Quasi-periodic surface structures

Quasi-periodic surface structures are generated under laser irradiation exposure and they exhibit regularity in their pattern.Their geometrical sizes (e.g., height, periodicity) are much smaller than the diameter of the focused laser beam. r the structure parameter, defrned as the ratio between the structured enlarged surface area and the same area projected on a flat surface. 

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... 

The composition and structure of Ti, Zr, Mo - based thin films formed on silicon and rubber by ion-beam-assisted deposition were investigated by utilizing the AFM and RBS technique. It was found that the films included not only metal atoms but also C, O, H, Si (from Si substrate), S, Ca and Zn (from the rubber). The coatings on the rubber have quasi-periodical topography which may be due to build in stress. The coatings on silicon are uniform with a smooth surface. 

There is another class of frictional interaction that we might call semi-deterministic. These actually behave like a hybrid between stick/slip oscillations and random peak/valley fiiction interactions. Most of these semi-deterministic interactions are caused by human-made objects, created through intentional engineering of the surface features of these objects. Essentially any surface that has a deterministic (especially periodic) structure has the potential to slide with a quasi-periodic motion. Some obvious examples of these come from our driving experience, like the ka-dunk, ka-dunk... sound produced by the seams between freeway concrete tiles, or the scored pavement patterns (or Botts dots) placed by the road edges to tell us we re straying from the allowed driving surface. 

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. 

As can be seen from the data presented in Table 3, metal surfaces structured with quasi periodic spikes, as well as irregular combination of micro-and nanoroughness, meet the criteria of superhydrophobic surfaces. 

Such transition between superhydrophobic wetting and homogeneous wetting has been studied for titanium samples structured with quasi-periodical spikes while immersed in water (Fadeeva et al., 2011).These authors observed that most of the air trapped on the superhydrophobic surface, directly after immersion in water, was gradually replaced by water over time (Figure 9). 

It is noteworthy that the superhydrophobic properties of laser structured metal surfaces with quasi-periodic spikes could be restored by cleaning the samples in acetone using an ultrasonic bath, followed by drying in a desiccator. 

Figure 9 The surface of a superhydrophobic titanium sample structured with quasi-periodic spikes after immersion in water bright areas of the image correspond to air trapped in the structure, dark areas correspond to the wetted surface.

While the period of the interference curve does not depend on the properties of a metal surface, the magnitude of effect, that is the amplitude of the interference curve, can reveal a strong dependence of such a kind. Indeed, Kadomtsev s theory is based on the assumption, that the atom interacts with quasi-free electrons in the thin surface layer. Therefore, the state of such electrons must be tightly connected with the properties of such a layer-for instance its temperature and crystal structure. 

The direct measurement of the interaction force between two mica surfaces1 indicated a large repulsion at relatively short distances, which could not be accounted for by the DLVO theory. This force was associated with the structuring of water in the vicinity of the surface.2 Theoretical work and computer simulations8-5 indicated that, in the vicinity of a planar surface, the density of the liquid oscillates with the distance, with a periodicity of the order of molecular size. This reveals that, near the surface, the liquid is ordered in quasi-discrete layers. When two plan ar surfaces approach each other at sufficiently short distances, the molecules of the liquid reorder in discrete layers, generating an oscillatory force.6... 

The first phase of the process of polymer dissolution is the penetration of solvent molecules into the polymer structure. This results in a quasi-induction period, i.e. the time necessary to build up a swollen surface layer. The relationship between this "swelling time" tsw and the thickness of the swollen surface layer S is ... 

The intensity variation along the rod (i.e. as a function of or /) is solely contained in the structure factor it is thus related to the z-co-ordinates of the atoms within the unit-cell of this quasi-two dimensional crystal. In general, the rod modulation period gives the thickness of the distorted layer and the modulation amplitude is related to the magnitude of the normal atomic displacements. This is the case of a reconstructed surface, for which rods are found for fractional order values of h and k, i.e. outside scattering from the bulk. 

The next slightly more complicated situation concerns a fluid confined to a nanoscopic slit-pore by structured rather than unstructured solid surfaces. For the time being, we shall restrict the discussion to cases in which the symmetry of the external field (represented by the substrates) i)reserves translational invarianee of fluid properties in one spatial dimension. An example of such a situation is depicted in Fig. 5.7 (see Section 5.4.1) showing substrates endowed with a chemical structm e that is periodic in one direction (x) but quasi-infinite (i.e., macroscopically large) in the other one (y). 

The action of compression plasma flows (CPF), generated by quasi-stationary plasma accelerators, upon solid surfaces leads to a substantial modification of surface properties of exposed materials [1-3]. It was found that exposure of silicon crystals to CPF causes formation of sub-micron bulk periodic structures on its surface. These structures are of great interest for development of nanoelectronic devices. 

In this paper, we examine the electron correlation of one-dimensional and quasi-one-dimensional Hubbard models with two sets of approximate iV-representability conditions. While recent RDM calculations have examined linear [20] as well as 4 x 4 and 6x6 Hubbard lattices [2, 57], there has not been an exploration of ROMs on quasi-one-dimensional Hubbard lattices with a comparison to the one-dimensional Hubbard lattices. How does the electron correlation change as we move from a one-dimensional to a quasi-one-dimensional Hubbard model How are these changes in correlation reflected in the required A -repre-sentability conditions on the 2-RDM One- and two-par-ticle correlation functions are used to compare the electronic structure of the half-filled states of the 1 x 10 and 2x10 lattices with periodic boundary conditions. The degree of correlation captured by approximate A -repre-sentability conditions is probed by examining the one-particle occupations around the Fermi surfaces of both lattices and measuring the entanglement with a size-extensive correlation metric, the Frobenius norm squared of the cumulant part of the 2-RDM [23]. 

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