Selected Papers, Volume 4: Plasma Physics, Hydrodynamic and Hydromagnetic Stability, and Applications of the Tensor-Virial Theorem

by S. Chandrasekhar

University of Chicago Press, 1989 Paper: 978-0-226-10097-5 | Cloth: 978-0-226-10096-8 Library of Congress Classification QC718.C38 1989 Dewey Decimal Classification 530.44

ABOUT THIS BOOK | TOC

ABOUT THIS BOOK

This is the fourth of six volumes collecting significant papers of the distinguished astrophysicist and Nobel laureate S. Chandrasekhar. His work is notable for its breadth as well as for its brilliance; his practice has been to change his focus from time to time to pursue new areas of research. The result has been a prolific career full of discoveries and insights, some of which are only now being fully appreciated.

Chandrasekhar has selected papers that trace the development of his ideas and that present aspects of his work not fully covered in the books he has periodically published to summarize his research in each area.

Volume 4 has three parts. The first, on plasma physics, includes joint work with A. N. Kaufman and K. M. Watson on the stability of the pinch, as well as a paper on Chandrasekhar's own approach to the topic of adiabatic invariants. Part 2 includes work with specific scientific applications of hydrodynamic and hydromagnetic stability not covered in his monograph on the subject. The final part contains Chandrasekhar's papers on the scientific applications of the tensor-virial theorem, in which he restores to its proper place Riemann's neglected work with ellipsoidal figures.

TABLE OF CONTENTS

Foreword by Norman R. Lebovitz Part One - Plasma Physics
1. Properties of an Ionized Gas of Low Density in a Magnetic Field, III. With A. N. Kaufman and K. M. Watson Annals of Physics 2, no. 5 (1957): 435-70
2. Properties of an Ionized Gas of Low Density in a Magnetic Field, IV. With A. N. Kaufman and K. M. Watson Annals of Physics 5, no. 1 (1958): 1-25
3. The Stability of the Pinch. With A. N. Kaufman and K. M. Watson Proceedings of the Royal Society, A, 245 (1958): 435-55
4. Adiabatic Invariants in the Motions of Charged Particles The Plasma in a Magnetic Field: A Symposium Magnetohydrodynamics, 3-22. Stanford University Press, 1958

Part Two - Hydrodynamic and Hydromagnetic Stability
5. The Stability of Viscous Flow Between Rotating Cylinders in the Presence of a Radial Temperature Gradient Journal of Rational Mechanics and Analysis 3, no. 2 (1954): 181-207
6. The Stability of Viscous Flow Between Rotating Cylinders, II.
With Donna D. Elbert Proceedings of the Royal Society, A, 268 (1962): 145-52
7. The Character of the Equilibrium of an Incompressible Fluid Sphere of Variable Density and Viscosity Subject to Radial Acceleration Quarterly Journal of Mechanics and Applied Mathematics 8, pt. 1 (1955): 1-21
8. Thermal Convection (Rumford Medal Lecture) Proceedings of the American Academy of Arts and Sciences 86, no. 4 (1957): 323-39
9. The Thermodynamics of Thermal Instability in Liquids Max-Planck-Festschrift 1958, 103-14. Veb Deutscher Verlag der Wissenschaften, Berlin, 1959
10. Variational Methods in Hydrodynamics Proceedings of the Eighth Symposium in Applied Mathematics, vol. 8 (1958): 139-41
11. On Characteristic Value Problems in High Order Differential Equations Which Arise in Studies on Hydrodynamic and Hydromagnetic Stability American Mathematical Monthly 61, no. 7 (1954): 32-45
12. Adjoint Differential Systems in the Theory of Hydrodynamic Stability
Journal of Mathematics and Mechanics 10, no. 5 (1961): 683-90

Part Three - Tensor Virial Theorem and Its Applications
13. The Virial Theorem in Hydromagnetics Journal of Mathematical Analysis and Applications 1, no. 2 (1960): 240-52
14. The Virial Equations of the Various Orders. (Chapter 1 in The Higher Order Virial Equations and Their Applications to the Equilibrium and Stability of Rotating Configurations) Lectures in Theoretical Physics, vol. 6, 1-16. University of Colorado Press, 1964
15. A Theorem on Rotating Polytropes The Astrophysical Journal 134, no. 2 (1961): 662-64
16. On Super-potentials in the Theory of Newtonian Gravitation.
With Norman R. Lebovitz The Astrophysical Journal 135, no. 1 (1962): 238-47
17. On Superpotentials in the Theory of Newtonian Gravitation.
II, Tensors of Higher Rank. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1032-36
18. The Potentials and the Superpotentials of Homogeneous Ellipsoids. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1037-47
19. On the Oscillations and the Stability of Rotating Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 135, no. 1 (1962): 248-60
20. On the Oscillations and the Stability of Rotating Gaseous Masses. II, The Homogenous, Compressible Model. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1069-81
21. On the Oscillations and the Stability of Rotating Gaseous Masses. III, The Distorted Polytropes. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1082-1104
22. On the Occurrence of Multiple Frequencies and Beats in the B Canis Majoris Stars. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1105-7
23. Non-Radial Oscillations and Convective Instability of Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 138, no. 1 (1963): 185-99
24. A General Variational Principle Governing the Radial and the Non-Radial Oscillations of Gaseous Masses The Astrophysical Journal 139, no. 2 (1964): 664-74
25. Non-Radial Oscillations of Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 140, no. 4 (1964): 1517-28
26. The Pulsations and the Dynamical Stability of Gaseous Masses in Uniform Rotation. With Norman R. Lebovitz The Astrophysical Journal 152, no. 1 (1968): 267-91
27. The Ellipticity of a Slowly Rotating Configuration. With P. H. Roberts The Astrophysical Journal 138, no. 3 (1963): 801-8
28. The Points of Bifurcation Along the Maclaurin, the Jacobi, and the Jeans Sequences The Astrophysical Journal 137, no. 4 (1963): 1185-1202
29. The Equilibrium and the Stability of the Roche Ellipsoids The Astrophysical Journal 138, no. 4 (1963): 1182-1213
30. The Equilibrium and the Stability of the Riemann Ellipsoids The Astrophysical Journal 142, no. 3 (1965): 890-921
31. The Equilibrium and the Stability of the Riemann Ellipsoids, II The Astrophysical Journal 145, no. 3 (1966): 842-77
32. The Virial Equations of the Fourth Order The Astrophysical Journal 152, no. 1 (1968): 293-304
33. A Tensor Virial-Equation for Stellar Dynamics. With Edward P. Lee Monthly Notices of the Royal Astronomical Society 139, no. 2 (1968): 135-39
34. Some Elementary Applications of the Virial Theorem to Stellar Dynamics. With Donna D. Elbert Monthly Notices of the Royal Astronomical Society 155, no. 4 (1971): 435-47
35. The Stability of a Rotating Liquid Drop Proceedings of the Royal Society, A, 286 (1965): 1-26

Selected Papers, Volume 4: Plasma Physics, Hydrodynamic and Hydromagnetic Stability, and Applications of the Tensor-Virial Theorem

by S. Chandrasekhar

University of Chicago Press, 1989 Paper: 978-0-226-10097-5 Cloth: 978-0-226-10096-8

This is the fourth of six volumes collecting significant papers of the distinguished astrophysicist and Nobel laureate S. Chandrasekhar. His work is notable for its breadth as well as for its brilliance; his practice has been to change his focus from time to time to pursue new areas of research. The result has been a prolific career full of discoveries and insights, some of which are only now being fully appreciated.

Chandrasekhar has selected papers that trace the development of his ideas and that present aspects of his work not fully covered in the books he has periodically published to summarize his research in each area.

Volume 4 has three parts. The first, on plasma physics, includes joint work with A. N. Kaufman and K. M. Watson on the stability of the pinch, as well as a paper on Chandrasekhar's own approach to the topic of adiabatic invariants. Part 2 includes work with specific scientific applications of hydrodynamic and hydromagnetic stability not covered in his monograph on the subject. The final part contains Chandrasekhar's papers on the scientific applications of the tensor-virial theorem, in which he restores to its proper place Riemann's neglected work with ellipsoidal figures.

TABLE OF CONTENTS

Foreword by Norman R. Lebovitz Part One - Plasma Physics
1. Properties of an Ionized Gas of Low Density in a Magnetic Field, III. With A. N. Kaufman and K. M. Watson Annals of Physics 2, no. 5 (1957): 435-70
2. Properties of an Ionized Gas of Low Density in a Magnetic Field, IV. With A. N. Kaufman and K. M. Watson Annals of Physics 5, no. 1 (1958): 1-25
3. The Stability of the Pinch. With A. N. Kaufman and K. M. Watson Proceedings of the Royal Society, A, 245 (1958): 435-55
4. Adiabatic Invariants in the Motions of Charged Particles The Plasma in a Magnetic Field: A Symposium Magnetohydrodynamics, 3-22. Stanford University Press, 1958

Part Two - Hydrodynamic and Hydromagnetic Stability
5. The Stability of Viscous Flow Between Rotating Cylinders in the Presence of a Radial Temperature Gradient Journal of Rational Mechanics and Analysis 3, no. 2 (1954): 181-207
6. The Stability of Viscous Flow Between Rotating Cylinders, II.
With Donna D. Elbert Proceedings of the Royal Society, A, 268 (1962): 145-52
7. The Character of the Equilibrium of an Incompressible Fluid Sphere of Variable Density and Viscosity Subject to Radial Acceleration Quarterly Journal of Mechanics and Applied Mathematics 8, pt. 1 (1955): 1-21
8. Thermal Convection (Rumford Medal Lecture) Proceedings of the American Academy of Arts and Sciences 86, no. 4 (1957): 323-39
9. The Thermodynamics of Thermal Instability in Liquids Max-Planck-Festschrift 1958, 103-14. Veb Deutscher Verlag der Wissenschaften, Berlin, 1959
10. Variational Methods in Hydrodynamics Proceedings of the Eighth Symposium in Applied Mathematics, vol. 8 (1958): 139-41
11. On Characteristic Value Problems in High Order Differential Equations Which Arise in Studies on Hydrodynamic and Hydromagnetic Stability American Mathematical Monthly 61, no. 7 (1954): 32-45
12. Adjoint Differential Systems in the Theory of Hydrodynamic Stability
Journal of Mathematics and Mechanics 10, no. 5 (1961): 683-90

Part Three - Tensor Virial Theorem and Its Applications
13. The Virial Theorem in Hydromagnetics Journal of Mathematical Analysis and Applications 1, no. 2 (1960): 240-52
14. The Virial Equations of the Various Orders. (Chapter 1 in The Higher Order Virial Equations and Their Applications to the Equilibrium and Stability of Rotating Configurations) Lectures in Theoretical Physics, vol. 6, 1-16. University of Colorado Press, 1964
15. A Theorem on Rotating Polytropes The Astrophysical Journal 134, no. 2 (1961): 662-64
16. On Super-potentials in the Theory of Newtonian Gravitation.
With Norman R. Lebovitz The Astrophysical Journal 135, no. 1 (1962): 238-47
17. On Superpotentials in the Theory of Newtonian Gravitation.
II, Tensors of Higher Rank. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1032-36
18. The Potentials and the Superpotentials of Homogeneous Ellipsoids. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1037-47
19. On the Oscillations and the Stability of Rotating Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 135, no. 1 (1962): 248-60
20. On the Oscillations and the Stability of Rotating Gaseous Masses. II, The Homogenous, Compressible Model. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1069-81
21. On the Oscillations and the Stability of Rotating Gaseous Masses. III, The Distorted Polytropes. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1082-1104
22. On the Occurrence of Multiple Frequencies and Beats in the B Canis Majoris Stars. With Norman R. Lebovitz The Astrophysical Journal 136, no. 3 (1962): 1105-7
23. Non-Radial Oscillations and Convective Instability of Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 138, no. 1 (1963): 185-99
24. A General Variational Principle Governing the Radial and the Non-Radial Oscillations of Gaseous Masses The Astrophysical Journal 139, no. 2 (1964): 664-74
25. Non-Radial Oscillations of Gaseous Masses. With Norman R. Lebovitz The Astrophysical Journal 140, no. 4 (1964): 1517-28
26. The Pulsations and the Dynamical Stability of Gaseous Masses in Uniform Rotation. With Norman R. Lebovitz The Astrophysical Journal 152, no. 1 (1968): 267-91
27. The Ellipticity of a Slowly Rotating Configuration. With P. H. Roberts The Astrophysical Journal 138, no. 3 (1963): 801-8
28. The Points of Bifurcation Along the Maclaurin, the Jacobi, and the Jeans Sequences The Astrophysical Journal 137, no. 4 (1963): 1185-1202
29. The Equilibrium and the Stability of the Roche Ellipsoids The Astrophysical Journal 138, no. 4 (1963): 1182-1213
30. The Equilibrium and the Stability of the Riemann Ellipsoids The Astrophysical Journal 142, no. 3 (1965): 890-921
31. The Equilibrium and the Stability of the Riemann Ellipsoids, II The Astrophysical Journal 145, no. 3 (1966): 842-77
32. The Virial Equations of the Fourth Order The Astrophysical Journal 152, no. 1 (1968): 293-304
33. A Tensor Virial-Equation for Stellar Dynamics. With Edward P. Lee Monthly Notices of the Royal Astronomical Society 139, no. 2 (1968): 135-39
34. Some Elementary Applications of the Virial Theorem to Stellar Dynamics. With Donna D. Elbert Monthly Notices of the Royal Astronomical Society 155, no. 4 (1971): 435-47
35. The Stability of a Rotating Liquid Drop Proceedings of the Royal Society, A, 286 (1965): 1-26