Method nearest-neighbor distance

The method based on the orientation of pairs of vectors of length L produces slower dynamics than the method based on next-nearest neighbor distances. Since the acceptance rates for single-bead moves differ very little in the two methods, it appears that the probability for immediate reversal of a successful move is higher in the method based on the orientation of the pairs of vectors, such that the chain shivers rapidly, but moves its center of mass slowly. This problem is more severe in PP melts than in PE melts. Significant diffusion of the center of mass of the chains in PP melts is achieved when reptation, as well as single-bead moves, is allowed [158, 158A]. 

Sokel carried out the variational calculations necessary to calculate C44 for a few materials. In a similar way Chadi and Martin used the special points method to calculate C44 with the artificial restriction that all nearest-neighbor distances remain fixed. They then did a valence force field calculation, such as will be discussed in the next section, to correct for internal displacements. The results of these calculations are listed in Table 8-3. In spite of the extra complications, the theory seems to be about as accurate as it was for the calculation of c, — c,2. 

Below we will use a simple example to explain the principle of the standard, non-self-optimizing method. Say that we have five data pairs x,y such that the x-values are equidistant, with a nearest-neighbor distance S. For any odd-numbered set of equidistant data (such as the five considered here), the x- value in the middle of the set is the average x of the x-values in the set. We now start by subtracting x from all five x-values, so that the new x- values will be-25, -5, 0, 5, and 25. 

Twelve parameters were required for every specific element in order to develop the function within the modified embedded-atom method [40]. The Usted values include the sublimation energy of elements, nearest-neighbor distance, embedding energy, factors for atomic densities, and so on. The modified embedded-atom method was successfiiUy applied to calculating various bonding characteristics. 

Bond lengths play an important role in the structural characterization of microclusters. The majority of the experimental studies have shown that the nearest neighbor distances contract as the cluster size decreases. [55] The determination of the bond lengths in supported clusters or clusters in a matrix have been based, in general, on the EXAFS technique. The bond lengths in a cluster are easily obtained computationally, although it is well known that some computational techniques, such as the HF method, substantially overestimate the equilibrium... 

For the purposes of comparison, the nearest-neighbor distance (NND) method [45-47] was adopted for the current 2D models and results are shown in Figure 3.6. In this method, each particle/void has a nearest particle/void so that it is compared with all... 

Figure 3.6. Connected lines based on the nearest-neighbor distance method [351 (a) relatively even dispersion referred to as Type I , (b) intermediate dispersion referred to as Tvm II and (o) relatively flocculated dispersion referred to as Type III . The scale bar indicates 50 ...

Fig. 4.9. Average atomic coordination number N, (solid squares, left-hand scale) and nearest-neighbor distance (solid circles, right-hand scale) as a function of density for liquid mercury. Inset, integration method used to determine N. Horizontal lines indicate nearest-neighbor distances in solid mercury (R i) and in the dimer...

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