小世界网络上的扩散限制的聚集-湮没反应动力学

Kinetics of diffusion-limited aggregation-annihilation processes on small-world networks

通过Monte-Carlo模拟,研究了基于NW网络的两种类集团不可逆聚集-湮没过程的动力学行为.在系统中,两个同种类集团相遇,将不可逆地聚集成一个更大的集团;不同种类的两个集团相遇,则发生部分湮没反应.模拟结果表明,1)当捷径量化参数p相对较大或较小时,系统经较长时间演化后,集团密度c(t)和粒子密度g(t)呈现幂律形式,c(t)∝t-α和g(t)∝t-β,其中幂指数α和β满足α=2β的关系;2)当p为其他值时,集团密度和粒子密度随时间按非严格的幂律形式演化.模拟结果与文献[10,11]的理论分析相符得很好.

Kinetics of diffusion-limitied aggregation-annihilation processes on NW small-world networks is investigated by Monte Carlo simulation. In the system,if two clusters of the same species meet at the same node,they will aggregate and form a large one; while if two clusters of different species meet at the same node,they will annihilate each other. Simulation results show that,if the value of p （a parameter that quantifies the number of shortcuts） is large or small enough,the concentration of clusters c（t） and the concentration of particles g（t） follow power laws at large times,i. e. c（t）∝t-α and g（t）∝t-β. Moreover,the relation between the exponents α and β is found to satisfy α = 2β. However,if p is of medium value,the concentration of clusters and the concentration of particles do not follow the power laws exactly. Our simulation results agree with the reported theoretical analysis very well.