Recurring set

The method involves choosing m of the original variables to form what is called a recurring set. Any set m of the variables may be chosen with the following two provisions ... 

It must not be possible to form a dimensionless group from some or all of the variables within the recurring set. If it were so possible, this dimensionless group would, of course, be one of the n terms. 

The recurring set must contain three variables that cannot themselves be formed into a dimensionless group. This imposes the following two restrictions ... 

Outside these constraints, any three variables can be chosen. It should be remembered, however, that the variables forming the recurring set are liable to appear in all the dimensionless groups. As this problem deals with the effect of conditions on the pressure difference AP, it is convenient if AP appears in only one group, and therefore it is preferable not to include it in the recurring set. 

If the variables d, u, p are chosen as the recurring set, this fulfils all the above condi tions. Dimensionally ... 

With six variables and three fundamental dimensions. (6 — 3) = 3 dimensionless groups are expected. Choosing d. p and p as the recurring set ... 

Choosing as the recurring set p, N and D, then these three variables themselves cannot be grouped together to give a dimensionless number. M, L, T can now be expressed in terms of combinations of p, N, D. 

Recurring sets must, among them, include all n fundamental dimensions. 

Using M, L and T as fundamentals, there are five variables and three fundamentals and therefore by Buckingham s n theorem, there will be two dimensionless groups. Choosing D, N and p as the recurring set, dimensionally ... 

Metabolism is characterized by common motifs. A small number of activated carriers, such as ATP, NADH, and acetyl CoA, are used in many metabolic pathways. NADPH, which carries two electrons at a high potential, provides reducing power in the biosynthesis of cell components from more-oxidized precursors. ATP and NADPH are continually generated and consumed. Most transfers of activated groups in metabolism are mediated by a recurring set of carriers. Moreover, key reaction types are used repeatedly in metabolic pathways. 

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