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Random fields related to the symmetry classes of second-order symmetric tensorsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 173-185Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2018. Vol. 271, p. 173-185
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
##### Keywords [en]

Random field, Spectral expansion, Symmetry class, Eigenvalues and eigenfunctions, Expansion, Heat conduction, Mathematical operators, Permittivity, Random processes, Stochastic models, Stochastic systems, Tensors, Electric permittivities, Natural representation, Random fields, Spectral expansions, Three dimensional space, Transversely isotropic, Typical application, Matrix algebra
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-41836DOI: 10.1007/978-3-030-02825-1_10Scopus ID: 2-s2.0-85058569471ISBN: 9783030028244 OAI: oai:DiVA.org:mdh-41836DiVA, id: diva2:1274026
##### Conference

International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

Under the change of basis in the three-dimensional space by means of an orthogonal matrix g, a matrix A of a linear operator is transformed as A → gAg-1 Mathematically, the stationary subgroup of a symmetric matrix under the above action can be either (Formula Presented), when all three eigenvalues of A are different, or (Formula Presented), when two of them are equal, or O(3), when all three eigenvalues are equal. Physically, one typical application relates to dependent quantities like a second-order symmetric stress (or strain) tensor. Another physical setting is that of dependent fields, such as conductivity with such three cases is the conductivity (or, similarly, permittivity, or anti-plane elasticity) second-rank tensor, which can be either orthotropic, transversely isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is invariant with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.

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