  In this paper we present a new model for single-celled, non-branching hypha
tip growth. The growth mechanism of hypha cells consists of transport of cell
wall building material to the cell wall and subsequent incorporation of this
material in the wall as it arrives. To model the transport of cell wall
building material to the cell wall we follow Bartnicki-Garcia et al in assuming
that the cell wall building material is transported in straight lines by an
isotropic point source. To model the dynamics of the cell wall, including its
growth by new material, we use the approach of Campas and Mahadevan, which
assumes that the cell wall is a thin viscous sheet sustained by a pressure
difference. Furthermore, we include a novel equation which models the hardening
of the cell wall as it ages. We present numerical results which give evidence
that our model can describe tip growth, and briefly discuss validation aspects.
