Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Phys Rev E. 2019 Jan;99(1-1):012104. doi: 10.1103/PhysRevE.99.012104.
The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability W(Q,t) to find the system in a given mass spectrum Q={n_{1},n_{2},⋯,n_{g}⋯}, with n_{g} being the number of particles of size g. The exact expression for the average number of particles 〈n_{g}(t)〉 at arbitrary time t is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.
研究了在乘积核和任意初始条件下的粒子凝聚系统的时间演化。使用改进的马库斯-卢什尼科夫方法，对主方程进行了解析，以求解系统在给定的质量谱 Q={n_{1},n_{2},⋯,n_{g}⋯}中出现的概率 W(Q,t)，其中 n_{g} 是尺寸为 g 的粒子数。导出了任意时间 t 时的平均粒子数〈n_{g}(t)〉的精确表达式，并通过对几个选定的初始质量谱的数值模拟验证了其有效性。
