| Summary: | Filamentary structures are observed to be common over a wide range of spatial scales and are strongly linked to star formation. In this thesis I present the results of a range of numerical simulations which investigate the stability, collapse and fragmentation of filaments. The global longitudinal collapse timescale for filaments is found to be considerably longer than for equally dense spheres, allowing sufficient time for local collapse to occur, and to solely occur via the distinctive end-dominated mode. A new freefall timescale equation for filaments is presented, as well as a semi-analytic model of longitudinal collapse. The fragmentation of accreting filaments is found to be more complicated than that of equilibrium filaments, and is dominated by the behaviour of longitudinal gravo-acoustic oscillations. This results in the fastest growing perturbation mode being independent of filament width. The non-equilibrium model presented here allows observers to estimate the age of a fragmenting filament and the mass accretion rate. Simulations of filaments accreting from a inhomogenous, turbulent medium show that turbulence has a large impact on the fragmentation of a filament. When the turbulence is sub-sonic, a filament fragments in a two-tiered hierarchical manner. As the energy in the turbulent field increases, the filament fragments into elongated fibre-like sub-structures. The formation of these fibre-like structures is intimately linked to the vorticity of the velocity field in the filament and the accretion onto the filament. In addition, I present synthetic C18O observations and show that the fibrelike sub-structures appear as velocity-coherent structures, well separated in velocity space, similar to the fibres observed by Hacar & Tafalla (2011).
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