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

James Montaldi, Tadashi Tokieda

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    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. © 2011 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)1636-1643
    Number of pages7
    JournalPhysica D: Nonlinear Phenomena
    Issue number20
    Publication statusPublished - 1 Oct 2011


    • Complex variable strengths
    • Geometric optics
    • Hybrid systems
    • Snell's law
    • Vortex dynamics


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