  Three component models of the IMF are made to consider possible origins for
the observed relative variations in the numbers of brown dwarfs,
solar-to-intermediate mass stars, and high mass stars. Three distinct physical
processes are noted. The characteristic mass for most star formation is
identified with the thermal Jeans mass in the molecular cloud core, and this
presumably leads to the middle mass range by the usual collapse and accretion
processes. Pre-stellar condensations (PSCs) observed in mm-wave continuum
studies presumably form at this mass. Significantly smaller self-gravitating
masses require much larger pressures and may arise following dynamical
processes inside these PSCs, including disk formation, tight-cluster ejection,
and photoevaporation as studied elsewhere, but also gravitational collapse of
shocked gas in colliding PSCs. Significantly larger stellar masses form in
relatively low abundance by normal cloud processes, possibly leading to steep
IMFs in low-pressure field regions, but this mass range can be significantly
extended in high pressure cloud cores by gravitationally-focussed gas accretion
onto PSCs and by the coalescence of PSCs. These models suggest that the
observed variations in brown dwarf, solar-to-intermediate mass, and high mass
populations are the result of dynamical effects that depend on environmental
density and velocity dispersion. They accommodate observations ranging from
shallow IMFs in cluster cores to Salpeter IMFs in average clusters and whole
galaxies to steep and even steeper IMFs in field and remote field regions. They
also suggest how the top-heavy IMFs in some starburst clusters may originate
and they explain bottom-heavy IMFs in low surface brightness galaxies.
