  14. C. Radin and B. Simon, Invariant domains for the time-dependent Schrödinger equation, J. Diff. Eqns. 29(1978), 289-296. print.pdf
  15. J. A. Goldstein, C. Radin and R. E. Showalter, Convergence rates of ergodic limits for semigroups and cosine functions, Semigroup Forum, 16(1978), 89-95. print.pdf
  16. C. Radin, Signal propagation in lattice models of quantum many body systems, Comm. Math. Phys., 62(1978), 159-166. print.pdf
  17. C. S. Gardner and C. Radin, The infinite volume ground state of the Lennard-Jones potential, J. Stat. Phys., 20(1979), 719-724. print.pdf; (higher resolution)
  18. G. Hamrick and C. Radin, The symmetry of ground states under perturbation, J. Stat. Phys., 21(1979), 601-607. print.pdf; (higher resolution)
  19. R. Heitmann and C. Radin, The ground state for sticky disks, J. Stat. Phys., 22(1980), 281-287. print.pdf; (higher resolution)
  20. B. Borden and C. Radin, The crystal structure of the noble gases, J. Chem. Phys., 75(1981), 2012-2013. print.pdf
  21. C. Radin, The ground state for soft disks, J. Stat. Phys., 26(1981), 365-373. print.pdf; (higher resolution)
  22. C. Radin, Crystalline symmetry and surface tension, Physica, 113A(1982), 338-342. print.pdf
  23. F. Nicolò and C. Radin, A first-order phase transition between crystal phases in the shift model, J. Stat. Phys., 28(1982), 473-478. print.pdf; (higher resolution)
  24. C. Radin and L. Schulman, Periodicity of classical ground states, Phys. Rev. Letts., 51(1983), 621-622. print.pdf
  25. C. Radin, Classical ground states in one dimension, J. Stat. Phys., 35(1984), 109-117. print.pdf; (higher resolution)
  26. C. Radin, Tiling, periodicity, and crystals, J. Math. Phys. 26(1985), 1342-1344. print.pdf
  27. C. Radin, Crystals and quasicrystals: a lattice gas model, Phys. Lett., 114A(1986), 381-383. print.pdf
  28. C. Radin, Crystals and quasicrystals: a continuum model, Comm. Math. Phys., 105(1986), 385-390. print.pdf
  29. C. Radin, Correlations in classical ground states, J. Stat. Phys., 43(1986), 707-712. print.pdf; (higher resolution)
  30. J. Miekisz and C. Radin, The unstable chemical structure of quasicrystalline alloys, Phys. Lett., 119A(1986), 133-134. print.pdf
  31. J. Miekisz and C. Radin, The third law of thermodynamics, Mod. Phys. Lett., B1(1987), 61-66. print.pdf; (higher resolution)
  32. C. Radin, Low temperature and the origin of crystalline symmetry, Intl. J. Mod. Phys., B1(1987), 1157-1191. print.pdf; (higher resolution)
  33. C. Radin, Symmetry: Unifying Human Understanding, Amer. Scientist, 76(1988), 392-393. print.pdf; (higher resolution)
  34. J. Miekisz and C. Radin, Why solids are not really crystalline, Phys. Rev., B39(1989), 1950-1952. print.pdf
  35. C. Radin, Ordering in lattice gases at low temperature, J. Phys., A22(1989), 317-319. print.pdf
  36. C. Gardner, J. Miekisz, C. Radin and A. Van Enter) Fractal ground state for an Ising model, J. Phys. A22(1989), L1019-L1023. print.pdf
  37. C. Radin, Disordered Ground States of Classical Lattice Models, Revs. Math. Phys. 3(1991), 125-135. print.pdf; (higher resolution)
  38. C. Radin, Global Order from Local Sources, Review-Expository Paper, Bull. Amer. Math. Soc. 25(1991), 335-364. print.pdf; (higher resolution)
  39. C. Radin and M. Wolff, Space tilings and local isomorphism, Geometriae Dedicata 42(1992), 355-360. print.pdf; (higher resolution)
  40. C. Radin, Z^n versus Z actions for systems of finite type, Contemporary Mathematics 135(1992), 339-342. print.pdf; (higher resolution)
  41. D. Berend and C. Radin, Are there chaotic tilings?, Comm. Math. Phys. 152(1993), 215-219. print.pdf; Original, longer version: preprint.pdf
  42. C. Radin, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. 29(1993), 213-217. print.pdf
  43. C. Radin, The pinwheel tilings of the plane, Annals of Math. 139(1994), 661-702.;  print.pdf
  44. C. Radin, Symmetry and tilings, Notices Amer. Math. Soc. 42(1995), 26-31.;  print.pdf
  45. C. Radin, Space tilings and substitutions, Geometriae Dedicata 55(1995), 257-264. print.pdf; (higher resolution)
  46. C. Radin, Aperiodic tilings in higher dimensions, Proc. Amer. Math. Soc. 123(1995), 3543-3548.;  print.pdf
  47. C. Radin, Quasicrystals and geometry, Notices Amer. Math. Soc. 43(1996), 416-421.;  print.pdf
  48. 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.pdf
  49. C. Radin and L. Sadun, The isoperimetric problem for pinwheel tilings, Comm. Math. Phys. 177(1996), 255-263. print.pdf
  50. H. Koch, R. de la Llave and C. Radin, Aubry-Mather theory for functions on lattices, Discrete Contin. Dynam. Systems 3(1997), 135-151.;  preprint.pdf
  51. 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)
  52. J.H. Conway and C. Radin, Quaquaversal tilings and rotations, Inventiones math. 132(1998), 179-188.;  print.pdf
  53. C. Radin and L. Sadun, Subgroups of SO(3) associated with tilings, J. Algebra 202(1998), 611-633.;  print.pdf
  54. C. Radin, Statistical Symmetry, chapter in "Geometry at Work", MAA Notes volume 53 (Math. Assoc. Amer., Washington, DC, 2000). print.pdf; (higher resolution)
  55. C. Radin and L. Sadun, An algebraic invariant for substitution tiling systems, Geometriae Dedicata, 73(1998), 21-37.;  print.pdf
  56. C. Radin, Rashomon: pavages et rotations, Gaz. Soc. Math. de France 79(1999), 49-57. print.pdf; (higher resolution)
  57. C. Radin and L. Sadun, On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351(1999), 4469-4480.;  print.pdf
  58. J.H. Conway, C. Radin and L. Sadun, On angles whose squared trigonometric functions are rational, Discrete Comput. Geom. 22(1999), 321-332.;  print.pdf
  59. C. Radin, Symmetries of quasicrystals, J. Stat. Phys. 95(1999), 827-833.;  print.pdf
  60. J.H. Conway, C. Radin and L. Sadun, Relations in SO(3) supported by geodetic angles, Discrete Comput. Geom. 23(2000), 453-463.;  print.pdf
  61. C. Radin and L. Sadun, Isomorphism of hierarchical structures, Ergodic Theory Dynam. Systems 21(2001), 1239-1248.;  print.pdf
  62. N. Ormes, C. Radin and L. Sadun, A homeomorphism invariant for substitution tiling spaces, Geometriae Dedicata 90(2002), 153-182.;  print.pdf
  63. L. Bowen and C. Radin, Densest packing of equal spheres in hyperbolic space, Discrete Comput. Geom. 29(2003), 23-39.;  print.pdf
  64. L. Bowen and C. Radin, Optimally dense packings of hyperbolic space, Geometriae Dedicata 104(2004), 37-59. print.pdf
  65. 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)
  66. 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.pdf
  67. C. Radin, Orbits of orbs: sphere packing meets Penrose tilings, Amer. Math. Monthly 111(2004), 137-149.;  print.pdf
  68. C. Holton, C. Radin and L. Sadun, Conjugacies for tiling dynamical systems, Comm. Math. Phys. 209(2005), 343-359.;  print.pdf
  69. C. Radin, Existence of ground state configurations, Math. Phys. Electron. J. 10(2004), Paper 6, 7pp. (electronic).;  print.pdf
  70. C. Holton and C. Radin, Topological conjugacy between aperiodic tiling dynamical systems.;  preprint.pdf
  71. C. Radin and L. Sadun, Structure of the hard sphere solid, Phys. Rev. Lett. 94(2005), 015502.;  print.pdf
  72. C. Radin, A review of two books on sphere packing, Amer. Math. Monthly 113(2006), 87-90. print.pdf
  73. H. Koch, C. Radin and L. Sadun, Most stable structure for hard spheres, Phys. Rev. E 72(2005), 016708.;  print.pdf
  74. L. Bowen, R. Lyons, C. Radin and P. Winkler, Fluid-solid transition in a hard-core system, Phys. Rev. Lett. 96(2006), 025701.;  print.pdf
  75. 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
  76. M. Schröter, S. Nägle, C. Radin and H.L. Swinney, Phase transition in a static granular system, EPL 78(2007), 44004. print.pdf
  77. C. Radin, Conference report II, Appl. Rheol. 17:3(2007), 166.
  78. C. Radin, Random close packing of granular matter, J. Stat. Phys. 131(2008), 567-573. print.pdf
  79. D. Aristoff and C. Radin, Random loose packing in granular matter, J. Stat. Phys., 135(2009), 1-23. print.pdf
  80. J. Bellissard, C. Radin and S. Shlosman, The characterization of ground states, J. Phys. A: Math. Theor. 43(2010), 305001. print.pdf
  81. D. Aristoff and C. Radin, Random close packing in a granular model, J. Math. Phys. 51(2010), 113302. print.pdf
  82. H. Koch and C. Radin, Modelling quasicrystals at positive temperature, J. Stat. Phys., 138(2010), 465-475. print.pdf
  83. D. Aristoff and C. Radin, Layering in crumpled sheets, EPL 91(2010), 56003. print.pdf
  84. D. Aristoff and C. Radin, Dilatancy transition in a granular model, J. Stat. Phys. 143(2011), 215-225. print.pdf
  85. 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
  86. J.-F. Métayer, D.J. Suntrup III, C. Radin, H.L. Swinney and M. Schröter, Shearing of frictional sphere packings, EPL 93(2011), 64003 print.pdf
  87. D. Aristoff and C. Radin, First order phase transition of a long polymer chain, J. Phys. A: Math. Theor. 44(2011), 065004. print.pdf
  88. D. Aristoff and C. Radin, First order phase transition in a model of quasicrystals, J. Phys. A: Math. Theor. 44(2011), 255001. print.pdf
  89. D. Aristoff and C. Radin, Rigidity in solids, J. Stat. Phys. 144(2011) 1247-1255. print.pdf
  90. C. Radin and M. Yin, Phase transitions in exponential random graphs, Ann. Appl. Probab. 23(2013) 2458-2471. print.pdf
  91. D. Aristoff and C. Radin, Emergent structures in large networks, J. Appl. Probab. 50(2013) 883-888. print.pdf
  92. C. Radin, A revolutionary material, Notices Amer. Math. Soc. 60(2013), 310-315. print.pdf
  93. C. Radin and L. Sadun, Phase transitions in a complex network, J. Phys. A: Math. Theor. 46 (2013) 305002 print.pdf;    The previous version, with title `A mean field analysis of the fluid/solid phase transition', is here
  94. C. Radin and L. Sadun, Singularities in the entropy of asymptotically large simple graphs, J. Stat. Phys. 158 (2015) 853-865 print.pdf
  95. 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
  96. R. Kenyon, C. Radin, K. Ren and L. Sadun, Multipodal structure and phase transitions in large constrained graphs, arXiv:1405.0599v2 preprint
  97. R. Kenyon, D. Král’, C. Radin and P. Winkler, Permutations with fixed pattern densities, arXiv:1506.02340v2 preprint
  98. R. Kenyon, C. Radin, K. Ren and L. Sadun, Bipodal structure in oversaturated random graphs, arXiv:1509.05370v1 preprint
  99. C. Radin, Phases in large combinatorial systems, arXiv:1601.04787v2 preprint
  100. C. Radin, K. Ren and L. Sadun, A symmetry breaking transition in the edge/triangle network model, arXiv:1604.07929v1 preprint


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

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"

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