  We use numerical simulations of the fragmentation of a 1000 solar mass
molecular cloud and the formation of a stellar cluster to study how the initial
conditions for star formation affect the resulting initial mass function (IMF).
In particular, we are interested in the relation between the thermal Jeans mass
in a cloud and the knee of the initial mass function, i.e. the mass separating
the region with a flat IMF slope from that typified by a steeper,
Salpeter-like, slope. In three isothermal simulations with M_J=1 solar mass,
M_J=2 solar masses and M_J=5 solar masses, the number of stars formed, at
comparable dynamical times, scales roughly with the number of initial Jeans
masses in the cloud. The mean stellar mass also increases (though less than
linearly) with the initial Jeans mass in the cloud. It is found that the IMF in
each case displays a prominent knee, located roughly at the mass scale of the
initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs
which are shallow to higher masses. This implies that a universal IMF requires
a physical mechanism that sets the Jeans mass to be near 1 solar mass.
Simulations including a barotropic equation of state as suggested by Larson,
with cooling at low densities followed by gentle heating at higher densities,
are able to produce realistic IMFs with the knee located at approximately 1
solar mass, even with an initial M_J=5 solar masses. We therefore suggest that
the observed universality of the IMF in the local Universe does not require any
fine tuning of the initial conditions in star forming clouds but is instead
imprinted by details of the cooling physics of the collapsing gas.
