Krein's spectral theory of strings and generalized diffusion processes

Functional Analysis in Markov Processes - Lecture Notes in Mathematics ◽

10.1007/bfb0093046 ◽

1982 ◽

pp. 235-259 ◽

Cited By ~ 34

Author(s):

S. Kotani ◽

S. Watanabe

Keyword(s):

Spectral Theory ◽

Diffusion Processes

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Spectral theory of semi-groups connected with diffusion processes and its application

Czechoslovak Mathematical Journal ◽

10.21136/cmj.1961.100484 ◽

1961 ◽

Vol 11 (4) ◽

pp. 558-569 ◽

Cited By ~ 6

Author(s):

Petr Mandl

Keyword(s):

Spectral Theory ◽

Diffusion Processes

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Meridional Circulation, Turbulence, and Diffusion Processes in Stars

International Astronomical Union Colloquium ◽

10.1017/s0252921100080477 ◽

1976 ◽

Vol 32 ◽

pp. 109-116 ◽

Cited By ~ 1

Author(s):

S. Vauclair

Keyword(s):

Convection Zone ◽

Diffusion Processes ◽

Meridional Circulation ◽

Diffusion Time ◽

Work In Progress ◽

First Results ◽

Stellar Envelopes ◽

And Diffusion ◽

Turbulence And Diffusion ◽

Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

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