deletions | additions       diff --git a/Kinetic model with dynamic disorder.tex b/Kinetic model with dynamic disorder.tex  index ad9bda2..beba32f 100644  --- a/Kinetic model with dynamic disorder.tex  +++ b/Kinetic model with dynamic disorder.tex 
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In general we can write the $n^{th}$ order rate law for the KWW model using the new formulations for the nonlinear differential KWW and survival functions.  \begin{equation}  S_{n,KWW}(t)=(\frac{1}{1+(n-1)(\omega t C_A(0)^{n-1})^\beta})^{\frac{1}{n-1}}=\frac{1}{1+(n-1)(z^\beta t^\beta})^{\frac{1}{n-1}} \frac{d}{dt}[S(t)]=\frac{1}{n-1}(\frac{1}{1+z^\beta t^\beta})^{\frac{2-n}{n-1}}(\frac{-z^\beta\beta t^{\beta -1}}{(1+z^\beta t^\beta)^2})  \end{equation}  Such that z contains all the time independent variables $\omega C_a(o)^{n-1}$  Assuming an overall second-order process with a time depedent rate coefficient the survival function is $S_2(t) = 1/\left(1+(\omega tC_2(0))^{\beta}\right)$. The time-depedent rate coefficient characterizing the decay is $k_{2,KWW}(t) = \beta(C_A(0)\omega t)^{\beta}/t$, from the time-derivative of the inverse of the survival function. This definition of the rate coefficient depends on the initial concentration of the reactants which is consistent with units of rate constants in traditional kinetics. Integrating the time-depedent rate coefficient gives the statistical length  \begin{equation}  \mathcal{L}_{KWW}(\Delta{t}) = \left(C_A(0)\omega t\right)^{\beta}\big|_{t_i}^{t_f}