Quasicrystals: Structure and Growth

• Introduction (24/02)
  
  • Dan Shechtman, Ilan Blech, Denis Gratias, John Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53 (1984).
    
  • Michael Baake, Uwe Grimm, Surprises in aperiodic diffraction, J. Phys.: Conf. Ser. 226 (2010).
    
    
• Robinson Tilings (03/03)
  
  • Hao Wang, Proving theorems by pattern recognition II, Bell Systems technical journal 40 (1961).
    
  • Robert Berger, The Undecidability of the domino problem, PhD thesis, Harvard University, 1964.
  • Raphael Robinson, Undecidability and nonperiodicity for tilings of the plane, Inventiones Mathematicae 12 (1971).
  • Thomas Fernique, Yet another proof of the aperiodicity of Robinson tiles, short note (2010).
    
    
• Penrose Tilings (10/03)
  
  • Roger Penrose, Pentaplexity: a class of non-periodic tilings of the plane, Eureka 39 (1978).
    
  • Nicolaas Govert de Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane, Indag. Math. 43 (1981).
    
    
• Rhombus Tilings (17/03)
  
  • Nicolas Govert de Bruijn, Dualization of multigrids, J. Phys. France 47 (1986).
    
  • Leonid Levitov, Local rules for quasicrystals, Comm. Math. Phys. 119 (1988).
    
  • Joshua Socolar, Weak matching rules for quasicrystals, Comm. Math. Phys. 129 (1990).
    
  • Thang Tu Quoc Le, Local rules for quasiperiodic tilings, in: The Mathematics of long-range aperiodic order, 1997.
    
    
• Hierarchical Tilings (24/03)
  
  • Shahar Mozes, Tilings, substitutions and dynamical systems generated by them, J. Anal. Math. 53 (1989).
    
  • Chaim Goodman-Strauss, Matching rules and substitution tilings, Ann. Math. 147 (1998).
  • Thomas Fernique, Nicolas Ollinger, Combinatorial substitutions and sofic tilings, in proc. of JAC (2010).
    
    
• Self-assembled Tilings (14/04)
  
  • Joshua Socolar, Growth rules for quasicrystals, in Quasicrystals: The State of the Art, 1991.
  • Steven Dworkin, Jiunn-I Shieh, Deceptions in quasicrystal growth, Commun. Math. Phy. 128 (1995).
  • Florent Becker, Eric Rémila, Nicolas Schabanel, Time optimal self-assembly for 2D and 3D shapes: the case of squares and cubes, in proc. DNA’08 (2008).
    
    
• Random Tilings (21/04)
  
  • Henry Cohn, Michael Larsen, James Propp, The Shape of a typical boxed plane partition, New York J. Math. 4 (1997).
  • Henry Cohn, Richard Kenyon, James Propp, A Variational principle for domino tilings, J. Amer. Math. Soc. 14 (2001).
  • Dieter Joseph, Veit Elser, A Model of quasicrystal growth, Phys. Rev. B 79 (1997).
  • Michael Luby, Dana Randall, Alistair Sinclair, Markov chain algorithms for planar lattice structures, SIAM J. Comput. 31 (2001).
    
    
• Cooled Tilings (28/04)
  
  • Olivier Bodini, Thomas Fernique, Damien Regnault, Crystallization by stochastic flips, J. Phy.: Conf. ser. 226 (2010).
  • Olivier Bodini, Thomas Fernique, Damien Regnault, Stochastic flips on two-letter words, in proc. of ANALCO’10 (2010).
    
  • Thomas Fernique, Damien Regnault, Stochastic flips on dimer tilings, Disc. Math. Theor. Comput. Sci. (2010).
    
    

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