  A computational procedure is developed for determining the conversion
probability for reaction-diffusion systems in which a first-order catalytic
reaction is performed over active particles. We apply this general method to
systems on metric graphs, which may be viewed as 1-dimensional approximations
of 3-dimensional systems, and obtain explicit formulas for conversion. We then
study numerically a class of 3-dimensional systems and test how accurately they
are described by model formulas obtained for metric graphs. The optimal
arrangement of active particles in a 1-dimensional multiparticle system is
found, which is shown to depend on the level of catalytic activity: conversion
is maximized for low catalytic activity when all particles are bunched together
close to the point of gas injection, and for high catalytic activity when the
particles are evenly spaced.
