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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/5556
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dc.contributor.authorGanguly, Saswati-
dc.contributor.authorSengupta, Surajit-
dc.contributor.authorSollich, Peter-
dc.contributor.authorRao, Madan-
dc.date.accessioned2013-04-24T06:43:55Z-
dc.date.available2013-04-24T06:43:55Z-
dc.date.issued2013-04-
dc.identifier.citationPhysical Review E, 2013, Vol.87, p042801en
dc.identifier.issn1539-3755-
dc.identifier.issn1550-2376 (Online)-
dc.identifier.urihttp://hdl.handle.net/2289/5556-
dc.descriptionOpen Access.en
dc.description.abstractA systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor D as well as a positive definite scalar χ measuring nonaffinity, i.e., the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of χ and D and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution P(χ,D) and the two-point spatial correlation functions for χ and D. We show that nonaffine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse-graining volume Ω and dimensionality. As a corollary to our work, we identify the field hχ conjugate to χ and show that this field may be tuned to produce a transition to a state where the ensemble average <χ> and the correlation length of χ diverge. Our work should be useful as a template for understanding nonaffine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of nonaffine displacements in melting, plastic flow, and the glass transition.en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.urihttp://dx.doi.org/10.1103/PhysRevE.87.042801en
dc.relation.urihttp://adsabs.harvard.edu/abs/2013PhRvE..87d2801Gen
dc.relation.urihttp://arxiv.org/abs/1212.6377en
dc.rights2013 American Physical Societyen
dc.subjectElasticityen
dc.subjectGlassesen
dc.subjectamorphous solidsen
dc.subjectGeneral theoryen
dc.titleNonaffine displacements in crystalline solids in the harmonic limiten
dc.typeArticleen
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