Dierckx Hans, Verschelde Henri
Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281 S9 WE05, 9000 Ghent, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062907. doi: 10.1103/PhysRevE.88.062907. Epub 2013 Dec 4.
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.
卷轴波是围绕中心细丝曲线旋转的三维激发模式；它们出现在许多物理、生物和化学系统中。我们明确推导了具有各向同性扩散的反应扩散系统中卷轴波细丝的运动方程，该方程在细丝的扭曲和曲率方面达到三阶。净漂移分量在每个时刻定义了一条靠近瞬时细丝的虚拟细丝。重要的是，虚拟细丝遵循更简单的、与时间无关的运动定律，我们在此进行了分析推导并用数值示例进行了说明。使用虚拟细丝对卷轴波进行稳定性分析，结果表明细丝曲率和扭曲作为二次项添加到标称细丝张力中。还讨论了在振荡化学反应和心脏组织中的应用。
