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1.
We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for . We discuss possible reasons and mention a simpler framework that could give some hint about this problem. 相似文献
2.
《Comptes Rendus Physique》2014,15(1):70-81
We analyse the transport properties in approximants of quasicrystals α-AlMnSi, 1/1-AlCuFe and for the complex metallic phase λ-AlMn. These phases present strong analogies in their local atomic structures and are related to existing quasicrystalline phases. Experimentally, they present unusual transport properties with low conductivities and a mix of metallic-like and insulating-like characteristics. We compute the band structure and the quantum diffusion in the perfect structure without disorder and introduce simple approximations that allow us to treat the effect of disorder. Our results demonstrate that the standard Bloch–Boltzmann theory is not applicable to these intermetallic phases. Indeed their dispersion relations are flat, indicating small band velocities, and corrections to quantum diffusion, which are not taken into account in the semi-classical Bloch–Boltzmann scheme, become dominant. We call this regime the small velocity regime. A simple relaxation time approximation to treat the effect of disorder allows us to reproduce the main experimental facts on conductivity qualitatively and even quantitatively. 相似文献
3.
Existence of the perfect transmission resonances of spin waves in a one-dimensional Thue–Morse magnonic quasicrystal is proposed. We find that occurrence of the perfect transmission just corresponds to the repeated bandedges in the bandedge map. Frequencies at the perfect transmissions for system with arbitrary generation order can be predicted by the bandedge map of the second and third order systems using two iterative schemes. These results show that density of the perfect transmission resonance increases exponentially for increasing the order of the system. However, the perfect transmissions are kept for higher order systems even if the peaks become denser. 相似文献
4.
Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer?s quasicrystals. 相似文献
5.
In this work, we present a new and semi-analytical method to investigate one-dimensional Fibonacci-class photonic quasicrystals from waveguiding properties point of view. Usually, the exact treatment for obtaining band diagram in these situations is very hard and the numerical methods are used. In this paper, we investigate the waveguiding properties of one-dimensional quasicrystals by using perturbation method. In this direction, the band diagram and field distribution of this structure are investigated. 相似文献
6.
Overlap coincidence in a self-affine tiling in Rd is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in Rd and find an efficient algorithm to check the pure point dynamical spectrum. This algorithm is easy to implement into a computer program. We give the program and apply it to several examples. In the course of the proof of the algorithm, we show a variant of the conjecture of Urbański (Solomyak (2006) [40]) on the Hausdorff dimension of the boundaries of fractal tiles. 相似文献
7.
We show that the basic building blocks of a perfect Penrose pattern (PPT) in two dimensions can be established by adding another
condition to the Penrose’s original edge rules. The implications of this result are discussed in the context of recent papers
by Onada, Jaric, Ronchetti and others concerning growth algorithm for PPT’s. 相似文献
8.
K. Wang P. Donnadieu P. Garoche 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(2):279-287
We report on grain growth and related structure change in single phased Al-Li-Cu quasicrystals. The icosahedral phase grains
have been investigated using scanning ion microscopy and transmission electron microscopy. Regular boundaries between large
grains have been observed both before and after high temperature annealing. The electron diffraction study shows that the
grain growth is accompanied by a reduction of the phason-strains. The orientation relation between grains sets the 2-fold
icosahedral axes parallel, and the coincidence of the planes depends on the phason strain-field. The effect of phason-strain
field on these boundaries is discussed. It is proposed that the phason strain elimination can play a role in the grain growth.
Received 1 February 1999 and Received in final form 12 May 1999 相似文献
9.
The propagation of phonons in one-dimensional quasicrystals is investigated. We use the projection method which has been recently proposed to generate almost periodic tilings of the line. We define a natural Laplace operator on these structures, which models phonon (and also tight-binding electron) propagation. The selfsimilarity properties of the spectrum are discussed, as well as some characteristic features of the eigenstates, which are neither extended nor localized. The long-wavelength limit is examined in more detail; it is argued that one is the lower critical dimension for this type of models. 相似文献
10.
M. Ricker J. Bachteler H.-R. Trebin 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(3):351-363
In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We
have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations
in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic
isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic
fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which
can be seen from the contributions of all orders.
Received 21 February 2001 and Received in final form 27 June 2001 相似文献