论文标题
具有不可定向缺陷的计算：nematics，emectics和自然模式
Computing with non-orientable defects: nematics, smectics and natural patterns
论文作者
论文摘要
缺陷是有序媒体的无处不在特征。它们具有某些通用特征，独立于基础物理系统，反映了它们的拓扑起源。尽管缺陷的拓扑特性是鲁棒的，但它们看起来是“非物理”奇异性，在粗粒宏观模型中具有不可积分的能量密度。我们开发了一种有原则的方法，可以用足够的“微型物理学”来丰富粗粒理论，以获得热力学一致的，良好的模型，从而可以研究扩展系统中缺陷的动力学和相互作用。我们还开发了相关的数值方法，这些方法适用于在无定形 - 软晶体材料谱系中计算能量驱动的缺陷行为。我们的方法可以处理具有头尾对称性的订单参数，即导演字段，在具有连续翻译对称性的系统中，如在夜间液晶中，以及在近距离和对流模式中损坏翻译对称性的系统中。我们用明确的计算说明了我们的方法。
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models, that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.
