Sutcliffe Paul M, Winfree Arthur T
Institute of Mathematics, University of Kent, Canterbury CT2 7NF, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016218. doi: 10.1103/PhysRevE.68.016218. Epub 2003 Jul 23.
Through extensive numerical simulations we investigate the evolution of knotted and linked vortices in the FitzHugh-Nagumo model. On medium time scales, of the order of a hundred times the vortex rotation period, knots simultaneously translate and precess with very little change of shape. However, on long time scales, we find that knots evolve in a more complicated manner, with particular arcs expanding and contracting, producing substantial variations in the total length. The topology of a knot is preserved during the evolution, and after several thousand vortex rotation periods the knot appears to approach an asymptotic state. Furthermore, this asymptotic state is dependent upon the initial conditions and suggests that, even within a given topology, a host of metastable configurations exists, rather than a unique stable solution. We discuss a possible mechanism for the observed evolution, associated with the impact of higher-frequency wavefronts emanating from parts of the knot which are more twisted than the expanding arcs.
通过广泛的数值模拟，我们研究了FitzHugh-Nagumo模型中打结和链接涡旋的演化。在中等时间尺度上，即涡旋旋转周期的大约一百倍，结同时平移和进动，形状变化很小。然而，在长时间尺度上，我们发现结以更复杂的方式演化，特定的弧段膨胀和收缩，导致总长度产生显著变化。在演化过程中，结的拓扑结构保持不变，经过几千个涡旋旋转周期后，结似乎接近一个渐近状态。此外，这种渐近状态取决于初始条件，这表明即使在给定的拓扑结构内，也存在许多亚稳态构型，而不是唯一的稳定解。我们讨论了观察到的演化的一种可能机制，它与结中比膨胀弧段更扭曲的部分发出的高频波前的影响有关。
