A non-traditional view on the modeling of nematic disclination dynamics
A non-traditional view on the modeling of nematic disclination dynamics
复制标题
向列向错动力学建模的非传统观点
DOI：
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
N. Walkington
中科院分区：
文献类型：
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作者：
Chiqun Zhang;Xiaohan Zhang;A. Acharya;D. Golovaty;N. Walkington
非奇异向错动力学在单轴向列液晶建模的数学框架内的运动学是一个直接延伸的经典方式来识别这些线缺陷的奇异性的单位矢量场表示的方向盘。众所周知，对于含有向错线缺陷的组态，普遍接受的Oseen-Frank能量是无穷大的。我们设计了一个自然的增强的Oseen-Frank能源占物理的情况下，在某些条件下，无限的董事梯度有零相关的能量成本，将是必要的建模半整数强度向错的董事理论的框架内。平衡和动态（在没有流动）线缺陷的研究在所提出的模型。使用适当的初始/边界数据，这种能量的梯度流动力学导致非奇异，线缺陷平衡的解决方案，包括那些半整数强度。然而，我们表明，这种能量的梯度流动动力学是不能够充分描述缺陷的演变。基于与固体中位错动力学的相似性，提出了一种新的二维向列相向错动力学模型。该模型是基于扩展的Oseen-Frank能量，并考虑到热力学和运动学的缺陷拓扑电荷守恒。我们通过对向错平衡、湮灭、排斥和分裂的计算来验证这个模型。我们发现，我们设计的能量函数，适当的解释，可以作为以及为模型的平衡和动力学的位错线缺陷在固体中，使本文的结论有关的固体和液晶的力学。
Nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. It is well known that the universally accepted Oseen-Frank energy is infinite for configurations that contain disclination line defects. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where, under certain conditions, infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. Equilibria and dynamics (in the absence of flow) of line defects are studied within the proposed model. Using appropriate initial/boundary data, the gradient-flow dynamics of this energy leads to non-singular, line defect equilibrium solutions, including those of half-integer strength. However, we demonstrate that the gradient flow dynamics for this energy is not able to adequately describe defect evolution. Motivated by similarity with dislocation dynamics in solids, a novel 2D-model of disclination dynamics in nematics is proposed. The model is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. We show that the energy function we devise, suitably interpreted, can serve as well for the modeling of equilibria and dynamics of dislocation line defects in solids making the conclusions of this paper relevant to mechanics of both solids and liquid crystals.
影响因子：
0.7
作者：
Ball, J. M.;Bedford, S. J.
通讯作者：
Bedford, S. J.