Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints.
Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints.
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DOI：
10.1103/physreve.86.046103
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
T. Emmerich;A. Bunde;S. Havlin
中科院分区：
文献类型：
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作者：
T. Emmerich;A. Bunde;S. Havlin
我们考虑嵌入在一维（de=1）和二维（de=2）欧氏空间中的Erdös-Rényi型网络，其链路长度分布p（r）为<$r-δ。这些网络的维数d，作为δ的函数，已经被研究过了，并且已经被证明依赖于δ。在这里，我们考虑这些空间约束网络的扩散，湮灭和化学反应过程，并表明它们的动力学是由系统的维数d控制的。我们研究随机步行者在t个时间步后行进的平均距离t 1/dw以及随机步行者返回原点的概率P0（t），作为指数δ和嵌入维度de的函数。根据这些量，我们确定网络维数d和随机游动维数dw作为δ的函数。我们发现在湮灭过程（A+A→0）和化学反应过程（A+B→0）中，分数d/dw控制着作为时间t的函数的幸存者的数量，这表明对于具有短程链接的有序和无序晶格导出的关系在具有长程链接的复杂嵌入网络的情况下也是有效的。
We consider Erdö]s-Rényi-type networks embedded in one-dimensional (de=1) and two-dimensional (de=2) Euclidean space with the link-length distribution p(r)∼r-δ. The dimension d of these networks, as a function of δ, has been studied earlier and has been shown to depend on δ. Here we consider diffusion, annihilation, and chemical reaction processes on these spatially constrained networks and show that their dynamics is controlled by the dimension d of the system. We study, as a function of the exponent δ and the embedding dimension de, the average distance ∼t1/dw a random walker has traveled after t time steps as well as the probability of the random walker's return to the origin P0(t). From these quantities we determine the network dimension d and the dimension dw of the random walk as a function of δ. We find that the fraction d/dw governs the number of survivors as a function of time t in the annihilation process (A+A→0) and in the chemical reaction process (A+B→0), showing that the relations derived for ordered and disordered lattices with short-range links remain valid also in the case of complex embedded networks with long-range links.