复杂网络上聚集-部分消灭动力学的模拟

SIMULATION OF THE KINETICS OF AGGREGATION-PARTIAL ANNIHILATION PROCESSES ON COMPLEX NETWORKS

通过Monte-Carlo模拟,研究了基于复杂网络上的聚集-部分消灭动力学行为.在系统中,同种类集团相遇后聚合成一个更大的集团,异种类集团相遇后发生消灭反应形成一个更小的集团甚至完全消灭.模拟结果表明,在二维环状规则网络上,经过长时间演化后,系统中剩余的集团浓度和粒子浓度随时间的演化满足幂律形式：c（t）-t^-α和g（t）-t^-β,且幂指数α和β满足α=2β;在小世界网络上,当捷径化参量p相对较小或较大时,经过长时间演化后,集团浓度和粒子浓度随时间的演化也满足幂律形式：c（t）-t^-α和g（t）-t^-β,且幂指数α和β满足α=2β;当p为其他值时,集团密度和粒子密度随时间的演化按非严格的幂律形式.

Kinetics of aggregation-partial annihilation processes on complex networks is investigated by Monte Carlo simulation.In the system,when two clusters of the same kinds meet at the same node,they will aggregate and form a large one;while,if two clusters of different kinds meet at the same node,they will annihilate each other even eliminate completely.Simulation results show that,（1）The concentration of clusters c（t） and the concentration of particles g（t） follow power laws on the two dimension ring regular network at large times,c（t）-t^-α and g（t）-t^-β;It is found that the relation between the exponents α and β satisfy α=2β.（2）For the NW network,when the value of p（a parameter that quantifies the number of shortcuts） is small enough or large,the concentration of clusters c（t） and the concentration of particles g（t） approach power laws at large times,c（t）-t^-α and g（t）-t^-β;Also the relation between the exponents α and β is found to satisfy α=2β.While,if p is of medium value,the concentration of clusters and the concentration of particles don′t take the power laws exactly.