Fast variable description dynamics

We next briefly overview our fast variable description of liquid chemical dynamics. 

IV. THE FAST VARIABLE DESCRIPTION OF LIQUID PHASE CHEMICAL DYNAMICS... 

In Section III, we combine the analyses of Section II and the Appendix with the results of recent experiments [13] and simulations [14] to discuss the slow variable description [7-10] of liquid phase activated barrier crossing. In Section IV, using these same ideas we review our fast variable theory of liquid phase reaction dynamics [19-26] from the standpoint of the recent literature [6,11-17,27,28]. Finally, in Section V we summarize our main points. 

We can now proceed with the analysis as described in Section 6.3. Let us define the stretched, fast time variable r = t/e. On rewriting the model in terms of r and considering the limit e — 0, we obtain a description of the fast dynamics of the process ... 

An overview of the methods used previously in mechanism reduction is presented in Tomlin et al. (1997). The present work uses a combination of existing methods to produce a carbon monoxide-hydrogen oxidation scheme with fewer reactions and species variables, but which accurately reproduces the dynamics of the full scheme. Local concentration sensitivity analysis was used to identify necessary species from the full scheme, and a principle component analysis of the rate sensitivity matrix employed to identify redundant reactions. This was followed by application of the quasi-steady state approximation (QSSA) for the fast intermediate species, based on species lifetimes and quasi-steady state errors, and finally, the use of intrinsic low dimensional manifold (ILDM) methods to calculate the mechanisms underlying dimension and to verify the choice of QSSA species. The origin of the full mechanism and its relevance to existing experimental data is described first, followed by descriptions of the reduction methods used. The errors introduced by the reduction and approximation methods are also discussed. Finally, conclusions are drawn about the results, and suggestions made as to how further reductions in computer run times can be achieved. 

We have already emphasized several times that fast but correlated fluctuations give rise to dissipation on the coarse-grained level of description, which is described here by the friction matrix M, Eq. (7.10) or (7.28). The notion fast is defined here by times t smaller than the timescale Xs, which separates the evolution of the relevant variables X from rapid dynamics of the remaining degrees of freedom. The existence of such a timescale (which is equivalent to the crucial assumption of timescale separation discussed in Section 7.3) is not obvious. Here, we observe that the correlation... 

---