小世界网络上的扩散限制的聚集-湮没反应动力学

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.

全局耦合网络上的两种类集团的聚集-湮没反应动力学

利用Monte-Carlo模拟研究了全局耦合网络上扩散限制的不可逆聚集-湮没过程的动力学行为.在系统中,同种类集团相遇,将发生聚集反应;不同种类的集团相遇,则发生部分湮没反应.模拟结果表明:1)当两种粒子初始浓度相等时,系统长时间演化后,集团浓度c(t)和粒子浓度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,且α=2/(2+q);集团大小分布随时间的演化满足标度律,a_k(t)=k^(-Τ)t^(-ω)φ(k/t^z),其中Τ≈-1.27q,ω≈(3+1.27q)/(2+q),z=α/2=1/(2+q);2)当两种粒子初始浓度不相等时,系统经长时间演化后,初始浓度较小的种类完全湮没,而初始浓度较大的那个种类的集团浓度cA(t)仍具有幂律形式,cA(t)～t^(-α),其中α=1/(1+q),其集团大小分布随时间的演化也满足标度律,标度指数为Τ≈-1.27q,ω≈(2+1.27q)/(1+q)和z=α=1/(1+q).模拟结果与已报道的理论分析结果相符得很好.

Novel Biased Aggregation-Annihilation Model

We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.