曲面上活性物质的拓扑缺陷和非平衡统计性质的研究

活性物质的研究开辟了从统计物理角度来研究生命体系和复杂非平衡体系的新方向，具有重要科学意义。最近，在实验中发现活性物质在曲面上运动，表现出新奇的非平衡统计行为，基于自由空间的规律不再适用。为解决该问题，项目拟选取活性颗粒物质和活性融合性组织为研究对象，首先结合黎曼几何和自由空间的运动方程，推出曲面上活性物质的运动方程，再采用多尺度数值方法，研究活性物质在曲面上的微观拓扑缺陷，宏观非平衡结构(集体运动，相分离，玻璃化转变和结晶)和热力学状态(压强，熵和非平衡涨落关系)。项目重点研究曲面上拓扑缺陷形成机制以及曲面拓扑性质, 粒子性质，物质混合特性对非平衡统计性质的影响。开展项目，一方面，理论上解决活性物质非平衡统计规律，从自由空间到曲面约束，从微观拓扑缺陷到宏观非平衡结构，从平衡态到非平衡态过渡中的一些关键科学问题，另一方面，相关理论为实验研究活性物质提供理论解释和分析。

The study of active matter has opened up a new direction for the study of life systems and complex non-equilibrium systems from the perspective of statistical physics, which is of great scientific significance. Recently, it has been found that active matter can move on curved surfaces and exhibit novel non-equilibrium statistical behaviors, and the laws based on plane or free space are no longer applicable. In order to solve this problem, we select granular matter and confluent tissues as the research objects, the theoretical framework of the movement of active matter on the surface is derived by combining the Riemannian geometry and the motion equation of free space. We plan to use the multi-scale simulation method to study microscopic topological defects and macroscopic non-equilibrium structures (collective motion, phase separation, glass phase transition and crystallization) and thermodynamic states (pressure, entropy and non-equilibrium fluctuations) of active matter on curved surfaces. The project will focus on the formation mechanism of topological defects on the surface and the influence of topological properties, particle properties and mixed properties of the surface on non-equilibrium statistical properties. Through the development of the project, on the one hand, we solve some key scientific problems of the non-equilibrium statistical law of active matter in the transition, from the plane constraint or free space to the surface constraint, from the microscopic topological defects to the macroscopic collective behavior, from the equilibrium state to the non-equilibrium state. On the other hand, relevant theories provide theoretical explanations and analyses for experimental studies of active matter on curved surfaces.