1998A&A...333..647B

Thorough discussion of the previous theoretical works on the pulsation of Long Period Variables leads us to the conclusion that the mode periods predicted by linear models must significantly differ from the reality, and that, if one nevertheless relies upon such a modelling, it is at least necessary to change the mixing length. The hypothesis that the so-derived mode periods be reasonably reliable is supported by confrontation between a model grid based on these grounds and the luminosities of LPVs in the Large Magellanic Cloud and in LMC clusters, as well as the luminosities and effective temperatures of Miras in the solar neighbourhood. A wide majority of the Miras appear probably pulsating on the first overtone, and the sample Semi-Regulars on the second. However, a significant proportion of Miras seem to be fundamental pulsators. Individual masses are derived. A few stars are probably undergoing hot bottom burning, while two seem to have a peculiar dust envelope.