Convective overshooting in stars

Numerous observations provide evidence that the standard picture, in which convective mixing is limited to the unstable layers of a star, is incomplete. The mixing layers in real stars are significantly more extended than what the standard models predict. Some of the observations require changing the thermal structure of the stellar model, e.g. the poorly-fitting evolutionary tracks of intermediate-mass and massive stars, or the "inflated" cores of OB stars seen by asteroseismic techniques. On the other hand, there are effects that can be explained by some form of weak mixing with no influence the structure of the star, e.g. the Li and Be depletion in low-mass stars, or the abundance anomalies observed in red giants. Both kinds of mixing have traditionally been covered be the umbrella term "convective overshooting," although the physics involved is clearly different. There is a need to look at the overshooting problem from a more fundamental perspective. In this thesis, we investigate two mixing process, which could explain the Li and Be depletion in low-mass stars ("convective settling," Chapters 2 and 3) and contribute to slow mixing at the boundaries of internal convection zones in a whole range of different stars ("differential heating," Chapter 4)