Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director $\widehat{\mathbf{n}}$. The nematic director field $\widehat{\mathbf{n}}\left(\mathbf{r}\right)$ of a chiral twist-bend nematic ($N_{\mathrm{TB}}$) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in $N_{\mathrm{TB}}$ phases, and find that the predilection of curved rods to diffuse in the direction of the twisting $\widehat{\mathbf{n}}\left(\mathbf{r}\right)$ yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the $N_{\mathrm{TB}}$ phase thereby connecting its structural and dynamical properties.

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无监督机器学习技术揭示双轴弯曲杆在扭曲弯曲向列相中的螺旋动力学

向列相的单轴棒优先沿平行于向列导向器的方向扩散 $\widehat{\mathbf{ñ}}$。向列导演领域$\widehat{\mathbf{ñ}}（\mathbf{[R}）$ 手性曲折向列（${ñ}_{\mathrm{结核病}}$最近通过实验发现的非手性香蕉状颗粒的相，表现出给定惯性和周期性的螺旋扭曲。使用模拟，我们调查了长期的宏观扩散${ñ}_{\mathrm{结核病}}$ 相，发现弯曲杆的偏向向扭转方向扩散 $\widehat{\mathbf{ñ}}（\mathbf{[R}）$即使非手性弯曲的杆显示布朗运动且旋转平移耦合不平凡，沿螺旋线仍会产生迷人的手性动力学。我们设计了一种机器学习协议来表征螺旋粒子的轨迹，发现它们的螺距和半径是由螺距和圆锥角决定的。${ñ}_{\mathrm{结核病}}$ 相连接其结构和动力学特性。