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Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics
Abstract
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.
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Citations
Cited by
Self-similarity in ultrafast nonlinear optics
Dudley, J. M., Finot, C., Richardson, D. J., & Millot, G. (2007) · Nature Physics · doi:10.1038/nphys705 · Cited by 379
Archean geodynamics and the thermal evolution of Earth
Korenaga, J. (2006) · Geophysical Monograph Series · doi:10.1029/164gm03 · Cited by 356
Scaling, Universality, and Geomorphology
Dodds, P. S., & Rothman, D. H. (2000) · Annual Review of Earth and Planetary Sciences · doi:10.1146/annurev.earth.28.1.571 · Cited by 304
Singularity dynamics in curvature collapse and jet eruption on a fluid surface
Zeff, B. W., Kleber, B., Fineberg, J., & Lathrop, D. P. (2000) · Nature · doi:10.1038/35000151 · Cited by 267
Universality of rain event size distributions
Peters, O., Deluca, A., Corral, A., Neelin, J. D., & Holloway, C. E. (2010) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2010/11/p11030 · Cited by 96
Metadata
- Authors
- Barenblatt, G. I.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1996-12-12
- OpenAlex
- W4210992751
- Cited by
- 2,017
- References
- 0
- FWCI
- 7.52
- Type
- book
- Language
- en
- Open access
- closed
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- Barenblatt, G. I. (1996). Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge University Press eBooks. https://doi.org/10.1017/cbo9781107050242
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
