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Creators/Authors contains: "Glukhovskiy, Daniil"

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  1. ; ; (, International Mathematics Research Notices)
    Abstract We consider pairs of point vortices having circulations $$\Gamma _{1}$$ and $$\Gamma _{2}$$ and confined to a two-dimensional surface $$S$$. In the limit of zero initial separation $$\varepsilon $$, we prove that they follow a magnetic geodesic in unison, if properly renormalized. Specifically, the “singular vortex pair” moves as a single-charged particle on the surface with a charge of order $$1/\varepsilon ^{2}$$ in an magnetic field $$B$$ that is everywhere normal to the surface and of strength $$|B|=\Gamma _{1} +\Gamma _{2}$$. In the case $$\Gamma _{1}=-\Gamma _{2}$$, this gives another proof of Kimura’s conjecture [11] that singular dipoles follow geodesics. 
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