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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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.
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
|Deposited By:||Dr James Montaldi|
|Deposited On:||03 April 2011|
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