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2010.65: Dynamics of poles with position-dependent strengths and its optical analogues

2010.65: James Montaldi and Tadashi Tokieda (2011) Dynamics of poles with position-dependent strengths and its optical analogues. Physica D, 240. pp. 1636-1643. ISSN 0167-2789

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DOI: 10.1016/j.physd.2011.07.004

Abstract

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 enough 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.

Item Type:Article
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To appear in Physica D

Uncontrolled Keywords:Vortex dynamics, complex variable strengths, Snell's law, geometric optics, hybrid systems
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 70 Mechanics of particles and systems
MSC 2000 > 76 Fluid mechanics
MIMS number:2010.65
Deposited By:Dr James Montaldi
Deposited On:03 April 2011

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