Elongated colloids with a permanent magnetic moment and immersed in a nematic liquid crystal are studied numerically using a mesoscopic scheme that supports fluctuations, hydrodynamics, and topological defects. Colloids are accompanied by disclinations curves and subjected to an effective torque caused by the nematic environment and to a magnetic torque due to an external magnetic field. The case is analyzed where these torques compete to bring colloids to two different mutually perpendicular equilibrium states. The fluctuating dynamics of the colloid-defect pair is studied in terms of orientational correlation functions. Analytical expressions for these correlations are derived on the basis of an approximated planar lineal model. A good agreement is found between the numerical and analytical methods when magnetic torques are much larger than nematic torques, while for smaller magnetic torques nonlinear effects are demonstrated to be important. As conclusion, the numerical technique could be considered a reliable approach to the rotational motion of polar nanoparticles in liquid crystals.

中文翻译：

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向列液晶中的磁性各向异性胶体：多粒子碰撞动力学模拟的波动动力学

使用支持波动、流体动力学和拓扑缺陷的介观方案对具有永久磁矩并浸入向列液晶的细长胶体进行了数值研究。胶体伴随向错曲线，并受到向列环境引起的有效扭矩和外部磁场引起的磁扭矩。分析了这些扭矩相互竞争以使胶体达到两种不同的相互垂直平衡状态的情况。根据方向相关函数研究了胶体缺陷对的波动动力学。这些相关性的分析表达式是在近似平面线性模型的基础上得出的。当磁转矩远大于向列转矩时，数值方法和解析方法之间存在良好的一致性，而对于较小的磁转矩，非线性效应被证明是重要的。总之，数值技术可以被认为是液晶中极性纳米粒子旋转运动的可靠方法。