论文标题
流体 - 电磁的螺旋性和打结的流体电磁方程的解决方案
Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations
论文作者
论文摘要
在本文中，我们考虑了与外部电磁耦合的欧拉液。我们证明，携带流体和电磁（EM）螺旋的跳液 - 电磁结，求解了流体动力学方程以及Helicities的Abanov Wiegmann（AW）方程，这些方程式是受到Dirac Fermion轴向电流的轴向电流式启发的启发。我们还找到了一个非平凡结溶液，具有真正相互作用的流体和电磁场。这些现象的关键要素是EM和流体螺旋。提出了一个带有磁性流体的EM双重系统，并写下了AW方程的类似物。我们考虑一种与非线性概括进行电磁的液体。跳跃被证明是通用方程的解决方案。我们在2+1个尺寸中写下流体的形式主义，并在尺寸上降低了3+1维溶液。我们通过在未打结的零恒定EM场上应用特殊的保形转换来确定EM打结的溶液，从中从中得出流体结。
In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspired by the axial-current anomaly of a Dirac fermion. We also find a nontrivial knot solution with truly interacting fluid and electromagnetic fields. The key ingredients of these phenomena are the EM and fluid helicities. An EM dual system, with a magnetically charged fluid, is proposed and the analogs of the AW equations are written down. We consider a fluid coupled to a nonlinear generalizations for electromagnetism. The Hopfions are shown to be solutions of the generalized equations. We write down the formalism of fluids in 2+1 dimensions, and we dimensionally reduce the 3+1 dimensional solutions. We determine the EM knotted solutions, from which we derive the fluid knots, by applying special conformal transformations with imaginary parameters on un-knotted null constant EM fields.
