标题： 通过涡旋弦的反应扩散动力学解开结 显示英文标题

标题： Untangling knots via reaction-diffusion dynamics of vortex strings

摘要： 我们引入并展示了一种通过反应扩散型非线性偏微分方程中涡旋弦的动力学来解决未打结问题的新方法。 为了解开给定的纽结，使用了Biot-Savart构造，将纽结初始化为FitzHugh-Nagumo方程中的涡旋弦。 令人惊讶的是，我们发现随后的演化保留了纽结的拓扑结构，并能够将未打结变为圆形。 展示了说明性的测试案例示例，包括解开一个被称为罪魁祸首的硬未打结。 我们对未打结问题的方法有两个新颖之处，即它应用了场论而非粒子力学，并用反应扩散动力学代替了能量最小化。 显示英文摘要

摘要： We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.