The data were subjected to a two-dimensional unsupervised hierarchical cluster analysis according to the similarities of sPCCs (Additional file 10: Table S9).
According to dimensional analysis and the concepts of complete and incomplete self-similarity, generalized Wöhler and Paris equations are determined, which provide a rational interpretation to a majority of empirical power-law criteria used in fatigue.
According to dimensional analysis, two dimensionless groups, an Einstein's parameter group and a modified densimetric Froude number group, were chosen to examine how injection affects the bedload transport rate.
However, in three dimensional analysis, there are at least 6 components of strain ratio tensor, which are calculated as shown below according to Eqs. (6 11) [21].
Dimensional analysis involving transcendental functions.
Dimensional analysis and similarity.
Similarity and dimensional analysis.
Dimensional analysis and dynamic similarity.
Dimensional analysis, similarity, and modeling.
