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Vortex Images and q-Elementary Function | | Oktay K. Pashaev
; Oguz Yilmaz
; | | Date: |
14 Aug 2007 | | Abstract: | In the present paper problem of vortex images in annular domain between two
coaxial cylinders is solved by the q-elementary functions. We show that all
images are determined completely as poles of the q-logarithmic function, where
dimensionless parameter $q = r^2_2/r^2_1$ is given by square ratio of the
cylinder radii. Resulting solution for the complex potential is represented in
terms of the Jackson q-exponential function. By composing pairs of q-exponents
to the first Jacobi theta function and conformal mapping to a rectangular
domain we link our solution with result of Johnson and McDonald. We found that
one vortex cannot remain at rest except at the geometric mean distance, but
must orbit the cylinders with constant angular velocity related to q-harmonic
series. Vortex images in two particular geometries in the $q o infty$ limit
are studied. | | Source: | arXiv, 0708.1856 | | Services: | Forum | Review | PDF | Favorites | |
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