  It is now widely accepted that dense filaments of molecular gas are integral
to the process of stellar birth. While numerical simulations have succeeded in
reproducing filamentary structure in turbulent gas and analytic calculations
have predicted the formation of dense gas filaments via radial collapse, the
exact process(es) that generate/s such filaments which then form prestellar
cores within them, is unclear. In this work we therefore study numerically the
formation of a dense filament using a relatively simple set-up of a
uniform-density cylinder in pressure equilibrium with its confining medium. In
particular, we examine if its propensity to form a dense filament and further,
to the formation of prestellar cores within this filament bears on the
gravitational state of the initial volume of gas. We report a radial collapse
leading to the formation of a dense filamentary cloud is likely when the
initial volume of gas is at least critically stable (characterised by the
approximate equality between the mass line-density for this volume and its
maximum value). Though self-gravitating, this volume of gas, however, is not
seen to be in free-fall. This post-collapse filament then fragments along its
length due to the growth of a Jeans-like instability to form prestellar cores
like \emph{beads on a string}. We suggest, dense filaments in typical
star-forming clouds classified as gravitationally super-critical under the
assumption of : (i) isothermality when in fact, they are not, and (ii) extended
radial profiles as against one that is pressure-truncated, thereby causing
significant over-estimation of their mass line-density, are unlikely to
experience gravitational free-fall. The radial density and temperature profile
derived for this post-collapse filament is consistent with that deduced for
typical filamentary clouds mapped in recent surveys of nearby star-forming
regions.
