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| Author | : FRÖHLICH |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-12-14 |
| Genre | : Science |
| ISBN | : 1489967621 |
| Author | : J. Frohlich |
| Publisher | : |
| Total Pages | : 440 |
| Release | : 2014-09-01 |
| Genre | : |
| ISBN | : 9781489967633 |
| Author | : G. I. Barenblatt |
| Publisher | : Cambridge University Press |
| Total Pages | : 412 |
| Release | : 1996-12-12 |
| Genre | : Mathematics |
| ISBN | : 9780521435222 |
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.
| Author | : Richard N. Henriksen |
| Publisher | : John Wiley & Sons |
| Total Pages | : 304 |
| Release | : 2015-04-23 |
| Genre | : Science |
| ISBN | : 3527687351 |
Bringing the concepts of dimensional analysis, self-similarity, and fractal dimensions together in a logical and self-contained manner, this book reveals the close links between modern theoretical physics and applied mathematics. The author focuses on the classic applications of self-similar solutions within astrophysical systems, with some general theory of self-similar solutions, so as to provide a framework for researchers to apply the principles across all scientific disciplines. He discusses recent advances in theoretical techniques of scaling while presenting a uniform technique that encompasses these developments, as well as applications to almost any branch of quantitative science. The result is an invaluable reference for active scientists, featuring examples of dimensions and scaling in condensed matter physics, astrophysics, fluid mechanics, and general relativity, as well as in mathematics and engineering.
| Author | : G. I. Barenblatt |
| Publisher | : Cambridge University Press |
| Total Pages | : 187 |
| Release | : 2003-11-13 |
| Genre | : Mathematics |
| ISBN | : 0521826578 |
The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
| Author | : G. I. Barenblatt |
| Publisher | : |
| Total Pages | : 386 |
| Release | : 1996 |
| Genre | : Differential equations |
| ISBN | : 9781107050242 |
| Author | : G. I. Barenblatt |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Grigory Isaakovich Barenblatt |
| Publisher | : |
| Total Pages | : 386 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
| Author | : L. Pietronero |
| Publisher | : Elsevier |
| Total Pages | : 489 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0444598413 |
Fractals in Physics
| Author | : J. Cardy |
| Publisher | : Elsevier |
| Total Pages | : 385 |
| Release | : 2012-12-02 |
| Genre | : Computers |
| ISBN | : 0444596062 |
Over the past few years, finite-size scaling has become an increasingly important tool in studies of critical systems. This is partly due to an increased understanding of finite-size effects by analytical means, and partly due to our ability to treat larger systems with large computers. The aim of this volume was to collect those papers which have been important for this progress and which illustrate novel applications of the method. The emphasis has been placed on relatively recent developments, including the use of the &egr;-expansion and of conformal methods.
