Date(s) - 20/01/2015
11 h 00 min - 12 h 00 min
In this talk, we introduce a cell growth model that combines the bio-mechanic growth effect of a viscoelastic membrane and the geometry of the cell wall. More specifically, we consider that the density of available building materials depends on the curvature of the cell wall. This particular assumption leads to introduce anisotropic growth in the model. We show that the dynamics of the cell wall is described as a system of coupled PDEs including a convection-diffusion equation and a generalized Laplace equation with Neumann boundary conditions. Using a stability analysis, we identify which structure parameters make the membrane wall unstable around a spherical shape. In particular, we show that the coupling between the two equations has to be highly non-linear to make the system unstable around the spherical shape.
Finally, we present numerical simulations which confirm this theoretical analysis of unstable patterns.