this is for holding javascript data
Shane Flynn edited Kinetic model with dynamic disorder.tex
over 9 years ago
Commit id: 03801224525d45430eb3adcd3c48b92cab0b0a9e
deletions | additions
diff --git a/Kinetic model with dynamic disorder.tex b/Kinetic model with dynamic disorder.tex
index 32ec82d..ee5f1d6 100644
--- a/Kinetic model with dynamic disorder.tex
+++ b/Kinetic model with dynamic disorder.tex
...
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 function.
\begin{equation}
\frac{d}{dt}[S(t)]=\frac{1}{n-1}(\frac{1}{1+z^\beta \frac{d}{dt}[S_n(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 $S_2(t) = 1/\left(1+(\omega tC_2(0))^{\beta}\right)$. We can then simplify the rate law expression.