High clustering

The result of intensity alternation for the boron nitride cluster ions is in accordance with the generation of high cluster ion beams MnXn, for several systems (e.g. NaCl, CuBr or Csl26 49) by other methods of cluster formation such as by quenching condensation in a cold rare gas or by ion bombardment of hahdes. 

This technique of producing clusters as a target for diffraction studies offers many advantages, such as the absence of a substrate and of impurities, and a fairly narrow cluster size distribution. Furthermore, the absence of efficient mechanisms for dissipating the heat of condensation accounts for relatively high cluster temjjeratures, which favors annealing processes. This ensures uniformity in the structures of same-size clusters. In most cases, the cluster structure is that of greatest stability. 

The cluster fractions versus temperature for the second-type liquid is shown in Fig. 6.21, and the free energies of the liquid-clusters system and the liquid-crystals system are depicted in Fig. 6.20. The calculations were performed with the following parameters P = 0, ASm = 0.9, 8p = 0.14 AHm, Co = 0.25 ASm, p — 1, /ci = 18, lL — 14 and r(x) = 1 — x3. It can be seen from Fig. 6.21 that there exist two liquid states one of which, the low-temperature state (LTS), exists in the temperature interval [rjj1, rc)] and the other, the high-temperature state (HTS), exists at T > Tc2. These states are in equilibrium at T = Te. In LTS, the liquid is highly clusterized while the cluster fraction in HTS does not exceed xc2 0.10. At x xc2 almost each of the clusters of size lcl x 10 is in contact with some other small-scale cluster, and therefore, small-scale clusters effectively coagulate and form large-scale clusters. The crystal fraction in the liquid and the... 

Let us consider the interconnection of steric factor p value with reaction products structure, which can be characterized by its fractal dimension Dj. Using the Eqs. (74) and (75) of Chapter 1 in the supposition that p = 1 is reached at very high cluster accessibility degree and estimating this degree by minimal value Dj.=1.5 [65] and assuming also that the indicated D, value is realized at small t of order 100 s [57], the authors [64] obtained the following relationship ... 

High "clustering ", meaning that there is a high probability that two vertices are connected one to another if they share the same neighbor. 

In a previous work (Gad Balev, 2008a), we have studied the two properties of SSE-IN related to the small-world model, namely their 1/Lrg and C/Crg ratios. Our results show (see Fig. 21) that nearly 60% of the proteins have SSE-IN consisting of between 100 and 500 amino acids. The small-world properties are satisfied mainly when the size of the network does not exceed 500 amino acids and there are about 15.3% small-world networks among all SSE-IN. Fig. 4 explains the reason for this low rate. One can see that although highly clustered, most SSE-IN do not satisfy the first small-world property. 

Small-world networks have been studied extensively since they were first described in Watts and Strogatz [3], who defined them as graphs with three properties power-law degree distribution, high clustering coefficient and small average shortest path. They are locally dense (sparse with dense sub-graphs.)... 

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