Difference between revisions of "Errata: Derivation of CME in Chapter 2 is missing terms"
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[[page::33]] | [[page::33]] | ||
− | [[line::]] | + | [[line::-18 to -7]] |
+ | [[version:1.1a]] | ||
− | + | In the master equation derivation of the simple reactions in equation (2.5), there are missing terms and an incorrect factor in one of the terms. The corrected equation, with modifications marked in blue, is | |
+ | <center><math> | ||
+ | \begin{align} | ||
+ | & \frac{dP}{dt}(n_\text{A}, n_\text{B}, n_\text{AB}) = \\ | ||
+ | & \qquad k_\text{rev} (n_\text{AB}{\color{blue}+1}) P(n_\text{A} - 1, n_\text{B} - 1, n_\text{AB} + 1) | ||
+ | - \frac{k_\text{fwd}}{\Omega}\, n_\text{A} n_\text{B} P(n_\text{A}, n_\text{B}, | ||
+ | n_\text{AB}) \\ | ||
+ | & \qquad | ||
+ | {\color{blue} + \frac{k_\text{fwd}}{\Omega}\, (n_\text{A}+1) (n_\text{B}+1) | ||
+ | P(n_\text{A} + 1, n_\text{B} + 1, n_\text{AB} - 1) | ||
+ | - k_\text{rev} n_\text{AB} P(n_\text{A}, n_\text{B}, n_\text{AB})}. | ||
+ | \end{align} | ||
+ | </math></center> | ||
+ | |||
+ | This also affects expanded equations further down the page. The corrected equations are | ||
+ | <center><math> | ||
+ | \begin{align} | ||
+ | q_0 &= (1, 0, 4), &\quad& | ||
+ | dP_0/dt = | ||
+ | {\color{blue} 2 (k_\text{fwd}/\Omega) P_1 - 4 k_\text{rev} P_0} \\ | ||
+ | q_1 &= (2, 1, 3), &\quad& | ||
+ | dP_1/dt = 4 k_\text{rev} P_0 - 2 (k_\text{fwd}/\Omega) P_1 | ||
+ | {\color{blue} + 6 (k_\text{fwd}/\Omega) P_2 - 3 k_\text{rev} P_1}, \\ | ||
+ | q_2 &= (3, 2, 2), &\quad& | ||
+ | dP_2/dt = 3 k_\text{rev} P_1 - 6 (k_\text{fwd}/\Omega) P_2, | ||
+ | {\color{blue} + 12 (k_\text{fwd}/\Omega) P_3 - 2 k_\text{rev} P_2}, \\ | ||
+ | q_3 &= (4, 3, 1), &\quad& | ||
+ | dP_3/dt = 2 k_\text{rev} P_2 - 12 (k_\text{fwd}/\Omega) P_3, | ||
+ | {\color{blue} + 20 (k_\text{fwd}/\Omega) P_4 - 1 k_\text{rev} P_3}, \\ | ||
+ | q_4 &= (5, 4, 0), &\quad& | ||
+ | dP_4/dt = 1 k_\text{rev} P_3 - 20 (k_\text{fwd}/\Omega) P_4, \\ | ||
+ | \end{align} | ||
+ | </math></center> | ||
[[Category:Errata]] | [[Category:Errata]] |
Revision as of 10:06, 11 September 2014
33 -18 to -7 version:1.1a
In the master equation derivation of the simple reactions in equation (2.5), there are missing terms and an incorrect factor in one of the terms. The corrected equation, with modifications marked in blue, is
This also affects expanded equations further down the page. The corrected equations are