The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave TeX Export

@misc{citeulike:3042815, abstract = {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.}, archivePrefix = {arXiv}, author = {Zhu, Tao and Ren, Ji-Rong and Mo, Shu-Fan}, citeulike-article-id = {3042815}, citeulike-linkout-0 = {http://arxiv.org/abs/0807.3787}, citeulike-linkout-1 = {http://arxiv.org/pdf/0807.3787}, day = {24}, eprint = {0807.3787}, keywords = {lagrangian, mixing}, month = {Jul}, posted-at = {2008-07-25 15:44:33}, priority = {2}, title = {The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave}, url = {http://arxiv.org/abs/0807.3787}, year = {2008} }

TY - ELEC ID - citeulike:3042815 L3 - citeulike-article-id:3042815 N2 - 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. TI - The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave KW - lagrangian KW - mixing AU - Zhu, Tao AU - Ren, Ji-Rong AU - Mo, Shu-Fan PY - 2008/Jul/24/ UR - http://arxiv.org/abs/0807.3787 ER -