We formulate a hydrodynamic theory of $p$-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic $p$-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of $p$-atic phases, allows us to unveil several unknown aspects of flowing $p$-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

中文翻译：

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剪切液晶中的长程有序和流动排列

我们制定了一个流体动力学理论$p$-atic 液晶，即具有通用性的二维各向异性流体$p$-折叠旋转对称。我们的方法，基于直接体现离散旋转对称性的顺序参数张量$p$-atic阶段，使我们能够揭示流动的几个未知方面$p$-atics，以前的理论，以 O(2) 旋转对称为特征，无法解释。这包括在存在任意剪切速率的简单剪切流的情况下长程取向有序的开始，与二维液晶的标准准长程有序相反，以及在大剪切下流动排列的可能性率。