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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 predicting non-expotential behavior. interpreting dynamic disorder.  The KWW use of this  model has been widely applicable is intended  to many fields of science such as the discharge be a proof  of capacitors[cite]. The KWW model adds an exponential term, $\beta$,to the survival function model. The term $\omega$ represents principle, however any system with  a time independent depedent  rate coefficient and $\beta$ represents dynamic disorder where $0<\beta\leq1$. Applying KWW to may be analyzed.   Assuming an overall  second order kinetics, process with a time depedent rate coefficient  the survival probability function  is represented written  as $S(t)=\frac{1}{1+(\omega t[A_0])^{\beta}}$. The t[A_0])^{\beta}}$.Thorugh the time derivitive of the inverse of the survival function the  time dependent depedent  rate coefficient characterising the deacy  is expressed as  $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$, where the second order t)^{\beta}}{t}$. We see this  definition of thetime dependent  rate coefficient was used. This maintains a depedence on the initial concentration of the reactants which is a unique result when compared to first order kinetics. Through integrating over the  time dependent depedent  rate coefficient gives we find the  statistical length and divergences of length.  \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0]^{\beta}\omega^{\beta}t^{\beta}\bigg|_{t_i}^{t_f}  \end{equation}  \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}