涡丝的分支过程与涡卷波的Hopf不变量约束
The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave
摘要：
本文利用Duan的拓扑流理论，详细讨论了可激发介质中涡丝的演化。在复变函数$Z(\vec{x},t)$的极限点处，涡丝产生或湮灭，在分岔点处，涡丝相遇、分裂或合并。它还表明，在分支过程（分裂，合并，或遇到）在这些打结的涡卷波丝的演变过程中，打结的涡卷波丝的Hopf不变量被保存。进一步揭示了某些化学介质中的“不相容原理”只是Hopf不变量约束的特例，在分支过程中“不相容原理”也受到拓扑学的保护.
英文摘要：
In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function $Z(\vec{x},t)$. It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology.
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