Tiling models for decagonal quasicrystals with quasiperiodic potentials

Properties of quasiperiodic functions

“…Quasiperiodic functions or quasiperiodic potentials (which will be taken to be synonyms) play an important role at several places in the theory of quasicrystals: they are used to model quasi crystalline surface morphology to study the arrangement and diffusion of colloids [1][2][3][4][5][6][7] or adatoms on quasicrystalline sur faces [8,9], they are employed to model photonic quasicrystals [10][11][12][13][14], to describe nematic cells in quasiperiodic electric fields [15,16], to treat complex nonlinear photonic quasi crystals [17,18] and to model optical quasicrystals generated by interfering laser beams [19][20][21][22][23][24][25][26][27]. Recently a new field has appeared: the behavior of cold atoms in a quasi periodic poten tial [28][29][30][31].…”