环形晶体

Two-Dimensional Matter: Order, Curvature and Defects

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls the detailed structured of ordered phases. Among the surprises are the appearance in the ground state of structures that would normally be thermal excitations and thus prohibited at zero temperature. Examples include excess dislocations in the…

Equilibrium configurations of nematic liquid crystals on a torus

The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our aim is to show how a different modeling of the effect of extrinsic curvature acts as a selection principle among equilibria of the classical energy, and how new configurations emerge. In particular, our analysis predicts the existence of new stable equilibria with complex windin…

Curvature-controlled defect localization in crystalline wrinkling patterns

We investigate the influence of curvature and topology on crystalline wrinkling patterns in generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elast…

Kibble-Zurek mechanism in curved elastic surface crystals

Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their va…

Nematics, Knots and Non-orientable Surfaces

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing no…

Topological colloids

Abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable - homeomorphic - to spheres). Although …

活性壳层中可调谐的缺陷-曲率耦合与拓扑转变

Tuneable defect-curvature coupling and topological transitions in active shells

该研究聚焦极性与向列型活性液晶构成的可变形壳层，通过线性稳定性分析与三维流体动力学模拟，揭示活性可调控缺陷-曲率耦合，且强拉伸活性可驱动极性系统发生球到环的拓扑转变，为缺陷作为拓扑形态发生素提供支撑与可验证预测。

套索鞍形展曲与拓扑缺陷的几何调控

Lassoing saddle splay and the geometrical control of topological defects

本文通过调控向列相液晶中孔洞阵列的几何形状和锚定条件，诱导鞍状形变并生成可调向错线阵列，为利用几何线索控制复杂弹性形变奠定基础。