Transposes, L-Eigenvalues and Invariants of Third Order Tensors

Preprint English OPEN
Qi, Liqun;
  • Subject: Mathematical Physics
    arxiv: Computer Science::Graphics

Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Le... View more
  • References (24)
    24 references, page 1 of 3

    [1] H. R. Brand, H. Pleiner, and P. E. Cladis, “Flow properties of the optically isotropic tetrahedratic phase”, Eur. Phys. J. E 7 (2002) 163-166.

    [2] Y. Chen, A. Ja´kli and L. Qi, “Spectral analysis of piezoelectric tensors”, arXiv:1703.07937, 2017.

    [3] Y. Chen, L. Qi, and E.G. Virga, “Octupolar tensors for liquid crystals”, arXiv:1701.06761, 2017.

    [4] J. Curie and P. Curie, “D´eveloppement, par pression, de l'´electricit´e polaire dans les cristaux h´emi`edres `a faces inclin´ees”, Comptes rendus (in French) 91 (1880) 294-295.

    [5] L. G. Fel, “Tetrahedral symmetry in nematic liquid crystals”, Physical Review E 52 (1995) 702-717.

    [6] G. Gaeta and E.G. Virga, “Octupolar order in three dimensions”, Eur. Phys. J. E 39 (2016) 113.

    [7] S. Haussu¨hl, Physical Properties of Crystals: An Introduction, Wiley-VCH Verlag, Weinheim, 2007.

    [8] A. Ja´kli, “Electro-mechanical effects in liquid crystals”, Liquid Crystals 37 (2010) 825-837.

    [9] A. Ja´kli, I.C. Pintre, J.L. Serrano, M.B. Ros and M.R. de la Fuente, “Piezoelectric and electric-field-induced properties of a ferroelectric bent-core liquid crstal”, Adv. Mater. 21 (2009) 3784-3788.

    [10] A. Ja´kli, T. To´th-Katona, T. Scharf, M. Schadt and A. Saupe, “Piezolelectricity of a ferroelectric liquid crystal with a gltransition”, Phys. Rev. E 66 (2002) 011701.

  • Similar Research Results (1)
  • Metrics
Share - Bookmark