Scale invariance : self-similarity of the physical world / Richard N. Henriksen.

Format:

Book

Author/Creator:

Henriksen, R. N., author.

Language:

English

Subjects (All):

Scaling laws (Statistical physics).

Self-similar processes.

Statistical mechanics.

Physical Description:

1 online resource (301 p.)

Edition:

1st ed.

Place of Publication:

Weinheim, Germany : Wiley-VCH, 2015.

Language Note:

English

Summary:

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.

Contents:

""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""

""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow ""

""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry ""

""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples ""

""3.2.1 Self-Similar Lorentz Boost ""

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on online resource; title from PDF title page (ebrary, viewed April 16, 2015).

ISBN:

3-527-68735-1

3-527-68734-3

3-527-68733-5

OCLC:

922955094