Numerical solution of the Smoluchowski kinetic equation and asymptotics of the distribution function
Numerical solution of the Smoluchowski kinetic equation and asymptotics of the distribution function
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Smoluchowski 动力学方程的数值解和分布函数的渐近
DOI：
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发表时间：
1995
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通讯作者：
D. S. Krivitsky
中科院分区：
文献类型：
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作者：
D. S. Krivitsky
本文给出了模型核U（M1，M2）随（M1+M2）λ变化和U（M1，M2）随（M1 M2）λ 2/变化的Smoluchowski动力学方程的数值解。我们证明了核U的解在0< lambda <or=1时随（M1+M2）lambda变化，在0< lambda <or=2时随（M1 M2）lambda/2变化，在一段时间后，解的行为变得自相似。分析了尺度函数的形状，特别是找到了它在U随（M_1 + M_2）λ变化时的一个简单的近似表达式，得到了当U随（M_1M_2）λ_2/，0<λ <1变化时的一个有趣结果：证明了尺度函数的渐近性态是非幂的.我们开发的程序确定TCR，临界指数和指数的幂律渐近的Smoluchowski方程的解决方案。这些量的模型核的具体值。分析了数值求解算法的稳定性条件。讨论了Smoluchowski方程数值解的可能性。
We obtain the numerical solution of the Smoluchowski kinetic equation for model kernels U(M1, M2) varies as (M1+M2)lambda and U(M1, M2) varies as (M1M2)lambda 2/, 0< lambda <or=2. We show that the behaviour of the solution for the kernel U varies as (M1+M2)lambda at 0< lambda <or=1 and U varies as (M1M2)lambda/2 at 0< lambda <or=2 becomes self-similar after some time. The shape of the scaling function is analysed; in particular, a simple approximate expression for it at U varies as (M1+M2)lambda is found. An interesting result is obtained for U varies as (M1M2)lambda 2/, 0< lambda <1: the asymptotic behaviour of the scaling function proved to be non-power. We develop the procedure for determining tcr, the critical indices and the exponent of the power-law asymptotics of the Smoluchowski equation solution. The concrete values of these quantities for the model kernels are obtained. The stability conditions of the algorithm for numerical solving are analysed. The possibilities afforded by numerical solution for investigation of the Smoluchowski equation are discussed.