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Fiz. Elem. Chast. Atom. Yadra, 2012, Volume 43, Issue 5, Pages 5–19 (Mi jinr1)  

Wedge dislocations, three-dimensional gravity, and the Riemann–Hilbert problem

M. O. Katanaev, I. G. Mannanov

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 117966 Russia

Abstract: An expression for the free energy of an arbitrary static distribution of wedge dislocations in a solid is proposed. It represents a Euclidean version of $(1+2)$-dimensional gravity interacting with an arbitrary number of point particles. It is shown that the solution of the equilibrium equations leads to the Cauchy prob lem for effective equations determining the form of dislocations, while the problem of finding a metric leads to the Riemann–Hilbert problem for a frame with an $\mathbb{O}(3)$ monodromy representation.

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
This work was supported in part by the Russian Foundation for Basic Research (project nos. 11-01-00828-a and 11-01-12114-ofi_m), by the program “Leading Scientific Schools” (project no. NSh-2928.2012.1), and by the program “Modern Problems in Theoretical Mathematics” of the Russian Academy of Sciences.



English version:
Physics of Particles and Nuclei, 2012, 43:5, 639–643

Bibliographic databases:

Document Type: Article
PACS: 04.20.Cv

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