FIG. 2.

Energies and shapes of deformation. (a) Normalized free energy of a budding membrane as a function of normalized domain radius ρ relative to the flat radius ρ_d, in the constant membrane tension ensemble, for a few values of domain size ρ_d and normalized surface tension σ. The solid lines are the numerical results; the dashed lines correspond to the simplified analytical model. Sketches at ρ/ρ_d = 0, 0.5, and 1 show corresponding analytical shapes. (b) Meridional curves from axisymmetric finite element numerical minimization of free energy for σ = 0.25. The domain is in red, and the matrix is in blue. Clockwise from upper left: equilibrium deformed configurations for $\rho ∕{\rho }_d=\left\{1,\frac{3}{4},\frac{1}{2},\frac{1}{8}\right\}$.