that setting $\epsilon_r = 0.6$ and $\epsilon_d=0.1$ are good control parameters. One check on the accuracy of the numerical solution is that $\sum_{i} y_{i} = 1$. We find in our results that the total abundance differs from unity by less than one part in $10^{11}$, where we have not imposed any additional normalization at each time step.

Figure \[fig:jump\] shows the time evolution of the abundances of selected charge states following a sudden jump in $T$ from $10^{5}$ K to $10^{7}$ K at a density of $n_{\mathrm{e}}=10^{9}$ $\mathrm{cm^{-3}}$. This is essentially the same scenario as was described above in Section \[subsec:timescales\], but using a direct calculation clarifies the relation between the timescales and charge state abundances. These results show that EIMI allows the CSD to evolve more rapidly than if only EISI is considered. Nevertheless, this change is relatively small, being faster in this case by only a few percent. At large $n_{\mathrm{e}}t$, the abundances asymptote to their CIE values.

Application to Nanoflares {#subsec:nanoflares}
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A much different situation can arise when the temperature is oscillating. In this case, the system can be prevented from reaching an equilibrium and the effects of EIMI are more important. To illustrate these effects 