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 \sim 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 \propto 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 \sim 5 ~ { } Myr , and for a low star formation efficiency of \sim 10 \% .