deletions | additions       diff --git a/Nonlinear irreversible kinetics.tex b/Nonlinear irreversible kinetics.tex  index f420fab..afb8746 100644  --- a/Nonlinear irreversible kinetics.tex  +++ b/Nonlinear irreversible kinetics.tex 
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\equiv \frac{d}{dt}\frac{1}{S_i(t)^{i-1}}  = (i-1)\omega C_i(0)^{i-1}  \end{equation}  As shown in equation 4, the The  statistical length $\mathcal{L}_i$ is the integral of the cumulative time dependent time-dependent  rate coefficient over a period of time $\Delta{t}$. The $\Delta{t}$, and the divergence is the cumulative square of the rate coefficient, multiplied by the time interval. %The  statistical length is \begin{equation} %\begin{equation}  %  \mathcal{L}_i(\Delta t)^2 = \left[\int_{t_i}^{t_f}(i-1)\omega(C_i^{i-1})dt\right]^2   \end{equation}  and \left[\int_{t_i}^{t_f}(i-1)\omega C_i^{i-1}(0)\,dt\right]^2   %\end{equation}  %and  the divergence is \begin{equation} %\begin{equation}  %  \frac{\mathcal{J}_i(\Delta t)}{\Delta t} = \int_{t_i}^{t_f}{(i-1)^2\omega^2}\left(C_i^{i-1}\right)^{2} \int_{t_i}^{t_f}{(i-1)^2\omega^2}\left(C_i^{i-1}(0)\right)^{2}  dt. \end{equation}  Both %\end{equation}  For  the equations governing traditional kinetics, both the statistical  length squared and the divergence are $(i-1)^2\omega^2([A_0]^{n-1})^2\Delta $(i-1)^2\omega^2\left(C_i^{i-1}(0)\right)^2\Delta  t^2$: the bound holds when there is no static or dynamic disorder, and a single rate coefficient is sufficient to characterize irreversible decay. The nonlinearity of the rate law leads to solutions that depend on concentration. This concentration dependence is also present in both $\mathcal{J}$ and $\mathcal{L}$.