Lectures on Fluid Dynamics
Subtitle: A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and d-Branes
By: by Roman Jackiw
Series: CRM Series in Mathematical Physics; CRM series in mathematical physics
Publisher: Springer New York
Published: 2002
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 114
ISBN-13: 9781441929938; 9781475736656
Subjects: Mathematical physics; Physics
Description: 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.
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Table of contents: title: Introduction; title: Classical Equations; title: Specific Models; title: Common Ancestry: The Nambu-Goto Action; title: Supersymmetric Generalization; title: One-Dimensional Case; title: Towards a Non-Abelian Fluid Mechanics; title: Noncommutative Fluid Mechanics.