Convective overshoot

Suggestions have been made that ON stars result from mass transfer in close binaries (13, 15), from mass loss by stellar winds (16), or from convective overshooting (17). The models in Figs. 1 and 2, which include overshooting and mass loss at the observed rates, clearly show that these two processes are unable alone to account for... 

Both points disagree with observations The observed main sequence width requires only a moderate core mass increase (cf. Mermilliod and Maeder, 1986), the LBVs exist, and very massive WNE and WC stars are not observed (cf. references in Langer, 1987 Doom, 1987). Evolutionary calculations without overshooting avoid both discrepancies. We conclude that convective overshooting is not very efficient in massive H-burning stars, but that the Schwarzschild-criterion may be a fair approximation in order to determine the size of the convective core. 

The maximum 13C abundance and its distribution in the 3 M model is, at first, similar to that found due to diffusive convective overshooting by Herwig et al (1997). However, the rotational mixing spreads the 13C peak out before the neutrons are produced (cf. Fig. 13), which is not the case in the models of Herwig et al (1997). At the present time one can not discriminate which of these scenarios would agree better with empirical constraints. However, we want to stress that both mechanisms of 13C production, rotation and overshooting, do not exclude each other, and that it is possible that they act simultaneously in AGB stars. 

Convective core overshooting during central He-burning should be much less efficient compared to that in the H-burning phase, since mostly during central He-burning the convective core is... 

The convective core size in massive He-burning stars can hardly be restricted by observations. However, the absence of very massive WC stars is consistent with the case of no overshooting at all. 

Concerning the scsattering of OB stars in the HR diagram (Humphry 1980), the effects of overshooting of convective core (Maeder 1984), mass loss (cf. Chios and Maeder 1986), and generous stability criterion of semi-convection (Stothers and Chin 1976) have been discussed Here, we will note the dredge up effect is caused by the sound waves emitted from a convective core. 

There is, as yet, no complete theory to explain the phenomenon of polarographic maxima which is manifested by the observed current overshooting the limiting current. The causes are convective mass transport in the solution and adsorption. Three types of maximum have been identified [61] ... 

Radial temperature profiles were almost constant as experimentally observed and later predicted by the model. This indicates that the thermal conductivity for the styrene/water systems studied is sufficiently high to quickly heat the liquid as it enters the tube, and efficiently remove the heat released by the reaction. In Figure 6 it is seen that as G2 increases, a high ratio of heat released by reaction to heat removed by convection causes a temperature overshoot. Such an overshoot was not observed for styrene, either experimentally or with the model. Figure 7 presents predicted axial temperature profiles for several monomers at standard conditions, with constants as in Table III. While equations (4) and (5) require the monomer to be only partially soluble, the results shown in Figure 7 indicate a strong exotherm for vinyl chloride, acrylonitrile and vinyl acetate. 

Maeder (1992), who applied convective core overshooting and thus arrives at larger core masses, obtains the smallest oxygen yields. 

For the same reason, no convective core overshooting was invoked. This has been applied in many massive star calculations in the recent years in order to obtain a wider main sequence band (cf., e.g., Schaller et al. 1992). However, as rotationally induced mixing has a very similar effect (e.g., Langer 1992, Fliegner et al. 1996), the interpretation that the main sequence widening is due to rotation and thus that the convective cores of non-rotating stars are not extended over their sizes predicted by the Schwarzschild criterion was adopted. 

To describe the polymer stress in this equation, one can probe any of rheological constitutive models proposed for the long-chain branched polymers the partially extending convection (PEC) model of R. Larson, [117], the molecular stress function (MSP) theory of M. Wagner et al. [118,119], the modified extended pom-pom (mXPP) model of M.H. Verbeeten et al. [120], etc. Here, the PEC model has been chosen as it can be easily tuned to describe the overshoot position for a wide class of polymers by changing a value of the non-linear parameter Thus, = 1 in the case of linear polymer (Doi-Edwards limit), 0 < < 1 in the case of branched polymers, and = 0 in the... 

---