By Grigory Isaakovich Barenblatt
Scaling (power-type) legislation display the elemental estate of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or house. the valuables of self-similarity simplifies considerably the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The publication starts from a non-traditional exposition of dimensional research, actual similarity concept and common thought of scaling phenomena. Classical examples of scaling phenomena are offered. it really is tested that scaling comes on a level whilst the effect of good information of preliminary and/or boundary stipulations disappeared however the process continues to be faraway from final equilibrium country (intermediate asymptotics). it really is defined why the dimensional research often is inadequate for setting up self-similarity and developing scaling variables. vital examples of scaling phenomena for which the dimensional research is inadequate (self-similarities of the second one variety) are offered and mentioned. a detailed connection of intermediate asymptotics and self-similarities of the second one sort with a primary proposal of theoretical physics, the renormalization workforce, is defined and mentioned. a number of examples from quite a few fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, stream in porous strata, atmospheric and oceanic phenomena are provided for which the information of scaling, intermediate asymptotics, self-similarity and renormalization workforce have been of decisive worth in modeling.