Logistic Map三维耦合格子模型模拟环带球晶

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

应用Logistic map三维耦合格子模型对环带球晶进行了模拟.利用数值计算的方法预测了与实验中环带球晶形貌一致的图案.对于本体体系,环带球晶形貌的带宽随Logistic map中可调参量μ的增大而变窄,随耦合模型中的扩散项系数ε的增大而变宽;对薄膜体系,环带球晶形貌的带宽随格子厚度的增加而变宽,模拟结果与实验结果一致.同时,还给出了螺旋状环带结构在三维空间中的形貌.

Banded spherulite patterns are simulated in three dimensions by means of a coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the band spacing is decreased with the increase of parameter μ in the Logistic map and increased with the increase of the coupling parameter ε for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.