The paper considers a simple model of radially symmetric cell which undergoes growth due to a continuous supply of nutrient, and disintegration as a result from the various tasks the cell performs. The boundary of the cell is a \free boundary", unknown in advance, which evolves by responding to both the growth and disintegration processes. If the nutrient concentration (at in nity) exceeds a ce...

We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with anisotropic Gibbs–Thomson law with kinetic undercooling, and quasi-static variants thereof. The phase field model is given by θwt + λ %(φ)φt = ∇ . (b(φ)∇w) , cΨ a α %...

Generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as Poisson sources of particles which then perform symmetric random walks with an attractive zero-range interaction until they reach the first site which has been visited by fewer than α particles, at which point they stop. Sites on which particles are frozen cons...