模拟多位粒子可逆聚集的Monte Carlo算法
Monte Carlo Algorithm for Simulating Reversible Aggregation of Multisite Particles
摘要：
我们提出了一种高效、精确的蒙特卡罗算法来模拟具有专用结合位点的粒子的可逆聚集。该方法引入了一种新的数据结构动态键树来记录键形成的簇和序列。该算法实现了一个恒定的时间成本，用于处理集群的关联和成本之间的$\mathcal{O}(\log M)$和$\mathcal{O}(M)$用于处理键解离的集群与$M$键。该算法在统计上是精确的，并且可以再现由标准方法获得的结果。我们应用该方法来模拟一个三价配体和二价受体的聚类系统，并获得了一个平均尺度的$\mathcal{O}(M^{0.45})$处理键解离在无环聚集，相比标准方法中的簇大小的线性缩放。该算法还需要比传统方法少得多的内存。
英文摘要：
We present an efficient and exact Monte Carlo algorithm to simulate reversible aggregation of particles with dedicated binding sites. This method introduces a novel data structure of dynamic bond tree to record clusters and sequences of bond formations. The algorithm achieves a constant time cost for processing cluster association and a cost between $\mathcal{O}(\log M)$ and $\mathcal{O}(M)$ for processing bond dissociation in clusters with $M$ bonds. The algorithm is statistically exact and can reproduce results obtained by the standard method. We applied the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtained an average scaling of $\mathcal{O}(M^{0.45})$ for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods. The algorithm also demands substantially less memory than the conventional method.
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