Connectivity correlation length

Z-averaged radius, 324, 346, 348-349. See also Connectivity correlation length C-potential. See Zeta potential Zeolite, 221, 852, 853 Zeolite silica composite film, 852 Zeotrope, 439... 

Compared to the diameter of sequence space, the correlation length of structure space for RNA folding is relatively small (Fontana et al., 1993). A small correlation length implies that a small sphere around any sequence can sample all possible secondary structures. The ability to sample many structures from any sequence point is a property of the fitness landscape referred to as shape space covering. Equation (32) predicts shape space covering of structures when the connectivity is greater than Ac (Reidys et al., 1997). The radius of the covering sphere rmv is defined as... 

Paramagnon energy is connected with antiferromagnetic correlation length ... 

Near Pc, we have additional problems. The current now flows through the infinite cluster made of all the possible paths from one electrode to the other. This infinite cluster can be seen as very tortuous arms connected at the nodes (see Section 1.2.1(d)). The current will be concentrated in a small number of links such that for p Pc, the last link may be broken by a very small current in the sample. This means that If goes to zero when p goes to Pc- Near Pc the failure current is related to the correlation length by... 

If po > Pc, on scales higher than the correlation length i (ln > ,), the connecting set becomes homogeneous with constant density, and Eq. (126) reads... 

The correlation length defines the connectivity of clusters. It defines the scale range within which percolation clusters behave self-similarly and, consequently, are characterized by a fractal dimension [38,39]. The correlation length E, for a percolation lattice can be defined as... 

The correlation length , of the connecting set is confined to the range of intermediate asymptotics, which may be defined as... 

In this range, the connecting set is a fractal that is, it is geometrically similar to a percolating cluster, and its properties depend on the linear scale. Therefore, both the correlation length and the P s of the connecting set (the upper index oo means that the limit / —> oo is taken) should scale with distance from the critical point (i.e., percolation threshold pc = p ) as... 

Here, the critical indices for the connecting set correlation length and density are related via the fractal dimension df(lo) and (3((o), v(fo) as... 

The correlation length is the average distance between branch points that are connected to several branches leading to infinity (the boundary of the gel). At/ Ri 2pc (al 1) the gelation regime ends and most of the network... 

Charlaix et al. (1988) also conducted a study of NaCl and dye transport in etched transparent lattices. A fully connected square lattice with a lognormal distribution of channel widths and a partially connected hexagonal lattice (a percolation network) were considered. They concluded that the disorder and heterogeneity of the medium determined the characteristic dispersion length. From experimental data on the percolation network, they showed that this dispersion length was close to the percolation correlation length, p. 

Let us consider two more important aspects of nanofiller particles aggregation within the frameworks of the model [31]. Some features of the indicated process are defined by nanoparticle diffusion at nanocomposite processing. Specifically, length scale, connected with diffusible nanoparticle, is correlation length of diffusion. By definition, the growth phenomena in sites, remote more than are statistically independent. Such definition allows to connect the value with the mean distance between nanofiller particle aggregates L. The value can be calculated according to the equation as in what follows [31] ... 

Consider the behavior of the m-component spin model on the disordered lattice with dilution near the percolation threshold cuid at low temperatures. As p decreases, also the critical temperature Tc(p) decreases and reaches zero at the percolation point Pc- At T = 0 the critical properties are determined by the properties of the connected spin clusters, i.e. this is a percolation problem. It has been argued [78] that the point p = Pc,T = 0 should be viewed as an multicritical point, here the thermal correlation length and correlation length of the percolation cluster diverge simultaneously. The studies of Ising model [91]... 

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