通过涡弦的反应扩散动力学解开结
Untangling knots via reaction-diffusion dynamics of vortex strings
摘要：
介绍并举例说明了一种新的方法，通过涡弦动力学的非线性反应扩散型偏微分方程的解结问题。为了解开一个给定的纽结，使用Biot-Savart构造将纽结初始化为FitzHugh-Nagumo方程中的涡弦。值得注意的是，我们发现，随后的演变保留了拓扑结构的结，可以解开一个解开成一个圆圈。说明性的测试案例的例子，包括解开一个硬解开称为罪魁祸首。我们的方法解开问题有两个新的特点，它适用于场论，而不是粒子力学和使用反应扩散动力学的地方，能量最小化。
英文摘要：
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.
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