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摘要翻译：
表面作为各种化学反应的高效催化剂。通常，这种表面反应涉及数十亿分子，这些分子在宏观区域扩散和反应。因此，随机涨落可以忽略不计，反应速率可以用基于平均场近似的速率方程来计算。然而，当表面被分割成大量不相连的微观结构域时，每个结构域中的反应物数量变少，且波动强烈。事实上，这就是星际介质中的情况，在那里，一些重要的反应发生在微小尘埃颗粒的表面。在这种情况下，速率方程失效，表面反应的模拟需要随机方法，如主方程。然而，在复杂反应网络的情况下，由于方程的数量呈指数增长，主方程变得不可行。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，方程式的数目大大减少到每个反应物种和每个反应只有一个方程式。此外，用图解法可以很容易地构造方程。我们为一组日益复杂的天体物理相关网络演示了该方法。它有望应用于许多其他领域，在这些领域中出现了具有类似结构的问题，如纳米尺度系统中的表面催化、平流层云中的气溶胶化学和细胞中的遗传网络。
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英文标题：
《Efficient Stochastic Simulations of Complex Reaction Networks on
Surfaces》
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作者：
B. Barzel and O. Biham
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/710.2263
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