Dynamics of poles with position-dependent strengths and its optical analogues
Dynamical Systems
2015-05-19 v2
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.
Keywords
Cite
@article{arxiv.1009.2097,
title = {Dynamics of poles with position-dependent strengths and its optical analogues},
author = {James Montaldi and Tadashi Tokieda},
journal= {arXiv preprint arXiv:1009.2097},
year = {2015}
}
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10 pages