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Jonathan Nichols edited Kinetic Model With Static Disorder.tex
over 9 years ago
Commit id: 8327416f75bc6ce6c81c0f5eb04c92b64000f326
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\begin{equation}
S(t)=\left(\frac{1}{2+2\omega tN_A(0)}+\frac{1}{2+2\omega'tN_A(0)}\right)
\end{equation}
The survival function in equation
26 36 shows a bi-exponential decay when $\omega\neq\omega'$, which shows that static disorder is present since a distribution of rate coefficients is necessary to describe the system.
When $\omega=\omega'$, the survival function in equation
29 37 turns into the standard survival function for a second order reaction shown in equation
2. 12.
\begin{equation}
S(t)=\left(\frac{1}{2+2\omega tN_A(0)}+\frac{1}{2+2\omega tN_A(0)}\right)=\frac{2}{2+2\omega t[A_0]}=\frac{1}{1+\omega t[A_0]}
\end{equation}