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\section{Dynamically Disordered System Analysis}  The effects of dynamic disorder on higher ordered kinetics can be investigated through the Kohlrausch-Williams-Watts (KWW) model. This expression takes the expotential decay predicted by classical kinetics and stretches the curve through a time depedent rate coefficient $\omega$ and the coopertavity of decay $\beta$, making it a conventient expression for interpreting dynamic disorder. The use of this model is intended to be a proof of principle, however any system with a time depedent rate coefficient may be analyzed.   Assuming an overall second order process with a time depedent rate coefficient the survival function is written as $S(t)=\frac{1}{1+(\omega t[A_0])^{\beta}}$.Thorugh the time derivitive of the inverse of the survival function the time depedent rate coefficient characterising the deacy is expressed as $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$. We see this definition of the rate coefficient maintains a depedence on the initial concentration of the reactants which is a unique result when compared to first order kinetics. Through integrating over kinetics, and propagates thorugh the remainder of the calculations.Next  the time depedent rate coefficient we find is integrated to determine  the statistical length. \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0\omega t]^{\beta}\bigg|_{t_i}^{t_f}  \end{equation}  To undertand the effect of fluctuations on the rate coefficient we then integrate over the square, determining the divergence.  \begin{equation}  \mathcal{J}_{KWW}(\Delta{t})=\frac{\Delta t[A_0]^{2\beta}\beta^{2}\omega^{2\beta}t^{2\beta-1}}{2\beta-1}\bigg|_{t_i}^{t_f}  \end{equation}  This form shows the $\frac{1}{2}$ $\beta$ valuse must be evaluated seperately which yields the final result for comparison.  And when $\beta=\frac{1}{2}$,   \begin{equation}  \mathcal{J}_{KWW}(\Delta{t})=\Delta t [A_0]\beta^2\omega^{2\beta} \ln(t)\bigg|_{t_i}^{t_f}  \end{equation}  These results closely match the results of the first order irreversible decay KWW model [citation], with the only difference being a dependence on the initial concentration, which is what we would expect seen in equation 19.