Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic" mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individua...

Cluster density maximization and (maximal) cluster covering have emerged as ordering principles for quasicrystalline structures. The concepts behind these ordering principles are reviewed and illustrated with several examples. For two examples, Gummelt’s aperiodic decagon model and a cluster model for octagonal Mn–Si–Al quasicrystals, these ordering principles can enforce perfectly ordered, qua...

2014 A variety of models for icosahedral quasicrystals is constructed such that atoms move continuously under displacements along the phason space R3*, while their positions are separated by distances larger than some h > 0, a « hard core » diameter. The models exhibit icosahedral symmetry and the diffraction properties of perfect quasiperiodic structures. J. Phys. France 50 (1989) 3181-31...

ABSTRACT The objective of the paper is to explain a modern Hilbert transform method for analysis and identification of mechanical non-linear vibration structures in the case of quasiperiodic signals. This special kind of periodicity arises in experimental vibration signals. The method is based on the Hilbert transform of input and output signals in a time domain to extract the instantaneous dyn...

This work studies the propagation of mechanical waves through lattices that form moir\'e patterns. These structures are not periodic, and their analysis generally requires special methods, most which based on theory quasiperiodic infinite systems, therefore suitable for finite manufactured structures. To attain a deeper understanding underlying physics patterns, authors study these complex usin...

The Fourier-space approach to crystal symmetry 1;2 is extended to colored quasiperiodic structures as an example of the general case of indistinguishable quasiperiodic multicomponent elds. Examples are given of 2-and 5-color space groups on the 10-fold 2-dimensional lattice. We consider a multicomponent quasiperiodic eld (r) whose components (r) could specify a tensor eld, as in magnetically or...

We experimentally study the phase behaviour of a charge-stabilized two-dimensional colloidal monolayer which is subjected to a one-dimensional quasiperiodic substrate potential. Upon increasing the laser intensity, we observe a transition from a periodic to a quasiperiodic state. It proceeds via the formation of an intermediate periodic average structure (PAS) which is related to the quasiperio...

The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the anticontinuum limit, which is the limit...