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Stationary vortex sheets and limits of polynomials

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CATW02 - Complex analysis in mathematical physics and applications

Stationary distributions of vorticity in a two-dimensional fluid are considered where the vorticity support consists of points (point vortices) and curves (vortex sheets.) The flow in many cases is determined by a simple rational function. By comparing the vorticity distributions to point vortex configurations associated with polynomials, these distributions can be related other questions such as non-uniqueness of Heine-Stieltjes polynomials and to the asymptotics of some non-classical special cases of orthogonal polynomials.

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