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  3. Scaling, Self-similarity, and Intermediate Asymptotics
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  • Publisher:
    Cambridge University Press
    Publication date:
    18 December 2014
    12 December 1996
    ISBN:
    9781107050242
    9780521435222
    DOI:
    https://doi.org/10.1017/CBO9781107050242
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.54kg, 412 Pages
    • Subjects:
    Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Fluid Dynamics and Solid Mechanics, Mathematical Modeling and Methods
    Series:
    Cambridge Texts in Applied Mathematics (14)
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    Subjects:
    Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Fluid Dynamics and Solid Mechanics, Mathematical Modeling and Methods
    Series:
    Cambridge Texts in Applied Mathematics (14)
    Information

    Book 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.

    Reviews

    ‘A splendid and very readable work … Greatly recommended!’

    Sjoerd Rienstra Source: ITW Nieuws

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