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This book is a reference for scientists featuring examples of dimensions and scaling in different areas of natural sciences and mathematics. It discusses recent advances in the theoretical techniques of scaling and applications to almost any branch of quantitative science.

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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.

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Introduction
Arbitrary Measures of the Physical World
Lie Groups and Scaling Symmetry
Poincaré Group Plus Rescaling Group
Instructive Classic Problems
Variations on Lie Selfsimilarity
Explorations
Renormalization Group and Noether Invariants
Scaling in Hydrodynamical Turbulence
Epilogue
Appendix: Examples from the Literature

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Dick Henriksen has been a full professor of astrophysics at Queen´s University, Ontario, since 1978 and is a recipient of their research excellence award. In addition, he has been a senior visitor at Stanford, a Humboldt Fellow in Germany and Engineur/chercheur at CEA Saclay in France. He was one of the two founders of the Canadian Institute for Theoretical Astrophysics in 1984-85, which resides at the University of Toronto and has become one of the world´s premier centres for Astrophysics. He has published more than 125 research papers, many of which employ scaling and relativistic concepts. He is author of the recent Wiley undergraduate textbook entitled "Practical Relativity", Professor Henriksen has extensive lecturing experience, having lectured at all graduate and undergraduate levels in physics, as well as presenting many professional colloquia.

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