强度依赖于位置的极点动力学及其光学模拟
Dynamics of poles with position-dependent strengths and its optical analogues
摘要：
点涡的动力学可以用两种方法来概括：第一，使强度变得复杂，这使得源和汇与通常的涡叠加，第二，使它们成为位置的函数。这些推广导致了一个丰富的动力系统，这是非线性的，但有守恒律来自一个类似汉密尔顿的形式主义。然后，我们发现，在这个系统中的运动对模仿的行为，在几何光学的光线。我们描述了几个精确解与光学类似物，特别是斯涅尔定律和反射定律的镜子，并进行数值实验，说明了一些惊人的行为。
英文摘要：
The dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making them functions of position. These generalizations lead to a rich dynamical system, which is nonlinear and yet has conservation laws coming from a Hamiltonian-like formalism. We then discover that in this system the motion of a pair mimics the behavior of rays in geometric optics. We describe several exact solutions with optical analogues, notably Snell's law and the law of reflection off a mirror, and perform numerical experiments illustrating some striking behavior.
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