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.

开发了用于确定反应-扩散系统的转化率的计算程序，在该反应-扩散系统中，对活性颗粒进行了一级催化反应。我们将此通用方法应用于度量图上的系统，该系统可以视为3维系统的1维近似，并获得用于转换的显式。然后，我们对一类3维系统进行数值研究，并测试通过度量图获得的模型公式对这些系统的描述是否准确。发现一维多粒子系统中活性粒子的最佳排列，这取决于催化活性的水平：当所有粒子在气体注入点附近聚集在一起时，转化率最大化，催化活性降低。