arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.21241cond-mat.soft
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从分子模型到向列相液晶的张量模型通过熵分解

From molecular model to tensor model of nematic liquid crystals through entropy decomposition

Columbia University(哥伦比亚大学);Peking University(北京大学);Wuhan University(武汉大学)

Baoming Shi, Dawei Wu, Lei Zhang, Pingwen Zhang

AI总结:

本文通过熵分解方法改进了向列相液晶的Q-张量模型,解决了奇异熵项带来的计算难题,并展示了其在相变和滴状配置模拟中的有效性。

摘要:

在向列相液晶的数学建模中,通过Bingham闭合条件从Onsager的分子模型可以推导出一个实用且物理上可靠的Q-张量模型。然而,这一过程导致了一个奇异的熵项,该项隐式地依赖于Q,从而产生计算和理论上的困难。在本文中,我们通过将熵贡献分解为一个奇异但显式的主导项和一个隐式但正则的修正项来表征这一熵贡献,后者已被证明足够正则,可以被数值方法准确近似,例如通过神经网络。这产生了一个计算上方便的自由能,可用于计算向列相液晶。我们的数值实验表明,所得到的自由能能够捕捉各向同性-向列相相变以及自由边界滴状配置。

英文摘要:

In the mathematical modeling of nematic liquid crystals, a practical and physically reliable $\mathbf{Q}$-tensor model can be derived from Onsager's molecular model with the Bingham closure. However, this procedure leads to a singular entropy term that implicitly depends on $\mathbf{Q}$, creating both computational and theoretical difficulties. In this paper, we characterize this entropy contribution by splitting it into a singular but explicit leading term and an implicit but regular correction term, the latter of which is proven to be sufficiently regular to be accurately approximated numerically, for example, by neural networks. This yields a computationally convenient free energy that can be used for the computation of nematic liquid crystals. Our numerical experiments demonstrate that the resulting free energy can capture the isotropic-nematic phase transition as well as the free-boundary droplet configurations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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