Scaling, Self-similarity, and Intermediate Asymptotics

Download or read book Scaling, Self-similarity, and Intermediate Asymptotics written by G. I. Barenblatt and published by Cambridge University Press. This book was released on 1996-12-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.