We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.

中文翻译：

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二维受限向列的基于粒子和连续介质模型

我们使用基于粒子的随机多粒子碰撞动力学（N-MPCD）算法来模拟正方形、五边形和六边形等规则二维多边形中的受限向列液晶。我们考虑一系列向列性U和模拟域大小R的值，这些值涵盖纳米尺寸的多边形到微米尺寸的多边形。我们使用闭包参数来定义 N-MPCD 参数与连续确定性 Landau-de Gennes 框架中的参数之间的映射。平均 N-MPCD 配置与 Landau-de Gennes 理论预测的一致，至少对于大多边形来说是这样。我们在 N-MPCD 框架中研究多边形中约束向列的弛豫动力学或非平衡动力学，并且动力学陷阱与 Landau-de Gennes 框架中的不稳定鞍点非常相似。最后，我们研究了 N-MPCD 框架中多边形内部的向列缺陷动力学，有限尺寸效应减缓了缺陷并将它们吸引到多边形顶点。我们的工作是基于粒子的随机 N-MPCD 方法和确定性/连续性 Landau-de Gennes 方法的全面比较，这种比较对于新时代的多尺度理论至关重要。