The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological curren...The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.展开更多
Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually fo...Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and can be even linked and knotted. We give a rigorous topological description of knotted vortex filaments. By using the Ф-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments, and using this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.展开更多
基金Support by the National Natural Science Foundation of China, and Cuiying Programme of Lanzhou University. The authors would like to thank Xin-Hui Zhang, Dong-Hui Xu, and Ran Li for helpful discussions.
文摘The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.
基金Support by the National Natural Science Foundation of China, and Cuiying Programme of Lanzhou University.
文摘Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and can be even linked and knotted. We give a rigorous topological description of knotted vortex filaments. By using the Ф-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments, and using this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.
