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Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2015-5pp.514-518

Archive of Issues

Since 2018, translations of PMM's articles have been published in special issues of the journals Mechanics of Solids and Fluid Dynamics:

Total articles in the database: 1923
In Russian (): 1124
In English (J. Appl. Math. Mech.): 799

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E.N. Bereslavskii, "The transformation of cuts in the conformational mapping of circular polygons in problems of liquid and gas mechanics," J. Appl. Math. Mech. 79 (5), 514-518 (2015)
Year 2015 Volume 79 Issue 5 Pages 514-518
DOI 10.1016/j.jappmathmech.2016.03.013
Title The transformation of cuts in the conformational mapping of circular polygons in problems of liquid and gas mechanics
Author(s) E.N. Bereslavskii (St Petersburg Civil Aviation State University, St Petersburg, Russia,
Abstract A linear differential equation of the Fuchs class with six regular singular points is considered, which corresponds to the problem of the conformal mapping of circular hexagons in polar nets with two cuts that are characteristic in the theory of jets and cavitation, the theory of gliding, in gas dynamics, in the theory of the motion of ground waters and in seepage theory. It is shown that, in the case of a fixed parameter, characterizing the ratio of the radii of the circular ares constituting the opposite sides of a polygon on which there are cuts, the configuration and mutual arrangement of the cuts depend considerably not so much on the known properties of theta-functions, on the basis of which special solutions of the equation considered are constructed, but on the ranges of variation in the constants of the conformal mapping occurring in the expression for the mapping functions as well as the modulus of the elliptic functions. It is found that cuts that are different in their configuration and mutual arrangement can correspond to different ranges of variation in these constants in the corresponding region of the velocity hodograph which is evidence of the transformation of the fluid seepage flows depending on the effect of various physical factors.
Received 01 December 2014
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