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Isotropic Limiting Behaviour of the Six‐Dimensional Formalism of Anisotropic Dislocation Theory and Anisotropic Green's Function Theory.ii. Perturbation Theory on the Isotropic N‐Matrix
Author(s) -
Nishioka K.,
Lothe J.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220520105
Subject(s) - isotropy , anisotropy , degenerate energy levels , eigenvalues and eigenvectors , limiting , mathematical analysis , perturbation (astronomy) , poincaré–lindstedt method , physics , classical mechanics , mathematics , mathematical physics , quantum mechanics , mechanical engineering , engineering
Perturbation expansions in terms of the deviation from isotropy are developed for the eigenvalues and eigenvectors of the N‐matrix, which appears in the six‐dimensional formalism for anisotropic dislocation theory and anisotropic Green's function. The strongly degenerate behaviour in the limit of isotropy is elucidated. It is shown that divergent terms in fact cancel among themselves in certain sums to leave well‐behaved isotropic limits. It was necessary to develop a perturbation method applicable to a non‐semisimple matrix.