Difference between revisions of "Errata: Extra term \xi f in derivation of reaction rate equations in Section 2.1"
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| text = | | text = | ||
The term <math>\xi_f</math> in the displayed equations for <math>n_\text{AB}(t + dt)</math> and <math>[\text{AB} ](t+dt) - [ \text{AB} ](t)</math> should be removed. In the derivation of the reaction rate equations, the propensity functions are evaluated at the current state. | The term <math>\xi_f</math> in the displayed equations for <math>n_\text{AB}(t + dt)</math> and <math>[\text{AB} ](t+dt) - [ \text{AB} ](t)</math> should be removed. In the derivation of the reaction rate equations, the propensity functions are evaluated at the current state. | ||
+ | |||
+ | The corrected equations are | ||
+ | <center><math> | ||
+ | n_\text{AB}(t + dt) = n_\text{AB}(t) + a_f({\color{blue} q}) dt - a_r(q) dt, | ||
+ | </math></center> | ||
+ | and | ||
+ | <center><math> | ||
+ | \begin{align} | ||
+ | [\text{AB}](t + dt) - [\text{AB}](t) | ||
+ | &= \Bigl( a_f({\color{blue} q}, t) - a_r(q) \Bigr) | ||
+ | / \Omega \cdot dt \\ | ||
+ | &= \Bigl( k_f n_\text{A} n_\text{B} / \Omega^2 - k_r n_\text{AB} | ||
+ | / \Omega \Bigr)\, dt \\ | ||
+ | &= \Bigl( k_f [\text{A}] [\text{B}] - k_r [\text{AB}] | ||
+ | \Bigr)\, dt. | ||
+ | \end{align} | ||
+ | </math></center> | ||
}} | }} |
Latest revision as of 18:54, 19 January 2015
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Location: page 35, line 16, -11
The term in the displayed equations for and should be removed. In the derivation of the reaction rate equations, the propensity functions are evaluated at the current state.
The corrected equations are
and
(Contributed by D. Del Vecchio, 10 Sep 2014)
This error appears in version 1.1a and earlier versions of the text.