Structure quasi-periodic

According to Yamamoto (1996) quasi-periodic structures belong to the following... 

Notes on the crystallography of quasi-periodic structures. A general way to face the problems related to the interpretation of quasi-periodic structures (modulated structures, quasicrystals) is based on the introduction and application of higher-dimensional crystallography (de Wolff 1974, 1977, Janner and Janssen 1980, Yamamoto 1982, 1996, Steurer 1995). 

Kim J., Moriyama E. N., Warr C. G., Clyne P. J. and Carlson J. R. (2000) Identification of novel multi-transmembrane proteins from genomic databases using quasi-periodic structural properties. Bioinformatics 16, 767-775. 

Motivated by the remarkable discovery of quasicrystalline ordering in solids in 1984 [1], wave propagation in deterministic non periodic media has been an area of intense research. Following the successful experimental realisation of a multitude of such structures through modem technologies, such as molecular beam epitaxy and laser ablation [2], their interest has increased ever since. The most widely known examples are quasi-periodic structures obtained by substitution rules, such as Fibonacci- or Thue-Morse-chains [3,4], Much less has been published on quasi-periodic chains constructed according to a Cantor-set algorithm, which are the subject of this note. 

In conclusion, the correct analytical expressions have been derived for transmission and reflection coefficients of a three-layer periodic structure surrounded by two different isotropic dielectric media. On the basis of the given formulas it was shown that for three-layer SPS it is possible to realize the enhancement of resonant interaction of light with the structure. By this way one can achieve an increased light energy localization inside the structure and decreased group velocity of light inside SPS. It is necessary to point out that the enhancement of these phenomena is put into practice by using quasi-periodic structures. The possibility to enhance the resonant phenomena by the use of finite periodic structure, optical properties of which are predictable, easily calculated and practically realizable, opens wide perspectives for their application. 

Apart from the simulation of ideal surfaces, increasing interest in real 2-D crystals now exists, which are quasi-periodic structures in two dimensions but only a few atomic layers thick, and which may present new and useful properties precisely because of their limited thickness. This branch of nanoscience is then an ideal ground for application of the slab model. 

Spikes quasi-periodical structures that are conical in shape. 

The stress needed to move a dislocation line in a glassy medium is expected to be the amount needed to overcome the maximum barrier to the motion less a stress concentration factor that depends on the shape of the line. The macro-scopic behavior suggests that this factor is not large, so it will be assumed to be unity. The barrier is quasi-periodic where the quasi-period is the average mesh size, A of the glassy structure. The resistive stress, initially zero, rises with displacement to a maximum and then declines to zero. Since this happens at a dislocation line, the maximum lies at about A/4. The initial rise can be described by means of a shear modulus, G, which starts at its maximum value, G0, and then declines to zero at A/4. A simple function that describes this is, G = G0 cos (4jix/A) where x is the displacement of the dislocation line. The resistive force is then approximately G(x) A2, and the resistive energy, U, is ... 

In this chapter, general aspects and structural properties of crystalline solid phases are described, and a short introduction is given to modulated and quasicrystal structures (quasi-periodic crystals). Elements of structure systematics with the description of a number of structure types are presented in the subsequent Chapter 7. Finally, both in this chapter and in Chapter 6, dedicated to preparation techniques, characteristic features of typical metastable phases are considered with attention to amorphous and glassy alloys. 

It may be mentioned that in 2D and 3D the possible rotations (the symmetry axes) that superimpose an infinitely periodic structure on itself are limited to angles 360°/n with n = 1, 2, 3, 4 or 6. Notice that for non-periodic, noncrystalline, quasi-crystalline structures, other symmetry axes are possible. See 3.11.3 and Fig. 3.45 on quasi-periodic crystals. 

Key words Diode-pumped lasers frequency conversion modelocked lasers waveguides periodic structures, quasi-phasematching, femtosecond pulses. 

More recent experiments [62] concerning the viscous sublayer have shown a three-dimensional structure for turbulence near the wall. In a plane normal to the mean flow, counterrotating eddy pairs are involved (Fig. 6c), whereas in the direction of the mean flow, the motion is quasi-periodic (as described earlier). Since the wavelength along the mean flow is much larger than along the perimeter of the tube, a simplified bidimensional model may account only... 

We now consider the phenomenon of entrainment (the development of resonances) on the torus (Meyer, 1983). When (and if) the off-diagonal band in Fig. 6 crosses the diagonal [Figs. 6(c) and 6(f)], there exist points whose images fall on themselves they are fixed points of the map we study. These points lie on periodic trajectories that are locked on the torus. Such trajectories appear in pairs in saddle-node bifurcations and are usually termed subharmonics . When this occurs there is no quasi-periodic attractor winding around the torus surface, but the basic structure of the torus persists the invariant circle is patched up from the unstable manifolds of the periodic saddle-points with the addition of the node-periodic point (Arnol d, 1973, 1982). As we continue changing some system parameter the periodic points may come to die in another saddle-node bifurcation (see Fig. 5). Periodic trajectories thus... 

An example of such order is shown by the hexagonal symmetry of SBS as revealed by LAXD, electron microscopy and mechanical measurements. In composite materials the choice of phase is at the disposal of the material designer and the phase lattice and phase geometry may be chosen to optimise desired properties of the material. The reinforcing phase is usually regarded elastically as an inclusion in a matrix of the material to be reinforced. In most cases the inclusions do not occupy exactly periodic positions in the host phase so that quasi-hexagonal or quasi-cubic structure is obtained rather than, as in the copolymers, a nearly perfect ordered structure. 

In this section we show that photo-induced light scattering is a powerful tool, especially to obtain information about the polar structure in the crystal bulk. The polar structure in SBN Ce can be considered as the composition of different periodical and/or quasi-periodical assemblies of ferroelectric 180°-domains distributed in the bulk aligned along the c-axis. The existence of... 

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