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Nicks, Rachel; Parry, Gareth P. (2012)
Publisher: Sage
Languages: English
Types: Article
Subjects:

Classified by OpenAIRE into

arxiv: Condensed Matter::Materials Science
We consider distributions of dislocations in continuum models of crystals which are such that the corresponding dislocation density tensor relates to a particular class of solvable Lie group, and discrete structures which are embedded in these crystals. We provide a canonical form of these structures and, by finding the set of all generators of a corresponding discrete subgroup, we determine the ‘material’ symmetries that constrain appropriate strain energy functions.
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    • [12] Elzanowski, M. and Parry, G. P., Material symmetry in a theory of continuously defective crystals, Journal of Elasticity, 74, 215{237 (2004).
    • [13] Parry, G. P. and Sigrist, R., Reconciliation of local and global symmetries for a class of crystals with defects, Journal of Elasticity, OnlineFirst, 4 May 2011 (doi:10.1007/s10659- 011-9342-5).
    • [14] Bachmuth, S., Automorphisms of free metabelian groups, Transactions of the American Mathematical Society, 118, 93{104 (1965).
    • [15] Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory, Dover, New York, 1976.
    • [16] Gorbatsevich, V. V., Lattices in solvable Lie groups and deformations of homogeneous spaces, Mathematics of the USSR { Sbornik 20, No. 2, 249{266 (1973).
    • [17] Gallier, J., Notes on Di erential Geometry and Lie Groups, Book in Progress, 2011.
    • [18] Warner, F. W. , Foundations of di erentiable manifolds and Lie groups, Springer{Verlag, Berlin, 1983.
    • [19] Varadarajan, V. S., Lie groups, Lie algebras, and their representations, Prentice{Hall, Englewood Cli s, 1974.
    • [20] Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups, 4th edn., Springer-Verlag, Berlin, 1980.
    • [21] Gantmacher, F. R., The theory of matrices, Chelsea Publishing Co., New York, 1960.
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