Ke Jianhong, Lin Zhenquan
Department of Physics, Wenzhou Normal College, Wenzhou 325027, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051107. doi: 10.1103/PhysRevE.65.051107. Epub 2002 May 6.
The kinetic behavior of an aggregation-annihilation process of an n-species (n> or =2) system is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible complete annihilation reaction occurs between any two different species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions for the cluster-mass distributions. We find that the cluster-mass distribution of each species satisfies a modified scaling law, which reduces to the standard scaling law in some special cases. The scaling exponents of the system may strongly depend on the reaction rates for most cases; however, for the case with all the aggregation rates twice the annihilation rate, these exponents depend only on the initial concentrations. All the species annihilate each other completely except in the case in which at least one aggregation rate is less than twice the annihilation rate.
研究了一个n物种（n≥2）系统的聚集-湮灭过程的动力学行为。在该模型中，同一物种的任意两个聚集体之间发生不可逆的聚集反应，任意两个不同物种之间发生不可逆的完全湮灭反应。基于平均场理论，我们研究了具有恒定反应速率的该过程的速率方程，以获得聚集体质量分布的渐近解。我们发现每个物种的聚集体质量分布满足一个修正的标度律，在某些特殊情况下该标度律可简化为标准标度律。在大多数情况下，系统的标度指数可能强烈依赖于反应速率；然而，对于所有聚集速率是湮灭速率两倍的情况，这些指数仅取决于初始浓度。除了至少有一个聚集速率小于湮灭速率两倍的情况外，所有物种都会完全相互湮灭。
