that we chose is small enough to diminish the effect of scission for the early time kinetics of the polymerised mass, as we find and also show below that this is true for our choice of set of parameters. For this small value of $\kmf$, the typical trajectory of the two moments is shown in Fig. \[fig3\]. We notice that the polymerised mass $M$ evolves much faster in time than the number density of polymers $P$. The inset in Fig. \[fig3\]b shows that in the asymptotic limit of vanishing scission rate $\kmf$, the lag phase for both moments is characterised by an approximately equal time scale. However, after the lag phase, $M$ relaxes to its equilibrium value much faster than $P$ does. Hence, for the early time kinetics of the polymerised monomeric mass, the number concentration of polymers remains effectively constant, i.e., equal to initial value $P(t)=P(0)$.

Making use of this, we can solve Eq. \[eq11\] for $M(t)$ for early times, yielding the explicit solution, \[eq13\] M(t) &=& - , where for the purpose of notational simplicity we define $\sigma \equiv \alpha+\gamma P(0)$ and $\eta \equiv \sqrt{\sigma ^2+4 \beta  \kpb P(0)}$. In Fig. \[fig4\] we show that Eq. \[eq13\] agrees 