Diagonal diffusion, 517 pairs

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

If the transport coefficients are position-independent, the extreme right-hand side expression can be used. Crumb and Baird [360] were unable to obtain an expression for the escape probability of an ion-pair when the diffusion coefficient was not a diagonal tensor (i.e. the diffusion was not directed parallel to the electric field direction). 

This is the same as Eq. (3.95) except that the last term with operator of encounter diffusion L is added. This operator is diagonal, but its elements may differ because of different inter-particle interactions or diffusion coefficients for different pairs. Nothing like that is expected for the given example of energy transfer, so that... 

Only when [g] is a diagonal matrix with all elements on the main diagonal equal to one another (i.e., [g] reduces to the form g[/]) will the three component efficiencies EQy2 ov2> have the same value. This will be the case in mixtures made up of components of a similar nature (e.g., close boiling hydrocarbons or mixtures of isomers). For mixtures made up of chemically dissimilar species, that is, mixtures with large differences between the binary pair diffusivities, we must except to have significant nondiagonal... 

Fig. 3.6 Left, diagonal SW wave for the N = 200 dual closed graphene at the diffusion step rj = 1 of the pentagon-heptagon pair red-green circles). The swapping hexagons are circled in pale blue. Right. Diagonal dislocations freely flow in the lattice minimizing, with an almost linear dependence from r), the topological potential W of the structure. At r) = 1,W = 115,870...

Fig. 3.7 Top the diagonal SW wave for the JV = 200 dual closed grapheme at the last diffusion step b ore the annihilation of the 5j7 pairs, it has W = 113,925. Bottom Diagonal dislocations at the annihilation point W = 114,000 when only rotated txmds (the bold-blue ones) populate the region modified by the diffusiem process. UndCTlined vtntices evidtmee the ptaiodic imposed conditirais...

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