St-Yves Ghislain, Davidsen Jörn
Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Canada T2N 1N4.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):032926. doi: 10.1103/PhysRevE.91.032926. Epub 2015 Mar 26.
Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect-mediated turbulence and its dependence on the dimensionality of a given system is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the importance of the thickness of the ventricular wall is contentious. Here, we study defect-mediated turbulence arising in two different regimes in a conceptual model of excitable media and investigate how the statistical character of the turbulence changes if the thickness of the medium is changed from (quasi-) two- dimensional to three dimensional. We find that the thickness of the medium does not have a significant influence in, far from onset, fully developed turbulence while there is a clear transition if the system is close to a spiral instability. We provide clear evidence that the observed transition and change in the mechanism that drives the turbulent behavior is purely a consequence of the dimensionality of the medium. Using filament tracking, we further show that the statistical properties in the three-dimensional medium are different from those in turbulent regimes arising from filament instabilities like the negative line tension instability. Simulations also show that the presence of this unique three-dimensional turbulent dynamics is not model specific.
振荡和可激发介质中的时空混沌通常以称为缺陷的相位奇点的存在为特征。理解这种由缺陷介导的湍流及其对给定系统维度的依赖性是非线性动力学中的一个重要挑战。在心脏室颤的背景下尤其如此，其中心室壁厚度的重要性存在争议。在这里，我们研究在可激发介质的概念模型中两种不同状态下产生的由缺陷介导的湍流，并研究如果介质厚度从（准）二维变为三维，湍流的统计特征将如何变化。我们发现，在远离起始点的充分发展的湍流中，介质厚度没有显著影响，而如果系统接近螺旋不稳定性，则会有明显的转变。我们提供了明确的证据，表明观察到的转变以及驱动湍流行为的机制变化纯粹是介质维度的结果。使用细丝跟踪，我们进一步表明，三维介质中的统计特性与由细丝不稳定性（如负线张力不稳定性）产生的湍流状态中的统计特性不同。模拟还表明，这种独特的三维湍流动力学的存在不是特定于模型的。
