Elementary fragment size

If g approaches unity, IJh = 0.5, and if e decreases, the ratio IJl decreases too. An interesting property of DS is that this ratio is independent of the catalytic element size, as illustrated by Fig. 26. This is not true only in the vicinity of the critical lengths for the formation of DS and multiplication of elementary fragments. The ratio is also weakly dependent on e when g 1. 

FIGURE 1.6 Schematic of a typical PEFC with the meandering flow field. Note that the figure is strongly not to scale the MEA thickness is 10 -10 times less, than the in-plane size of the current collector plate. The color indicates an elementary cell fragment, which is often considered in cell modeling. 

Before discussing size-extensivity, we consider the commutation relations between two operators Op and Ob associated with fragments A and B, respectively. We first assume that both operators represent a single string of elementary operators and recall that the elementary operators of Oa anticommute with those of Ob. The operators Op and Ob therefore anticommute if an odd number of transpositions of elementary operators is required to reorder Op and Ob and otherwise commute. The number of transpositions is equal to the number of elementary operators in Op times the number of elementary operators in Ob. Therefore, Op and Ob anticommute if both operators contain an odd number of elementary operators and otherwise commute ... 

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