Stellar and substellar initial mass function: a model that implements
  gravoturbulent fragmentation and accretion
  In this work, we derive the stellar initial mass function (IMF) from the
superposition of mass distributions of dense cores, generated through
gravoturbulent fragmentation of unstable clumps in molecular clouds (MCs) and
growing through competitive accretion. MCs are formed by the turbulent cascade
in the interstellar medium at scales L from 100 down to ~0.1 pc. Their internal
turbulence is essentially supersonic and creates clumps with a lognormal
distribution of densities n. Our model is based on the assumption of a
power-law relationship between clump mass and clump density: n~m^x, where x is
a scale-free parameter. Gravitationally unstable clumps are assumed to undergo
isothermal fragmentation and produce protostellar cores with a lognormal mass
distribution, centred around the clump Jeans mass. Masses of individual cores
are then assumed to grow further through competitive accretion until the rest
of the gas within the clump is being exhausted. The observed IMF is best
reproduced for a choice of x=0.25, for a characteristic star formation
timescale of ~5 Myr, and for a low star formation efficiency of ~10 %.
