Convection and Dust in Cool Stellar Atmospheres

We report on recent progress in hydrodynamical modelling of the surfacelayers of late M- and L-type main- as well as pre-main-sequence objects.Despite the complex chemistry encountered in the cool atmospheres ofsuch objects a reasonably accurate representation of the radiativetransfer is possible - even within time-dependent multi-dimensionalmodels. The detailed treatment of the interplay between radiation andconvection in the hydrodynamical models allows us to study processesusually not accessible within the framework of conventional modelatmospheres. In particular we derive the efficiency of the convectiveenergy transport expressed in terms of an equivalent mixing-lengthparameter e.g. suitable to construct global stellar structure models.The models also provide an estimate of convective overshooting into theatmospheric layers which are formally stable according to theSchwarzschild criterion. Preliminary brown dwarf models incorporatingthe atmospheric condensation transport and evaporation of dust cloudswill be presented