Yang Zhao, Gao Shiyuan, Ouyang Qi, Wang Hongli
State key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056209. doi: 10.1103/PhysRevE.86.056209. Epub 2012 Nov 14.
We investigated scroll waves in an inhomogeneous excitable 3D system with gradient of excitability. The gradient promotes twisting of the scroll waves. Sufficiently large excitability gradient enhances the twisting and causes simple scroll waves to transition to meandering scroll waves. For the twist-induced instability of scroll waves, we analyzed the stability of 2D spiral waves sliced from the twisted scroll in the vertical direction. The 3D problem is simplified by taking into account the diffusive coupling in the third direction as a time-delayed perturbation to the 2D spiral wave. An additional "negative mass" term measuring the twist thus arises in the 2D system and induces the transition from simple rotation to meandering. A further increase in the gradient ruins partially the unity of the meandering scrolls and generates semiturbulence, the analogs of which were observed in the Belousov-Zhabotinski reaction. We also generated the phase diagram in the parameter space by adjusting the threshold for excitation of the media.
我们研究了具有兴奋性梯度的非均匀可激发三维系统中的螺旋波。该梯度促进螺旋波的扭曲。足够大的兴奋性梯度会增强扭曲，并导致简单螺旋波转变为蜿蜒螺旋波。对于螺旋波的扭曲诱导不稳定性，我们分析了从垂直方向扭曲螺旋中切出的二维螺旋波的稳定性。通过将第三方向上的扩散耦合视为对二维螺旋波的时延扰动，三维问题得以简化。因此，二维系统中出现了一个测量扭曲的额外“负质量”项，并诱导了从简单旋转到蜿蜒的转变。梯度的进一步增加会部分破坏蜿蜒螺旋的整体性，并产生半湍流，在贝洛索夫 - 扎博廷斯基反应中观察到了其类似物。我们还通过调整介质激发阈值在参数空间中生成了相图。
