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. Lett., 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, J. Stat. Phys. 168(2017) 233-258. print
  97. R. Kenyon, D. Král’, C. Radin and P. Winkler, Permutations with fixed pattern densities, Random Structures Algorithms 56(2020) 220-250. print.
  98. R. Kenyon, C. Radin, K. Ren and L. Sadun, Bipodal structure in oversaturated random graphs, Int. Math. Res. Notices 2018(2016) 1009-1044. print
  99. C. Radin, Phases in large combinatorial systems, Ann. Inst. H. Poincaré D 5(2018) 287-308. print.
  100. 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.
  101. 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
  102. 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
  103. 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.
  104. C. Radin, K. Ren and L. Sadun, Surface effects in dense random graphs with sharp edge constraint, arXiv:1709.01036v2 preprint
  105. C. Radin and H. Swinney, Phases of granular matter, J. Stat. Phys. 175(2019) 542-553 print
  106. 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
  107. 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.
  108. C. Radin, Conway and aperiodic tilings, Math. Intell. 43 (2021) 15-20, print.
  109. J. Neeman, C. Radin and L. Sadun, Moderate deviations in cycle count, Random Struct. Alg. 63 (2023) 779-820, print.
  110. C. Radin, Equivalence between random close packing in granular matter and freezing in the hard sphere model, arxiv:2105.09982, preprint.
  111. J. Neeman, C. Radin and L. Sadun, Typical large graphs with given edge and triangle densities, Probab. Theory Relat. Fields (2023), arxiv:2110.14052.
  112. J. Neeman, C. Radin and L. Sadun, Existence of a symmetric bipodal phase in the edge-triangle model, arxiv:2211.10498, preprint.
  113. C. Radin and L. Sadun, Optimal graphons in the edge-2star model, arxiv:2305.00333 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"

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, Encyclopaedia Britannica etc.