Scaling, self-similarity, and intermediate asymptotics /
Barenblatt, G. I.,
Scaling, self-similarity, and intermediate asymptotics / Scaling, Self-similarity, & Intermediate Asymptotics Grigory Isaakovich Barenblatt. - Cambridge : Cambridge University Press, 1996. - 1 online resource (xv, 386 pages) : digital, PDF file(s). - Cambridge texts in applied mathematics ; 14 . - Cambridge texts in applied mathematics ; 14. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
9781107050242 (ebook)
Mathematical physics.
Dimensional analysis.
Differential equations--Asymptotic theory.
QA401 / .B3713 1996
530.1/5
Scaling, self-similarity, and intermediate asymptotics / Scaling, Self-similarity, & Intermediate Asymptotics Grigory Isaakovich Barenblatt. - Cambridge : Cambridge University Press, 1996. - 1 online resource (xv, 386 pages) : digital, PDF file(s). - Cambridge texts in applied mathematics ; 14 . - Cambridge texts in applied mathematics ; 14. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
9781107050242 (ebook)
Mathematical physics.
Dimensional analysis.
Differential equations--Asymptotic theory.
QA401 / .B3713 1996
530.1/5