Interplay between chemical reactions and transport in structured spaces.

The main motivation behind this study is to understand the interplay between the reactions and transport in a geometries that are not compact. Typical examples of compact geometries are a box or a sphere. A network made of containers C(1) , C(2),..., C(N) and tubes is an example of the space that is structured and noncompact. In containers, particles react with the rate lambda. Tubes connecting containers allow for the exchange of chemicals with the transport rate D. A situation is considered where a number of reactants is small and kinetics is noise dominated. A method is presented that can be used to calculate the average and higher moments of the reaction time. A number of different chemical reactions are studied and their performance compared in various ways. Two schemes are discussed in general, the reaction on a fixed geometry ensemble (ROGE) and the geometry on a fixed reaction ensemble, examples are given in the ROGE case. The most important findings are as follows. (i) There is a large number of reactions that run faster in a networklike geometry. Such reactions contain antagonistic catalytic influences in the intermediate stages of a reaction scheme that are best dealt with in a networklike structure. (ii) Antagonistic catalytic influences are hard to identify since they are strongly connected to the pattern of injected molecules (inject pattern) and depend on the choice of molecules that have to be synthesized at the end (task pattern). (iii) The reaction time depends strongly on the details of the inject and task patterns.