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

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

2010-09-10

arxiv.org/abs/1009.2097v2

Mathematics

Dynamical Systems

10 pages

Scientific paper

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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