# Selected Papers, Volume 3

## Stochastic, Statistical, and Hydromagnetic Problems in Physics and Astronomy

- Contents

Author’s Note

*Part One - Dynamical Friction and Brownian Motion*

1. A Statistical Theory of Stellar Encounters

*The Astrophysical Journal*94, no. 3 (1941): 511-25

2. The Statistics of the Gravitational Field Arising From a Random Distribution of Stars. I, The Speed of Fluctuations, with J. von Neumann

*The Astrophysical Journal*95, no. 3 (1942): 489-531

3. The Statistics of the Gravitational Field Arising From a Random Distribution of Stars. II, The Speed of Fluctuations; Dynamical Friction; Spatial Correlations, with J. von Neumann

*The Astrophysical Journal*97, no. 1 (1943): 1-27

4. The Statistics of the Gravitational Field Arising From a Random Distribution of Stars. III, The Correlations in the Forces Acting at Two Points Separated by a Finite Distance

*The Astrophysical Journal*99, no. 1 (1944): 25-46

5. The Statistics of the Gravitational Field Arising From a Random Distribution of Stars. IV, The Stochastic Variation of the Force Acting on a Star

*The Astrophysical Journal*99, no. 1 (1944): 47-53

6. On the Stability of Binary Systems

*The Astrophysical Journal*99, no. 1 (1944): 54-58

7. Dynamical Friction. I, General Considerations: The Coefficient of Dynamical Friction

*The Astrophysical Journal*97, no. 2 (1943): 255-62

8. Dynamical Friction. II, The Rate of Escape of Stars From Clusters and the Evidence for the Operation of Dynamical Friction

*The Astrophysical Journal*97, no. 2 (1943): 263-73

9. Dynamical Friction. III, A More Exact Theory of the Rate of Escape of Stars From Clusters

*The Astrophysical Journal*98, no. 1 (1943): 54-60

10. New Methods in Stellar Dynamics

*Annals of The New York Academy of Sciences*45, art. 3 (1943): 131-62

11. Galactic Evidences for the Time-Scale of the Universe

*Science*99, no. 2564 (1944): 133-36

12. Stochastic Problems in Physics and Astronomy

*Reviews of Modern Physics*15, no. 1 (1943): 1-89

13. Brownian Motion, Dynamical Friction and Stellar Dynamics

*Reviews of Modern Physics*21, no. 3 (1949): 383-88

14. Marian Smoluchowski as the Founder of the Physics of Stochastic Phenomena

R. S. Ingarden, ed.,

*Polish Men of Science: Marian Smoluchowski; His Life and Scientific Work*, 21-28. Polish Scientific Publishers, 1986

15. On a Class of Probability Distributions

Proceedings of the Cambridge Philosophical Society 45, Pt. 2, (1948): 219-24

*Part Two - Statistical Problems in Astronomy*

16. The Theory of the Fluctuations in Brightness of the Milky Way, I.

With G. Münch

*The Astrophysical Journal*112, no. 3 (1950): 380-92

17. The Theory of the Fluctuations in Brightness of the Milky Way, II. With G. Münch

*The Astrophysical Journal*112, no. 3 (1950): 393-98

18. The Theory of the Fluctuations in Brightness of the Milky Way, III. With G. Münch

*The Astrophysical Journal*114, no. 1 (1951): 110-22

19. The Theory of the Fluctuations in Brightness of the Milky Way, IV. With G. Münch

*The Astrophysical Journal*115, no. 1 (1952): 94-102

20. The Theory of the Fluctuations in Brightness of the Milky Way, V. With G. Münch

*The Astrophysical Journal*115, no. 1 (1952): 103-23

21. On Stellar Statistics. With G. Münch

*The Astrophysical Journal*113, no. 1 (1951): 150-65

22. A Statistical Basis for the Theory of Stellar Scintillation

*Monthly Notices of the Royal Astronomical Society*112, no. 5 (1952): 475-83

23. On the Integral Equation Governing the Distribution of the True and the Apparent Rotational Velocities of Stars. With G. Münch

*The Astrophysical Journal*111, no. 1 (1950): 142-56

*Part Three - Statistical Theory of Hydromagnetic Turbulence*

24. On Heisenberg’s Elementary Theory of Turbulence

*Proceedings of the Royal Society*, A, 200 (1949): 20-33

25. The Invariant Theory of Isotropic Turbulence in Magneto-Hydrodynamics

*Proceedings of the Royal Society*, A, 204 (1951): 435-49

26. The Invariant Theory of Isotropic Turbulence in Magneto-Hydrodynamics, II

*Proceedings of the Royal Society*, A, 207 (1951): 301-6

27. The Fluctuations of Density in Isotropic Turbulence

*Proceedings of the Royal Society*, A, 210 (1951): 18-25

28. The Gravitational Instability of an Infinite Homogeneous Turbulent Medium

*Proceedings of the Royal Society*, A, 210 (1951): 26-29

29. The Theory of Axisymmetric Turbulence

*Philosophical Transactions of the Royal Society of London*, A, 242, no. 855 (1950): 557-77

30. The Decay of Axisymmetric Turbulence

*Proceedings of the Royal Society*, A, 203 (1950): 358-64

31. On Turbulence Caused by Thermal Instability

*Philosophical Transactions of the Royal Society of London*, A, 244, no. 884 (1952): 357-84

32. Some Aspects of the Statistical Theory of Turbulence

*Proceedings of the 4th Symposium of the American Mathematical Society*: Fluid Dynamics, 1-17. University of Maryland, 1951

33. Turbulence--A Physical Theory of Astrophysical Interest (Henry Norris Russell Lecture)

*The Astrophysical Journal*110, no. 3 (1949): 329-39

*Part Four - Hydromagnetic Problems in Astrophysics*

34. Magnetic Fields in Spiral Arms. With E. Fermi

*The Astrophysical Journal*118, no. 1 (1953): 113-15

35. Problems of Gravitational Stability in the Presence of a Magnetic Field. With E. Fermi

*The Astrophysical Journal*118, no. 1 (1953): 116-41

36. On the Pulsation of a Star in Which There is a Prevalent Magnetic Field. With D. Nelson Limber

*The Astrophysical Journal*119, no. 1 (1954): 10-13

37. The Equilibrium of Magnetic Stars. With Kevin H. Prendergast

*Proceedings of the National Academy of Sciences*42, no. 1 (1956): 5-9

38. On Cowling’s Theorem on the Impossibility of Self-Maintained Axisymmetric Homogeneous Dynamos. With G. E. Backus

*Proceedings of the National Academy of Sciences*42, no. 3 (1956): 105-9

39. Axisymmetric Magnetic Fields and Fluid Motions

*The Astrophysical Journal*124, no. 1 (1956): 232-43

40. Effect of Internal Motions on the Decay of a Magnetic Field in a Fluid Conductor

*The Astrophysical Journal*124, no. 1 (1956): 244-65

41. Hydromagnetic Oscillations of a Fluid Sphere with Internal Motions

*The Astrophysical Journal*124, no. 3 (1956): 571-79

42. On Force-Free Magnetic Fields

*Proceedings of the National Academy of Sciences*42, no. 1 (1956): 1-5

43. On Force-Free Magnetic Fields, With P. C. Kendall

*The Astrophysical Journal*126, no. 2 (1957): 457-60

44. On Force-Free Magnetic Fields, With L. Woltjer

*Proceedings of the National Academy of Sciences*44, no. 4 (1958): 285-89

45. On the Equilibrium Configurations of an Incompressible Fluid with Axisymmetric Motions and Magnetic Fields

*Proceedings of the National Academy of Sciences*44, no. 9 (1958): 842-47

46. On Cosmic Magnetic Fields

*Proceedings of the National Academy of Sciences*43, no. 1 (1957): 24-27

**Physical Sciences: **
Astronomy and Astrophysics |
Physics and Astronomy |
Theoretical Physics

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