Hexagonal grid

Figure 3.110 Boron-atom numbering and the two-dimensional hexagonal grid pattern of two two-center and ten three-center bonds in the 0.10.3.0 styx structure for icosahedral Bi2Hi22. ...

These expressions, and also eqn. (34) make sense because (X tY/)/(X ) equals the conditional probability that there is an X t at site k if there is an X at site /. Such an easy interpretation is not possible if we have e.g. three sites that are pairwise neighbors as for a hexagonal grid. Eqn. (34) and similar equations like (38), (39), and (40) have been used before by Mai et al. in models of CO oxidation. 

A neutral macrocyclic receptor of nitrate was designed by a rational approach. [1] A hexagonal grid was constructed around the trigonal nitrate anion and the molecular frame was cut from the chicken wire pattern (Scheme 1). 

Fig. 16. Photographs of the surface plasmon field-enhanced diffraction patterns generated by various PS patterns on Au surfaces (A) parallel lines 40 pm wide, separated by 62.5 pm (B) parallel lines 28 pm wide, separated by 83 pm (C) square grid pattern, bar width 28 pm, grid width 83 pm, [D] hexagonal grid pattern, bar width 8 pm, hexagonal grid width 48 pm.

With its extension the KASCADE-Grande experiment is able to measure primary particles up to 1018 eV. This is achieved with 37 detector stations from the former EAS-Top experiment forming the Grande array. These stations are arranged in a 0.5 km2 hexagonal grid with an average distance of 137 m. 

Apart from hexagonal grids, the analysis maybe evenly applied to octagonal ones [Figure 3.8(b)]. As far as the extension of (3.88) to three dimensions is concerned, it should be stated that, despite its advanced discretization characteristics, total complexity is greatly increased. This is the reason for the relatively limited use of such lattices, especially in waveguide problems where their merits would be indeed fairly instmctive. 

Figure 33. The 19 achiral shapes of hexagonal grid having perimeter P = 22.

Fig. 7a, b. SEM images of a hexagonal grid b a free-standing micrometer-sized gear of Si/B/N/C ceramic [112]... 

In order to fully account for finite surface mobilities and the heterogeneous surface structure, we have to employ a stochastic description of the surface processes. The kinetic Monte Carlo method enables the incorporation of structural details at an atomistic level. This method has been apphed successfully in the field of heterogeneous (electro-) catalysis [59 1,65] and is further discussed in the chapter by Phil Ross in this book. In the model, hexagonal grids represent catalyst particles. The active sites are randomly distributed on the grid. Adsorbates are considered to bind to on-top sites. The first reaction method was used [66,67]. 

The genius of the cellular system is the division of a diy into small celis. This all extensive frequency reuse across a dty, so that millions of people can use cell phones simiiltaneously. In a typical analog cell phone system in the United States, the cell phone carrier reedves about 800 e-quendes to use across the dty. The carrier chops up the dty into cells. Each cell is typically sized at about 10 square miles (26 square Idometers). Cells are normally thought of as hexagons on a big hexagonal grid. 

A single cell in an analog system uses one-seventh of the available duplex voice chaimels. That is, one cell, plus the six cells around it on the hexagonal grid, are each using one-seventh of the available channels so that each cell has a unique set of frequencies and there are no collisions ... 

The extended stmcture consisting of rolled hexagonal grids with carbon atoms at the nodes, called nanotubes. 

The interfaces between finescale exsolution lamellae of ilmenite in hematite have been investigated and most were shown to be coherent and dislocation free [251]. Due to differences in lattice parameters, dislocation arrays decorate the interface [Fig. 8(b)]. Contrast analysis revealed a hexagonal grid of rhombohedral dislocations [250] rather than dislocations with basal Burgers vectors [252]. The ordering phase transition in ferrian ilmenite from the high-temperature R3c disordered structure to a R3 lower-temperature ordered structure results in the creation of twin domains [253,254]. No dislocations were involved. 

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