Invariant line integrals in the theory of defective crystals

Gareth P. Parry; Miroslav Šilhavý

Displaying similar documents to “Invariant line integrals in the theory of defective crystals”

General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns

Adriano Montanaro, Diego Pigozzi (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere...

A mixture theory for micropolar thermoelastic solids.

Galeş, C. (2007)

Mathematical Problems in Engineering

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Curl bounds grad on SO(3)

Ingo Münch, Patrizio Neff (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Let $F^{p} \in GL (3)$ be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form $Curl [F^{p}] \cdot {(F^{p})}^{T}$ applied to rotations controls the gradient in the sense that pointwise $\forall R \in C^{1} (ℝ^{3}, SO (3)) : ∥ Curl [R] \cdot R^{T} ∥_{𝕄^{3 \times 3}}^{2} \geq \frac{1}{2} {∥ D R ∥}_{ℝ^{27}}^{2}$ . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized...

Combinatorial proofs of Capelli's and Turnbull's identities from classical invariant theory.

Foata, Dominique, Zeilberger, Doron (1994)

The Electronic Journal of Combinatorics [electronic only]

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Remarks on invariant descriptive set theory

John Burgess, Douglas Miller (1975)

Fundamenta Mathematicae

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Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Muro, Masakazu (2004)

Journal of Lie Theory

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Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics

Miroslav Vondrák (1985)

Aplikace matematiky

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The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions. The notion “slab analogy” is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements,...