Evolutionary models for very-low-mass stars and brown dwarfs with dusty atmospheres

38 pages, Latex file, uses aasms4.styInternational audienceWe present evolutionary calculations for very-low-mass stars and brown dwarfs based on synthetic spectra and non-grey atmosphere models which include dust formation and opacity, i.e. objects with $\\te\\simle 2800$ K. The interior of the most massive brown dwarfs is shown to develop a conductive core after $\\sim 2$ Gyr which slows down their cooling. Comparison is made in optical and infrared color-magnitude diagrams with recent late-M and L-dwarf observations. The saturation in optical colors and the very red near-infrared colors of these objects are well explained by the onset of dust formation in the atmosphere. Comparison of the faintest presently observed L-dwarfs with these dusty evolutionary models suggests that dynamical processes such as turbulent diffusion and gravitational settling are taking place near the photosphere. As the effective temperature decreases below $\\te\\approx 1300-1400$ K, the colors of these objects move to very blue near-infrared colors, a consequence of the ongoing methane absorption in the infrared. We suggest the possibility ofa brown dwarf dearth in $J,H,K$ color-magnitude diagrams around this temperature