Invariant line integrals in the theory of defective crystals

Gareth P. Parry; Miroslav Šilhavý

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 2, page 111-140
  • ISSN: 1120-6330

Abstract

top
In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.

How to cite

top

Parry, Gareth P., and Šilhavý, Miroslav. "Invariant line integrals in the theory of defective crystals." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.2 (2000): 111-140. <http://eudml.org/doc/252295>.

@article{Parry2000,
abstract = {In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.},
author = {Parry, Gareth P., Šilhavý, Miroslav},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Invariant; Integral; Defect; continuum theory of crystals; invariant line integrals; defects of lattice structure; transformation properties; covariant vector-valued functions},
language = {eng},
month = {6},
number = {2},
pages = {111-140},
publisher = {Accademia Nazionale dei Lincei},
title = {Invariant line integrals in the theory of defective crystals},
url = {http://eudml.org/doc/252295},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Parry, Gareth P.
AU - Šilhavý, Miroslav
TI - Invariant line integrals in the theory of defective crystals
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/6//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 2
SP - 111
EP - 140
AB - In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.
LA - eng
KW - Invariant; Integral; Defect; continuum theory of crystals; invariant line integrals; defects of lattice structure; transformation properties; covariant vector-valued functions
UR - http://eudml.org/doc/252295
ER -

References

top
  1. Davini, C., A proposal for a continuum theory of defective crystals. Arch. Rational Mech. Anal., 96, 1986, 295-317. Zbl0623.73002MR855751DOI10.1007/BF00251800
  2. Davini, C., Elastic invariants in crystal theory. In: J. M. Ball (ed.), Material instabilities in continuum mechanics and related mathematical problems. Clarendon Press, Oxford1988, 85-105. Zbl0659.73001MR970520
  3. Davini, C. - Parry, G. P., On defect-preserving deformations in crystals. Int. J. Plasticity, 5, 1989, 337-369. Zbl0697.73036
  4. Davini, C. - Parry, G. P., A complete list of invariants for defective crystals. Proc. R. Soc. Lond. A, 432, 1991, 341-365. Zbl0726.73032MR1116537DOI10.1098/rspa.1991.0021
  5. Davini, C. - Parry, G. P., Uniform rearrangement in defective crystals. Proc. R. Soc. Lond. A, 439, 1992, 247-256. Zbl0766.73057MR1193002DOI10.1098/rspa.1992.0147
  6. Fonseca, I. - Parry, G. P., Equilibrium configurations of defective crystals. Arch. Rational Mech. Anal., 120, 1992, 245-283. Zbl0785.73007MR1183552DOI10.1007/BF00375027
  7. Fonseca, I. - Parry, G. P., On a class of invariant functionals. Proc. R. Soc. Lond. A, 436, 1992, 317-329. Zbl0767.73095MR1177132DOI10.1098/rspa.1992.0020
  8. Olver, P. J., Conservation laws and null divergences. Math. Proc. Camb. Phil. Soc., 94, 1983, 529-540. Zbl0556.35021MR720804DOI10.1017/S030500410000092X
  9. Olver, P. J., Applications of Lie groups to partial differential equations. Springer-Verlag, New York1986. Zbl0588.22001MR836734DOI10.1007/978-1-4684-0274-2
  10. Olver, P. J., Equivalence, invariants, and symmetry. Cambridge University Press, Cambridge1996. Zbl0837.58001MR1337276DOI10.1017/CBO9780511609565
  11. Parry, G. P., Defects and rearrangements in crystals. In: L. M. Brock (ed.), Defects and anelasticity in the characterization of crystalline solids. ASME, New York1992, 117-132. 
  12. Parry, G. P., Elastic-plastic decompositions of defect-preserving changes of state in solid crystals. In: M. D. P. Monteiro Marques - J. F. Rodrigues (eds.), Trends in applications of mathematics to mechanics. Longman, Harlow, Essex1994, 154-163. Zbl0865.73051MR1475480
  13. Parry, G. P., Material symmetry in solid crystals. In: D. F. Parker - A. H. England (eds.), IUTAM Symposium on Anisotropy, inhomogeneity and nonlinearity in solid mechanics. Kluwer Academic Publishers, Amsterdam1995, 229-234. Zbl0900.73054MR1367108
  14. Parry, G. P., On defective crystalography. Arch. Mech., 50, 1998, 567-575. Zbl0955.74016
  15. Parry, G. P. - Šilhavý, M., Elastic invariants in the theory of defective crystals. Proc. R. Soc. Lond. A, 455, 1999, 4333-4346. Zbl0954.74013MR1809363DOI10.1098/rspa.1999.0503

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.