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

James Montaldi; Tadashi Tokieda

doi:10.1016/j.physd.2011.07.004

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

James Montaldi, Tadashi Tokieda

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Abstract

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 language	English
Pages (from-to)	1636-1643
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	240
Issue number	20
DOIs	https://doi.org/10.1016/j.physd.2011.07.004
Publication status	Published - 1 Oct 2011

Keywords

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

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10.1016/j.physd.2011.07.004

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AB - 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.

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JF - Physica D: Nonlinear Phenomena

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

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Keywords

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