Irregular lattice

FIGURE 18.15 Plane string net of regular lattice (A) and irregular lattice indicated by a, b, c (B). 

The cells of the CA lie at the vertices of a regular lattice that homogenously covers a region of space. Although it is possible in principle to use an irregular lattice, we need to be able to define unambiguously the "neighborhood"... 

Database search identifies complementary molecules. These are joined on an irregular lattice... 

Cadmium pigments, especially cadmium red, are very sensitive to intensive grinding, which causes loss of brilliance due to an increase in the number of irregular lattice defects. A brilliant red shade may become a dirty brownish red. 

Let us consider 2D-projection of our knot as a certain irregular lattice. Crossings of projection are lattice vertices. We turn all these crossings into a standard position where two parts of chain projection near the crossing are normal to each other and form the angles of n/4 with the x-axis. It can be proved that the result does not depend on the method of this standardization. Now, we... 

Thus in the general case, if Air A, s is related with by a tensor-like factor which depends botS upon the direction of y wrtth respect to the various w and upon the angle between the chosen x direction and r hi view of this, Eq. (7) also applies for transport processes in an irregular lattice. 

The universal percolation probabilities for regular lattices are expected to be applicable also to irregular lattices. It is useful to consider two examples supporting this important statement. 

Employing Eq. (24), we may assume that the percolation probability for the sublattice of voids with r > rp is the same as the universal percolation probability for the bond problem (Section II). The latter probability was originally calculated only for regular lattices. The sublattice of voids with r > rp is not regular. In addition, some of the voids with r > rp are not connected with the other voids having r > rp. However, the numerical results obtained by Yanuka (33) for a randomized cubic lattice (see also the discussion in Section II) support the hypothesis on the universality of the percolation probability for both regular and irregular lattices. 

Spatially, the relatively high porosity of trabecular bone is in the form of a networic of interconnected pores filled with bone marrow. The trabecular tissue forms an irregular lattice of small rods and plates that are called trabeculae (Fig. 8.3). Typical thicknesses of individual trabeculae are in the range 100 to 300 /u.m, and t)rpical intertrabecular spacing is on the order of 500 to 1500 /u.m. The spatial arrangement of the trabeculae is referred to as the trabecular architecture. Architectural type varies across anatomic site and with age. Bone from the human vertebral body tends to be more rodlike, whereas bone from the bovine proximal tibia consists almost entirely of... 

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