From previously published Markov chain derivations of the coefficients (in terms of transition probabilities) in the collisionless Boltzmann equation it proves possible, with plausible assumptions about the transition probabilities, to reduce to a partial differential equation with spiral characteristics. This is applied to the case of a rotating galaxy which has already become disk-shaped. The contangent of the angle between radial and tangential directions is then given by the ratio of radial velocity to circumferential velocity.
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Which already takes account of the deterministic effects of gravitation and angular momentum.
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Kyrala, A. Sufficiency conditions for the development of spiral arms in galaxies. Astrophys Space Sci 69, 521–523 (1980). https://doi.org/10.1007/BF00661937
- Differential Equation
- Markov Chain
- Partial Differential Equation
- Radial Velocity
- Boltzmann Equation