Experiments with a thin gas-fluidized granular layer revealed a sequence of well-defined transitions as the amplitude and frequency of the gas flow modulation are varied. The observed patterns include subharmonic squares and stripes, quasiperiodic and disordered structures. The wavelength of subharmonic patterns increases with the mean flow rate and decreases with the modulation frequency.

In this paper the problem of the theory of a quasicrystal structures-the determination of coordinates of each atom of quasicrystal in analytical form-is solved. Within the framework of the proposed model a periodic crystal can be presented as a particular case of a quasicrystal. The simple and explicit analytical formulas which describe the location of each atom in a quasicrystal are given. The...

Stationary structures in two-dimensional Heisenberg ferromagnets. Abstract Stationary structures in a classical isotropic two-dimensional Heisenberg ferromagnetic are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of S(r, t) = S(r − vt) the Landau-Lifshitz equation is closely related to the Ablowitz-Ladik hierarchy. This relation is u...

Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on microscopic periodicity. The broadening of ordinary crystallography to include quasiperiodic materials is accomplished by defining the point group in terms of...

The concept of quasiperiodicity is a generalization of the notion of periodicity where in contrast to periodicity the quasiperiods of a quasiperiodic string may overlap. A lot of research has been concentrated around algorithms for the computation of quasiperiodicities in strings while not much is known about bounds on their maximum number of occurrences in words. We study the overlapping facto...

Steinhardt, Jeong, Saitoh, Tanaka, Abe & Tsai [Nature (London) (1998), 396, 55-57] have demonstrated that the structure of decagonal Al-Ni-Co can be built from overlapping clusters of a single type. The structure arises from a decoration of the decagons of a Gummelt covering. The unit (essentially a decagonal prism) was called by Steinhardt et al. a 'quasi unit cell'. In this work, a classifica...

– Contributions of quantum interference effects occuring in quasicrystals are reported. First conversely to metallic systems, quasiperiodic ones are shown to enclose original alterations of their conductive properties while downgrading long range order. Besides, origin of localization mechanism are outlined within the context of the original metal-insulator transition (MIT) found in these mater...

In this paper the problem of the theory of a quasicrystal structures-the determination of coordinates of each atom of quasicrystal in analytical form-is solved. Within the framework of the proposed model a periodic crystal can be presented as a particular case of a quasicrystal. The simple and explicit analytical formulas which describe the location of each atom in a quasicrystal are given. The...