Lectures on Fluid Dynamics : A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and d-Branes (CRM Series in Mathematical Physics) (2002. XVI, 114 p. 24,5 cm)

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Lectures on Fluid Dynamics : A Particle Theorist's View of Supersymmetric, Non-Abelian, Noncommutative Fluid Mechanics and d-Branes (CRM Series in Mathematical Physics) (2002. XVI, 114 p. 24,5 cm)

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Full Description


Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

Table of Contents

Series Preface                                     v
Preface vii
Precis ix
Introduction 1 (2)
Classical Equations 3 (20)
Equations of Motion 3 (3)
A Word on Canonical Formulations 6 (3)
The Irrotational Case 9 (3)
Nonvanishing Vorticity and the Clebsch 12 (3)
Parameterization
Some Further Remarks on the Clebsch 15 (8)
Parameterization
Specific Models 23 (18)
Galileo-Invariant Nonrelativistic Model 23 (8)
Lorentz-Invariant Relativistic Model 31 (4)
Some Remarks on Relativistic Fluid Mechanics 35 (6)
Common Ancestry: The Nambu-Goto Action 41 (8)
Light-Cone Parameterization 42 (1)
Cartesian Parameterization 42 (1)
Hodographic Transformation 42 (3)
Interrelations 45 (4)
Supersymmetric Generalization 49 (12)
Chaplygin Gas with Grassmann Variables 49 (4)
Supersymmetry 53 (2)
Supermembrane Connection 55 (1)
Hodographic Transformation 56 (2)
Light-Cone Parametrization 58 (1)
Further Consequences of the Supermembrane 59 (2)
Connection
One-Dimensional Case 61 (20)
Specific Solutions for the Chaplygin Gas on 62 (2)
a Line
Aside on the Integrability of the Cubic 64 (1)
Potential in One Dimension
General Solution for the Chaplygin Gas on a 65 (1)
Line
Born-Infeld Model on a Line 66 (3)
General Solution of the Nambu-Goto Theory 69 (4)
for a (d = 1)-Brane (String) in Two Spatial
Dimensions (on a Plane)
Supersymmetric Chaplygin Gas on a Line 73 (8)
Toward a Non-Abelian Fluid Mechanics 81 (10)
Proposal for Non-Abelian Fluid Mechanics 81 (1)
Non-Abelian Clebsch Parametrization (or, 82 (7)
Casting the Non-Abelian Chern-Simons
Density into Total Derivative Form)
Proposal for Non-Abelian 89 (2)
Magnetohydrodynamics
Noncommutative Fluid Mechanics 91 (10)
Noncommuting Particles 91 (3)
Noncommuting Fluids 94 (2)
Quantization 96 (2)
Various Algebras 98 (3)
Solutions to Problems 101(6)
References 107(6)
Index 113