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.ps;  print.pdf
  44. C. Radin, Symmetry and tilings, Notices Amer. Math. Soc. 42(1995), 26-31. print.ps;  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.ps;  print.pdf
  47. C. Radin, Quasicrystals and geometry, Notices Amer. Math. Soc. 43(1996), 416-421. print.ps;  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.ps;  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.ps;  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.ps;  print.pdf
  53. C. Radin and L. Sadun, Subgroups of SO(3) associated with tilings, J. Algebra 202(1998), 611-633. print.ps;  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.ps;  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.ps;  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.ps;  print.pdf
  59. C. Radin, Symmetries of quasicrystals, J. Stat. Phys. 95(1999), 827-833. print.ps;  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.ps;  print.pdf
  61. C. Radin and L. Sadun, Isomorphism of hierarchical structures, Ergodic Theory Dynam. Systems 21(2001), 1239-1248. print.ps;  print.pdf
  62. N. Ormes, C. Radin and L. Sadun, A homeomorphism invariant for substitution tiling spaces, Geometriae Dedicata 90(2002), 153-182. print.ps;  print.pdf
  63. L. Bowen and C. Radin, Densest packing of equal spheres in hyperbolic space, Discrete Comput. Geom. 29(2003), 23-39. print.ps;  print.pdf
  64. L. Bowen and C. Radin, Optimally dense packings of hyperbolic space, Geometriae Dedicata 104(2004), 37-59. print.ps 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.ps;  print.pdf
  67. C. Radin, Orbits of orbs: sphere packing meets Penrose tilings, Amer. Math. Monthly 111(2004) 137-149. print.ps;  print.pdf
  68. C. Holton, C. Radin and L. Sadun, Conjugacies for tiling dynamical systems, Comm. Math. Phys. 209(2005) 343-359. print.ps;  print.pdf
  69. C. Radin, Existence of ground state configurations, Math. Phys. Electron. J. 10(2004), Paper 6, 7pp. (electronic). print.ps;  print.pdf
  70. C. Holton and C. Radin, Topological conjugacy between aperiodic tiling dynamical systems. preprint.ps;  preprint.pdf
  71. C. Radin and L. Sadun, Structure of the hard sphere solid, Phys. Rev. Lett. 94(2005), paper 015502, 4pp. print.ps;  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), paper 016708, 3pp. print.ps;  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), paper 025701, 4pp. print.ps;  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.E. Fisher and C. Radin, Definitions of thermodynamic phases and phase transitions, linked on an AIM workshop (2006) web page.
  77. M. Schröter, S. Nägle, C. Radin and H.L. Swinney, Phase transition in a static granular system, Europhys. Lett. 78 (2007), paper 44004, 4 pp. print.pdf
  78. C. Radin, Random close packing of granular matter, J. Stat. Phys. 131(2008) 567-573. print.pdf

ARTICLES IN THE POPULAR PRESS

Encyclopaedia Britannica etc.
BOOK

C. Radin, Miles of Tiles, Student Mathematical Library, Vol 1 (Amer. Math. Soc., Providence, 1999).