Dynamics of poles with position-dependent strengths and its optical analogues

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Montaldi, James¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Vortex dynamics;    Complex variable strengths;    Snell's law;    Geometric optics;    Hybrid systems;   

DOI  :  10.1016/j.physd.2011.07.004

来源: Elsevier

【 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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free