AI 中文总结
该研究将阻力算子视为O(3)表示空间元素，利用特征标公式分类流体动力学对称性，完成了杰弗里等人的分类，确定了多面体对称性的显现顺序及可产生不规则全姿态动力学的手性正规形式。
AI 中文摘要
斯托克斯方程的线性特性将刚性粒子的流体动力学响应组织为阻力算子的层级结构，该结构将环境流射流的连续截断与表面牵引力的矩相耦合。自开尔文（Kelvin）和拉莫尔（Larmor）的研究以来，人们已知该响应无法忠实地分辨粒子几何形状：具有离散旋转对称性的物体可能与旋转体（布伦纳的螺旋对称性）无法区分，而手性物体可能表现出各向同性响应，如开尔文的各向同性螺旋体。我们将阻力算子视为有限维O(3)表示空间的元素，并利用特征标公式确定在层级的每一层级上，哪些点群对称性在流体动力学上可区分，以及每个不变空间的维度。这产生了从平移力层级到二次流层级的显式嵌套流体动力学对称群集序列。该框架揭示了无法通过几何形状实现的流体动力学类别，为螺旋对称性提供了层级依赖的定义，并表明多面体对称性按严格顺序显现：四面体对称性在剪切中显现，八面体对称性通过应力子显现，二十面体对称性在二次流中显现。将阻力算子投影到无力和无扭矩运动上，可提供基于对称性的参数计数，并为相应的动力学正规形式提供建设性路径。由此，我们完成了杰弗里-布雷瑟顿-石本（Jeffery-Bretherton-Ishimoto）分类，表征了所有产生杰弗里动力学的流体动力学类别，并确定了可产生不规则全姿态动力学的手性四面体和八面体正规形式。
英文摘要
The linearity of the Stokes equations organises the hydrodynamic response of a rigid particle into a hierarchy of resistance operators, coupling successive truncations of the ambient-flow jet to moments of the surface traction. Since the work of Kelvin and Larmor, it has been known that this response does not resolve particle geometry faithfully: bodies with discrete rotational symmetry may be indistinguishable from bodies of revolution (Brenner's helicoidal symmetry) and a chiral body may respond isotropically, as in Kelvin's isotropic helicoid. We regard the resistance operators as elements of finite-dimensional O(3)-representation spaces and use character formulae to determine, at every level of the hierarchy, which point-group symmetries are hydrodynamically distinguishable and the dimension of each invariant space. This yields an explicit nested sequence of hydrodynamic symmetry-group sets, from the translation-force level to the quadratic-flow level. The framework reveals hydrodynamic classes that no shape can realise geometrically, gives helicoidal symmetry a level-dependent definition, and shows that polyhedral symmetry becomes visible in a strict order: tetrahedral symmetry in shear, octahedral symmetry through the stresslet, and icosahedral symmetry in quadratic flow. Projecting the resistance operators onto force- and torque-free motion provides symmetry-based parameter counts and a constructive route to the corresponding dynamical normal forms. We thereby complete the Jeffery-Bretherton-Ishimoto classification, characterise all hydrodynamic classes producing Jeffery dynamics, and identify chiral tetrahedral and octahedral normal forms that can generate irregular full-attitude dynamics.
Comments43 pages, 7 figures, 4 tables
