论文标题
一维域中的一维域的出生和死亡
Birth and Death of One-dimensional Domains in Cylindrically Confined Liquid Crystals
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Nematic liquid crystal (LC) is a partially ordered matter that has been a popular model system for studying a variety of topological behaviors in condensed matter. In this work, utilizing a spontaneously twisting achiral LC, we introduce a one-dimensional (1D) model system to investigate how domains and topological defects arise and annihilate, reminiscing the Kibble-Zurek mechanism. Because of the unusual elastic properties, lyotropic chromonic LCs form a double-twist structure in a cylindrical capillary with degenerate planar anchoring, exhibiting chiral symmetry breaking despite the absence of intrinsic chirality. Consequently, the domains of different handedness coexist with equal probabilities, forming the topological defects between them. We experimentally measure the domain-length distribution and its time evolution, best fitted by a three-parameter log-normal distribution. We propose that the coalescence within a train of 1D domains having the normal length distribution and randomly assigned handedness, may lead to the domains of the log-normal-like length distribution. Our cylindrically confined LC provides a practical model system to study the formation and annihilation of domains and defects in 1D.