Three-phase eccentric annulus subjected to a potential field induced by arbitrary singularities

Author:
Yu. V. Obnosov

Journal:
Quart. Appl. Math. **69** (2011), 771-786

MSC (2010):
Primary 30E25, 76T30

DOI:
https://doi.org/10.1090/S0033-569X-2011-01242-8

Published electronically:
July 12, 2011

MathSciNet review:
2894000

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Abstract | References | Similar Articles | Additional Information

Abstract: An infinite planar, three-component heterogeneous medium with a pair of circles as interfaces between homogeneous zones forming an eccentric annulus is considered for refraction of a potential field on the two interfaces. The velocity field is generated by an arbitrary system of singularities of arbitrary order, in congruity with the Milne-Thomson case of a two-component medium and a single circular interface. An exact analytical solution of the corresponding -linear conjugation problem of two Laplacian fields in the eccentrical annulus structure is derived in the class of piecewise meromorphic functions with fixed principal part. Three general cases of loci of the singularities with respect to the interfaces are investigated. Flow nets (isobars and streamlines) are presented.

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Additional Information

**Yu. V. Obnosov**

Affiliation:
Institute of Mathematics and Mechanics, Kazan State University, Prof. Nughin Str.,1/37, Kazan, 420008, Russia

Email:
Yurii.Obnosov@ksu.ru

DOI:
https://doi.org/10.1090/S0033-569X-2011-01242-8

Keywords:
Refraction,
heterogeneous media,
$\mathbb R$-linear conjugation problem,
analytic functions

Received by editor(s):
May 3, 2010

Published electronically:
July 12, 2011

Article copyright:
© Copyright 2011
Brown University

The copyright for this article reverts to public domain 28 years after publication.