Scaling, self-similarity, and intermediate asymptotics
By: Grigory Isaakovich Barenblatt.
Series: Cambridge texts in applied mathematics ;; 14
Publisher: Cambridge University Press
Published: 1996
Place of publication: Cambridge; New York
Language: eng
Number of pages: 386
Subjects: Mathematical physics.; Dimensional analysis.; Differential equations -- Asymptotic theory.
Description: 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.
Notes: Includes bibliographical references (p. [366]-382) and index.