deletions | additions       diff --git a/Kinetic model with dynamic disorder.tex b/Kinetic model with dynamic disorder.tex  index f443e2e..d47d491 100644  --- a/Kinetic model with dynamic disorder.tex  +++ b/Kinetic model with dynamic disorder.tex 
...
\section{Kinetic model with \section{Dynamically Disordered System Analysis}  The effects of  dynamic disorder} 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.  As demonstrated already in first order kinetics, the Kohlrausch-Williams-Watts (KWW) stretched exponential function can measure the amount of dynamic disorder in a system.[cite]  The KWW model has been widely applicable to many fields of science such as the discharge of capacitors[cite]. The KWW model adds an exponential term, $\beta$,to the survival function model. The term $\omega$ represents a time independent rate coefficient and $\beta$ represents dynamic disorder where $0<\beta\leq1$. Applying KWW to second order kinetics, the survival probability is represented as $S(t)=\frac{1}{1+(\omega t[A_0])^{\beta}}$. The time dependent rate coefficient is $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$, where the second order definition of the time dependent rate coefficient was used. This time dependent rate coefficient gives statistical length and divergences of \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0]^{\beta}\omega^{\beta}t^{\beta}\bigg|_{t_i}^{t_f}  \end{equation}