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

Montaldi, James and Tokieda, Tadashi (2010) Dynamics of poles with position-dependent strengths and its optical analogues. [MIMS Preprint]

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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: MIMS Preprint
Uncontrolled Keywords: Vortex dynamics, complex variable strengths, Snell's law, geometric optics, hybrid systems
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User: Dr James Montaldi
Date Deposited: 01 Sep 2010
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1519

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