Titel: Lectures on Fluid Dynamics
Autor/en: Roman Jackiw
A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and d-Branes.
'CRM Series in Mathematical Physics'.
Springer New York
17. Mai 2002 - gebunden - 140 Seiten
This book contains lectures on fluid dynamics given in Montreal, while the author held the Aisenstadt Chair, as well as other lectures on the same topics. It begins by explaining the motivation and reviewing the classical theory, but in a manner different from textbook discussions. Among the topics discussed are the conservation laws and Euler equations, and a method for finding their canonical structure; C. Eckart's Lagrangian and a relativistic generalization for vortex-free motion; nonvanishing vorticity and the Clebsch parameterization for the velocity vector. Jackiw then discusses some specific models for nonrelativistic and relativistic fluid mechanics in spatial dimensions greater than one, including the Chaplygin gas (whose negative pressure is inversely proportional to density), and the scalar Born-Infeld model. He shows how both the Chaplygin gas and the Born-Infeld model devolve from the parameterization-invariant Nambu-Goto action, when specific parameterization is made. As in particle physics, Jackiw shows, fluid mechanics enhanced by supersymmetry. For one-dimensional cases, the models discussed above are completely integrable, and Jackiw gives the General solution of the Chaplygin gas and the Born-Infeld model on a line. General solution of the Nambu- Goto theory for a 1-brane (string) in two spatial dimensions. Jackiw discusses the need for a non-Abelian fluid mechanics and proposes a Lagrangian, which involves a non-Abelian auxiliary field whose Chern-Simons density should be a total derivative. The generalization to magnetohydrodynamics, which results from including a dynamical non-Abelian gauge field, reduces in the Abelian limit to conventional magnetohydrodynamics.
1. Introduction / 2. Classical Equations / 3. Specific Models / 4. Common Ancestry: The Nambu-Goto Action / 5. Supersymmetric Generalization / 6. One-Dimensional Case / 7. Towards a Non-Abelian Fluid Mechanics / 8. Noncommutative Fluid Mechanics
From the reviews:
"Bringing the 1E up to date has added more than 200 pages of additional text. Anyone seriously involved with the application of [principle component analysis] will certainly want to purchase a copy...Seldom had such a wealth of material on a single topic in statistics appeared in one book. Goodall (1998) noted that there 'should be something of interest for even the most seasoned and experiences practitioner of multivariate statistics' (p. 352). All that material has gotten a whole lot more comprehensive here in this new edition. Goodall (1998) also labeled the book 'a good read'. Now it may be a little heavy for that purpose, but it certainly is a fantastic reference book."
"This book by Jackiw differs significantly from what is traditionally understood as 'lectures on fluid dynamics'. The author's aim is to show that the apparatus, methods, language, etc. developed for physics of particles can be successfully applied to fluid mechanics. ... everyone interested in fundamentals and deep theoretical approach to fluid mechanics should become acquainted with it." (K Piechor, Applied Mechanics Reviews, Vol. 56 (3), 2003)