FIG. 7.

The kinetics of filament assembly with secondary nucleation and saturating elongation are almost exactly captured by Eq. (10a), which is a significant improvement upon an earlier analytical solution based on the Lambert-W function. However, the Richards solution offers little advantage over the Lambert solution for fragmenting systems. Black: numerical solution to the moment equations. Red: old (Lambert) analytical approximate solution. Blue: new (Richards) analytical approximate solution. ε = 0.01. (a) $n_2=2,{\mathcal{K}}_E=2$. (b) $n_2=2,{\mathcal{K}}_E=0.4$. (c) $n_2=0,{\mathcal{K}}_E=2$. (d) $n_2=0,{\mathcal{K}}_E=0.4$.