Molecular fluid simulation for self-organized/self-assembled pattern formation by applying group theory

为了阐明分子自组织或自组装导致的图案形成机制，我们进行了实验观察、理论发展和分子动力学模拟。我们用原子力显微镜成功地显示了DNA片段在云母和高度定向的热解石墨表面的自组装图案。除了粗粒度的分子动力学模拟外，还应用反应扩散模型来表示自组装图案的缓慢增长，其中表面的对称性可以由群论的不可约表示产生的对称函数来实现。因此，与实验相比，可以在实际的时间和空间尺度上模拟各种依赖于表面条件的自组装图案。找出了一些对表面条件敏感的参数。

To clarify a pattern formation mechanism resulting from self-organization or self-assembly of molecules, we have performed experimental observations, theoretical developments, and molecular dynamics simulations. We successfully visualized self-assembled patterns of DNA fragments on mica and highly oriented pyrolytic graphite surfaces by atomic force microscopy. In addition to a coarse-grained molecular dynamics simulation, a reaction-diffusion model is applied to represent slow growths of the self-assembled patterns, in which symmetries of surfaces can be implemented by symmetric functions resulting from irreducible representations of group theory. Consequently, various self-assembled patterns which depend on surface conditions could be simulated in the practical temporal and spatial scales in comparison with experiments. Some parameters sensitive to the surface conditions were found out.