Science. 1988 Mar 11;239(4845):1284-6. doi: 10.1126/science.239.4845.1284.
Rotating waves of activity are seen in various biological phenomena and in chemical mixtures. In thin layers of these media, the waves often appear as spirals spinning around a pivot point, but actually they are scroll-shaped waves rotating around curved filament in three-space. The filament about which the scroll rotates is not stationary, but rather moves through space until it achieves a stable configuration or disappears altogether. Some features of the temporal evolution of a planar scroll wave filament can be understood in terms of the simple equation N = Dkappa, where N is the velocity of the filament in the direction of its principal normal, kappa is the curvature of the filament, and D is the diffusion coefficient of the active chemical species. This equation of motion implies that a scroll ring shrinks in size and collapses in finite time, that an elongated spiral evolves into a symmetric spiral, and that an elongated target pattern becomes more symmetrical and vanishes in finite time. Characteristic times for these processes are estimated. In each case, good quantitative agreement is found between implications of the model and observations of scroll-wave evolution in shallow layers of the Belousov-Zhabotinsky reagent.
在各种生物现象和化学混合物中都可以看到旋转的活动波。在这些介质的薄层中，波通常表现为围绕枢轴点旋转的螺旋，但实际上它们是在三维空间中围绕弯曲细丝旋转的螺旋形波。螺旋围绕其旋转的细丝不是静止的，而是在空间中移动，直到达到稳定的构型或完全消失。平面螺旋波丝的时间演化的一些特征可以根据简单的方程 N = Dkappa 来理解，其中 N 是细丝沿其主法线的速度，kappa 是细丝的曲率，D 是活性化学物质的扩散系数。这个运动方程意味着螺旋环会缩小尺寸并在有限的时间内坍塌，一个拉长的螺旋会演变成一个对称的螺旋，一个拉长的目标图案会变得更加对称并在有限的时间内消失。这些过程的特征时间被估计。在每种情况下，模型的含义与在 Belousov-Zhabotinsky 试剂的浅层中观察到的螺旋波演化之间都存在很好的定量一致性。
