论文标题
麦克斯韦方程打结的解决方案的数值模拟
Numerical simulation of knotted solutions for Maxwell equations
论文作者
论文摘要
在这项工作中，我们使用时域（FDTD）数值方法的有限差异来计算和评估电磁场方程的HOPF解决方案或跳跃的有效性。在这些溶液中，磁线形成了以不同的结拓扑为特征的闭环，这些环在其时间演变过程中保存。从分析的角度来看，人们已经对跳跃进行了广泛的研究，但据我们所知，从数值方法中绝不研究。该技术的实施和验证减轻了对这种现象更复杂案例的研究；例如这些领域如何与材料（例如各向异性或非线性）相互作用，它们与其他物理系统（例如等离子体）耦合，并通过不同的方式（例如天线阵列或激光器）对其人工产生的路径开放。
In this work, we use the finite differences in time domain (FDTD) numerical method to compute and assess the validity of Hopf solutions, or hopfions, for the electromagnetic field equations. In these solutions, field lines form closed loops characterized by different knot topologies which are preserved during their time evolution. Hopfions have been studied extensively in the past from an analytical perspective but never, to the best of our knowledge, from a numerical approach. The implementation and validation of this technique eases the study of more complex cases of this phenomena; e.g. how these fields could interact with materials (e.g. anisotropic or non-linear), their coupling with other physical systems (e.g. plasmas), and also opens the path on their artificial generation by different means (e.g. antenna arrays or lasers).
