  A phase field model for dealing with shape instabilities in fluid membrane
vesicles is presented. This model takes into account the Canham-Helfrich
bending energy with spontaneous curvature. A dynamic equation for the
phase-field is also derived. With this model it is possible to see the vesicle
shape deformation dynamically, when some external agent instabilizes the
membrane, for instance, inducing an inhomogeneous spontaneous curvature. The
numerical scheme used is detailed and some stationary shapes are shown together
with a shape diagram for vesicles of spherical topology and no spontaneous
curvature, in agreement with known results.
