相关论文: Quasiperiodic packings of two-shell decagonal clus…
Many of the mathematical models used in quasicrystal physics are based on tilings of the plane or space obtained by using strip projection method in a superspace of dimension four, five or six. We present some mathematical results which…
The strip projection method is the most important way to generate quasiperiodic patterns with predefined local structure. We have obtained a very efficient algorithm for this method which allows one to use it in superspaces of very high…
Atomic-resolution electron microscope images show that a quasicrystal is a quasiperiodic packing of clusters. The outer atomic shells of multi-shell clusters occuring in quasicrystals are highly symmetric and rather robust, but some…
Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a…
The diffraction pattern of a quasicrystal admits as symmetry group a finite group G, and there exists a G-cluster C (a union of orbits of G) such that the quasicrystal can be regarded as a quasiperiodic packing of copies of C, generally,…
The diffraction image of a quasicrystal admits a finite group G as a symmetry group, and the quasicrystal can be regarded as a quasiperiodic packing of copies of a G-cluster C, joined by glue atoms. The physical space E containing C can be…
A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the…
We briefly review the standard methods used to construct quasiperiodic tilings, such as the projection, the inflation, and the grid method. A number of sample Mathematica programs, implementing the different approaches for one- and…
We present a cluster covering scheme to construct the two-dimensional octagonal quasilattice. A quasi-unit cell is successfully found which is a two-color cluster similar to the Gummelt's two-color decagon in five-fold quasilattice. The…
Single cluster covering approach provides a plausible mechanism for the formation and stability of octagonal and decagonal quasiperiodic structures. For dodecagonal quasiperiodic pattern such a single cluster covering scheme is still…
Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…
Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that…
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…
We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical…
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…
Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…
We propose a means to realize two-dimensional quasiperiodic structures by trapping atoms in an optical potential. The structures have eight-fold symmetry and are closely related to the well-known quasiperiodic octagonal (Ammann-Beenker)…
In the window approach to quasicrystals, the atomic position space E_parallel is embedded into a space E^n = E_parallel + E_perp. Windows are attached to points of a lattice Lambda \in E^n. For standard 5fold and icosahedral tiling models,…
We devise an ideal 3-dimensional octagonal quasicrystal that is based upon the 2-dimensional Ammann-Beenker tiling and that is potentially suitable for realization with patchy particles. Based on an analysis of its local environments we…
We describe the use of quasiperiodic oscillators for computation and control of robots. We also describe their relationship to central pattern generators in simple organisms and develop a group theory for describing the dynamics of these…