标题： 字符串、膜和扭子：在如心脏这样的可激发介质中相缺陷的拓扑分析 显示英文标题

标题： Strings, branes and twistons: topological analysis of phase defects in excitable media such as the heart

摘要： 几种可兴奋系统，如心脏，会自组织成涉及波浪碰撞、波浪断裂和旋转涡旋的复杂时空模式，其动力学尚不完全清楚。 最近，在二维介质中的传导阻滞线被识别为相位缺陷，在其上可以定义准粒子。 这些粒子也形成束缚态，其中一种对应于经典的相位奇点。 在这里，我们将准粒子与状态空间中动态吸引子的结构联系起来，并将该框架扩展到三维空间。 我们揭示出三维可兴奋介质由相位缺陷面（即膜）以及三种拓扑保留的曲线（即弦）所支配：头部曲线、尾部曲线和枢轴曲线。 我们将之前提出的扭子识别为头部曲线和枢轴曲线交叉处的共维三度点。 我们的框架预测了可以连接多个经典丝状体的分裂和分支相位缺陷面，从而提出了一种新的机制，用于解释复杂兴奋模式的起源、持续和控制，包括心室颤动。 显示英文摘要

摘要： Several excitable systems, such as the heart, self-organize into complex spatio-temporal patterns that involve wave collisions, wave breaks, and rotating vortices, of which the dynamics are incompletely understood. Recently, conduction block lines in two-dimensional media were recognized as phase defects, on which quasi-particles can be defined. These particles also form bound states, one of which corresponds to the classical phase singularity. Here, we relate the quasi-particles to the structure of the dynamical attractor in state space and extend the framework to three spatial dimensions. We reveal that 3D excitable media are governed by phase defect surfaces, i.e. branes, and three flavors of topologically preserved curves, i.e. strings: heads, tails, and pivot curves. We identify previously coined twistons as points of co-dimension three at the crossing of a head curve and a pivot curve. Our framework predicts splitting and branching phase defect surfaces that can connect multiple classical filaments, thereby proposing a new mechanism for the origin, perpetuation, and control of complex excitation patterns, including cardiac fibrillation.