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P-Adic Numbers Ultrametric Anal. Appl., 2012, Volume 4, Number 1, Pages 5–19 (Mi padic7)  

Wedge dislocations and three-dimensional gravity

M. O. Katanaev, I. G. Mannanov

Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow 119991, Russia

Abstract: The expression for the free energy of arbitrary static distribution of wedge dislocations in elastic media is proposed. In the framework of geometric theory of defects, the free energy is given by the Euclidean action for (1+2)-dimensional gravity interacting with N point particles. Relative movement of particles in gravity corresponds to bending of dislocations. The equations of equilibrium are obtained and analyzed. For two dislocations, the solution is found explicitly through hypergeometric functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00828-a
11-01-12114-ofi_m
Ministry of Education and Science of the Russian Federation NSh-2928.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work is partly supported by the RFBR (grants 11-01-00828-a and 11-01-12114-ofi_m), the supporting program for the leading scientific schools (grant NSh-2928.2012.1) and the program “Contemporary problems of theoretical mathematics” of the Russian Academy of Sciences.


DOI: https://doi.org/10.1134/S2070046612010025


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Received: 13.12.2011
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