Correlation length dispersivity

The cell sizes are expected to exceed any molecular (atomic) scale so that a number of particles therein are large, Ni(f) 1. The transition probabilities within cells are defined by reaction rates entering (2.1.2), whereas the hopping probabilities between close cells could easily be expressed through diffusion coefficients. This approach was successfully applied to the nonlinear systems characterized by a loss of stability of macroscopic structures and the very important effect of a qualitative change of fluctuation dispersion as the fluctuation length increases has also been observed [16, 27]. In particular cases the correlation length could be the introduced. The fluctuations in... 

Say, Pirogov and Palagashvili [36] in their 3d study used the system s size L close to the correlation length , which resulted in large concentration dispersion ( 10%) well seen in their steady-state. 

Figure 5. Permeability autocorrelograms realizations whose dispersivity is in Figure the dimensionless correlation length by varying...

Figure 9. Schematic representation of the growth of megascopic dispersivity with distance traveled. All displacement pass through three regimes (noii-Fickian, transition and Fickian) which may be large or small depending oii the correlation length and D. Even displacement which are strongly Fickian do not lose the evidence of their non-Fickian beginning. (Reproduced from Ref. 1.)...

Correlation lengths are as little as five grain diameters in laboratory experiments. This length is very much smaller than even the smallest experimental dimensions and we, therefore, expect time-invariant dispersivities even in the absence of diffusion. It is possible, in principle, to calculate C and X from this observation and Equation 7. 

Figure 11. Comparison of calculated macroscopic dispersivities (solid curve) to experimentally measured megascopic (laboratory scale) dispersivities. d is the grain diameter for the packing in the experimentSl measurements and the correlation length for the calculated curve. Better agreement could be obtained by letting d be about live times the correlation length in the calculated curve. (Reproduced from Ref. 4.)...

Figure 12. Comparison of megascopic (upper curve) and macroscopic (lower curve) dispersivities from simulations with large correlation length and no diffusion. In all cases, the macroscopic dispersivity is smaller and grows slower. (Reproduced from Ref. 5 )...

Dispersivity, L Exponent on velocity Discrete change Correlation length Porosity, fraction... 

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

A major advantage of hard mode spectroscopy has been described by Salje (1992) which stems from the short correlation length of high frequency phonons. The dispersion of the hard mode is expressed by... 

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. 

The effects of velocity, column size, and packing on dispersion of a conservative tracer were investigated in order to separate the effects of slow sorption and desorption from hydrodynamic dispersion. D values were obtained by fitting an equilibrium model to the breakthrough curves (Table III). There was no correlation between dispersion and column length or diameter, as expected. Dispersion and velocity are related, however. 

Figure 3 Temporal evolution of the correlation length A (pm) as determined by SALS on BLG/AG dispersions at 0.1 wt% total biopolymer concentration, pH 4.2 and Pr.Ps weight ratio of 2 1. Bars are standard deviation based on duplicate experiments. Drawn line is a power-law function with an exponent of 0.5...

This correlation function describes a structure of periodicity d (= In/k), i.e., a measure of the repeat distance between alternately arranged water and oil domains, dampened as a function of the correlation length which characterizes the decay of local order [65] and may also be interpreted [69] as a measure of the dispersion of d. The order parameter coefficients G2, C[, and C2 can be grouped together to define an amphiphilicity factor fa = C 7(4 2These parameters can also be used to express d and (. Figure 3 illustrates the use of this amphiphilicity scale [68]. 

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