Dynamics of topological defects in active matter on curved manifolds

拓扑缺陷在平衡状态下物质的静力学和动力学中起着重要的作用。不太清楚的是，这些缺陷是如何改变物质失去平衡的行为的。这个项目将研究拓扑缺陷在“活性物质”中所起的作用，“活性物质”是一种限制在弯曲流形中的非平衡范式。所使用的技术将包括微分几何、偏微分方程、随机过程和数值方法。

Topological defects are known to play an important role in the statics and dynamics of matter in equilibrium. It is less clear how such defects modify the behaviour of matter out of equilibrium. This project will investigate the role played by topological defects in "active matter", a paradigm of non-equilibrium, confined to curved manifolds. The techniques used will include differential geometry, partial differential equations, stochastic processes, and numerical methods.