Breathing spiral waves in the chlorine dioxide–iodine–malonic acid reaction-diffusion system

Igal Berenstein, Alberto P. Muñuzuri, Lingfa Yang, Milos Dolnik, Anatol M. Zhabotinsky, and Irving R. Epstein

Phys. Rev. E 78, 025101 (2008) – Published August 11, 2008

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.

1."Breathing spiral waves"这是一个新的现象，但是Breathing现象是常见的。这里的breathing是周期性驱动引起的，但是周期性驱动又如何引起这种现象的呢？文中并没有给出分析。我们正在用另外一个模型对此现象进行分析。

2.此文有实验结果，也有对应的模拟内容，但是有“武断”的地方出现。如关于周期波的起源“Periodic waves are usually generated by local pacemakers both in excitable and oscillatory media. If the pacemaker frequency is significantly higher than the intrinsic oscillation frequency of the medium, trigger waves are produced.”前一句没有问题，毕竟还有“usually”,但后一句却并不是必然的。因为pacemaker的频率就是低于介质的本征频率也可以产生相波，其实只要是有一个能产生相差（phase shift）的源，就有可能产生波。更令我不解的是接下来的一句话“If the pacemaker frequency is close to that of the basic oscillation of the medium, the resulting waves resemble phase waves.”难道前边所说的波里没有“phase waves”? 所以我觉得此文开头三句话就很是混乱。

3.“Our experimental results suggest that breathing occurs when the frequency of this forcing is relatively close to that of the spiral waves.”实验表明（提示，暗示）有这个结果，理论上是否必然如此？有待进一步讨论。文章用CDIMA反应的LE模型进行了模拟研究。因为实验中周期性驱动是CSTR中的振荡频率，而这个频率必然与膜中的螺旋波频率相近，所以为了符合实验情况，驱动的频率才设定与螺旋波频率相近。显然不能得出结论就是频率相近才会有breathing现象存在。有必要重复一下这个数值实验。

4.模拟结果与实验的对应问题依然是一个恼人的问题。显然这篇文章的模拟为了说明实验的结果存在，所以没对驱动模型下的数值实验开展多的分析，我们将进一步分析。其实一定要和实验对应上吗？

5.结尾部分（最后一段）出现“modulate breathing”和"spatially nonuniform breathing of spiral waves"说的是一回事。都是指波在空间的分布出现了新的模式，这种新的波模（多个波模，起码有2个）可观察到的直观现象就是“超螺旋波”。关于这个超结构的讨论是“a long story”。文章强调“Here we have demonstrated spatially uniform strong breathing of spiral waves both in the CDIMA reaction-diffusion system subjected to global periodic forcing and in the corresponding version of the Lengyel-Epstein model.”既然空间是均匀的（其实空间是非均匀的，其本意是指只存在单一波模），那么波必定是非漫游的，有待验证。

6.考虑这些，除了满足我的好奇心，对国民生产有什么直接的作用吗？我的心，摁下葫芦浮起瓢啊！