A scale-invariance formulation explains why dimensional analysis succeeds and partitions self-similar solutions into three categories based on whether unit-induced and parameter-induced scale functions coincide.
de Gennes,Scaling concepts in polymer physics(Cornell University Press, New York, 1979)
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Why dimensional analysis works: general classification of self-similarity based on scale-invariance
A scale-invariance formulation explains why dimensional analysis succeeds and partitions self-similar solutions into three categories based on whether unit-induced and parameter-induced scale functions coincide.