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采用六方格子上的动力学流行病模型描述流体凝固过程 ,根据流体中所含杂质粒子与固态粒子间的短程推斥作用 ,导出了被陷杂质粒子与固态粒子的密度比方程 .并得到方程所含的两个变量 χ 与r之间有如下关系 :当r为有限值时 ,分形生长局限于该区域 ;r无解时 ,集团可无限生长 ,在平面上形成较密集集团 ,维数Db→ 2 ;仅当r的解为∞时 ,分形生长可无限进行 ,该点 χ 即为阈值 χc.由此 ,得到六方格子上阈值 χc≈ 0 65 5 ,与计算机模拟结果相符合 ,大于四方格子的结果 χc(s) (∞ ) =0 5 60± 0 0 0 5 .
According to the kinetic epidemic model on the hexagonal lattice, the fluid solidification process is described. Based on the short-range repulsion between the impurity particles and the solid particles contained in the fluid, the density ratio equation of the trapped impurity particles to the solid particles is deduced. When r is finite, the fractal growth is confined to the region. When r is not solution, the group can grow indefinitely and form more dense clusters in the plane, the dimension Db → 2, the fractal growth can be carried out indefinitely only when the solution of r is ∞, and the point χ is the threshold χc. Thus, the threshold χc ≈ 0 65 5 of the hexagonal lattice is obtained, which is in good agreement with the computer simulation results, The results χc (s) (∞) = 0 5 60 ± 0 0 0 5.