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Efficient stochastic simulations of complex reaction networks on surfaces

机译：表面复杂反应网络的高效随机模拟

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摘要

Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds, and genetic networks in cells.
机译：表面可作为多种化学反应的高效催化剂。通常，这种表面反应涉及数十亿个在宏观区域上扩散和反应的分子。因此，随机波动可以忽略不计，并且可以使用基于平均场近似的速率方程式来评估反应速率。然而，在将表面划分为大量不连续的微观区域的情况下，每个区域中的反应物的数量变小并且剧烈波动。实际上，这就是星际介质中的情况，在这种情况下，微小尘埃颗粒的表面会发生一些关键的反应。在这种情况下，速率方程会失效，并且表面反应的模拟需要随机方法，例如主方程。但是，在复杂反应网络的情况下，主方程变得不可行，因为方程的数量呈指数增长。为了解决这个问题，我们引入了一种基于矩方程的随机方法。在这种方法中，方程式的数量显着减少为每个反应物种只有一个方程式，每个反应只有一个方程式。此外，可以使用图解方法轻松构建方程式。我们演示了一套方法，用于增加复杂性的一组天体相关网络。预期可将其应用于出现类似结构问题的许多其他情况，例如纳米级系统中的表面催化，平流层云中的气溶胶化学以及细胞中的遗传网络。

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