-
Previous Article
New inertial method for generalized split variational inclusion problems
- JIMO Home
- This Issue
-
Next Article
Modeling and computation of mean field game with compound carbon abatement mechanisms
C-eigenvalue intervals for piezoelectric-type tensors via symmetric matrices
1. | School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China |
2. | College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China |
C-eigenvalues of piezoelectric-type tensors play an crucial role in piezoelectric effect and converse piezoelectric effect. In this paper, by the partial symmetry property of piezoelectric-type tensors, we present three intervals to locate all C-eigenvalues of a given piezoelectric-type tensor. Numerical examples show that our results are better than the existing ones.
References:
[1] |
H. T. Che, H. B. Chen and Y. J. Wang,
C-eigenvalue inclusion theorems for piezoelectric-type tensors, Applied Mathematics Letters, 89 (2019), 41-49.
doi: 10.1016/j.aml.2018.09.014. |
[2] |
Y. Chen, A. Jákli and L. Qi, Spectral analysis of piezoelectric tensors, preprint, arXiv: 1703.07937v1. |
[3] |
Y. N. Chen, L. Q. Qi and E. G. Virga, Octupolar tensors for liquid crystals, J. Phys. A, 51 (2018), 025206, 20 pp.
doi: 10.1088/1751-8121/aa98a8. |
[4] |
J. Curie and P. Curie,
Développement, par compression de l'éctricité polaire dans les cristaux hémièdres à faces inclinées, Bulletin de Minéralogie, 3, 4 (1880), 90-93.
doi: 10.3406/bulmi.1880.1564. |
[5] |
M. De Jong, W. Chen, H. Geerlings, M. Asta and K. A. Persson, A database to enable discovery and design of piezoelectric materials, Scientific Data, 2 (2015), 150053.
doi: 10.1038/sdata.2015.53. |
[6] |
S. Haussl, Physical Properties of Crystals: An Introduction, Wiley-VCH Verlag, Weinheim, 2007.
doi: 10.1002/9783527621156. |
[7] |
A. Kholkin, N. Pertsev and A. Goltsev, Piezolelectricity and Crystal Symmetry, Piezoelectric and Acoustic Materials, Springer, New York, 2008. |
[8] |
C. Q. Li, Y. J. Liu and Y. T. Li,
C-eigenvalues intervals for piezoelectric-type tensors, Applied Mathematics and Computation, 358 (2019), 244-250.
doi: 10.1016/j.amc.2019.04.036. |
[9] |
D. Lovett, Tensor Properties of Crystals, 2$^{nd}$ edition, Institute of Physics Publishing, Bristol, 1989. |
[10] |
J. F. Nye, Physical properties of crystals: Their representation by tensors and matrices, Physics Today, 10 (1957), 26 pp.
doi: 10.1063/1.3060200. |
[11] |
L. Qi, Transposes, L-eigenvalues and invariants of third order tensors, preprint, (2017), arXiv: 1704.01327. |
[12] |
L. Q. Qi and Z. Y. Luo, Tensor Analysis: Spectral Theory and Special Tensors, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017.
doi: 10.1137/1.9781611974751.ch1. |
[13] |
W. J. Wang, H. B. Chen and Y. J. Wang, A new C-eigenvalue interval for piezoelectric-type tensors, Applied Mathematics Letters, 100 (2020), 106035, 6 pp.
doi: 10.1016/j.aml.2019.106035. |
[14] |
W.-N. Zou, C.-X. Tang and E. Pan, Symmetry types of the piezoelectric tensor and their identification, Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 469 (2013), 20120755.
doi: 10.1098/rspa.2012.0755. |
show all references
References:
[1] |
H. T. Che, H. B. Chen and Y. J. Wang,
C-eigenvalue inclusion theorems for piezoelectric-type tensors, Applied Mathematics Letters, 89 (2019), 41-49.
doi: 10.1016/j.aml.2018.09.014. |
[2] |
Y. Chen, A. Jákli and L. Qi, Spectral analysis of piezoelectric tensors, preprint, arXiv: 1703.07937v1. |
[3] |
Y. N. Chen, L. Q. Qi and E. G. Virga, Octupolar tensors for liquid crystals, J. Phys. A, 51 (2018), 025206, 20 pp.
doi: 10.1088/1751-8121/aa98a8. |
[4] |
J. Curie and P. Curie,
Développement, par compression de l'éctricité polaire dans les cristaux hémièdres à faces inclinées, Bulletin de Minéralogie, 3, 4 (1880), 90-93.
doi: 10.3406/bulmi.1880.1564. |
[5] |
M. De Jong, W. Chen, H. Geerlings, M. Asta and K. A. Persson, A database to enable discovery and design of piezoelectric materials, Scientific Data, 2 (2015), 150053.
doi: 10.1038/sdata.2015.53. |
[6] |
S. Haussl, Physical Properties of Crystals: An Introduction, Wiley-VCH Verlag, Weinheim, 2007.
doi: 10.1002/9783527621156. |
[7] |
A. Kholkin, N. Pertsev and A. Goltsev, Piezolelectricity and Crystal Symmetry, Piezoelectric and Acoustic Materials, Springer, New York, 2008. |
[8] |
C. Q. Li, Y. J. Liu and Y. T. Li,
C-eigenvalues intervals for piezoelectric-type tensors, Applied Mathematics and Computation, 358 (2019), 244-250.
doi: 10.1016/j.amc.2019.04.036. |
[9] |
D. Lovett, Tensor Properties of Crystals, 2$^{nd}$ edition, Institute of Physics Publishing, Bristol, 1989. |
[10] |
J. F. Nye, Physical properties of crystals: Their representation by tensors and matrices, Physics Today, 10 (1957), 26 pp.
doi: 10.1063/1.3060200. |
[11] |
L. Qi, Transposes, L-eigenvalues and invariants of third order tensors, preprint, (2017), arXiv: 1704.01327. |
[12] |
L. Q. Qi and Z. Y. Luo, Tensor Analysis: Spectral Theory and Special Tensors, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017.
doi: 10.1137/1.9781611974751.ch1. |
[13] |
W. J. Wang, H. B. Chen and Y. J. Wang, A new C-eigenvalue interval for piezoelectric-type tensors, Applied Mathematics Letters, 100 (2020), 106035, 6 pp.
doi: 10.1016/j.aml.2019.106035. |
[14] |
W.-N. Zou, C.-X. Tang and E. Pan, Symmetry types of the piezoelectric tensor and their identification, Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 469 (2013), 20120755.
doi: 10.1098/rspa.2012.0755. |
4.2514 | 0.1375 | 2.6258 | 12.4234 | 11.6674 | 7.7376 | 13.5021 | 27.4628 | |
7.3636 | 0.2834 | 5.6606 | 23.5377 | 16.8548 | 12.3206 | 20.2351 | 27.5396 | |
7.3636 | 0.2834 | 5.6606 | 23.5377 | 16.8548 | 12.3206 | 20.2351 | 27.5396 | |
7.3636 | 0.2744 | 4.8058 | 23.5377 | 16.5640 | 11.0127 | 18.8793 | 27.5109 | |
7.3636 | 0.2834 | 4.7861 | 23.5377 | 16.8464 | 11.0038 | 19.8830 | 27.5013 | |
7.3636 | 0.2737 | 3.3543 | 21.9667 | 16.0233 | 9.4595 | 16.7483 | 27.5012 | |
7.3636 | 0.2393 | 4.6717 | 22.7163 | 14.5723 | 12.1694 | 18.7025 | 27.5396 | |
6.3771 | 0.1943 | 3.7242 | 16.0259 | 11.9319 | 7.7540 | 13.5113 | 27.4629 | |
5.2069 | 0.1938 | 3.7025 | 14.9344 | 11.9319 | 7.7523 | 13.5054 | 27.4629 |
4.2514 | 0.1375 | 2.6258 | 12.4234 | 11.6674 | 7.7376 | 13.5021 | 27.4628 | |
7.3636 | 0.2834 | 5.6606 | 23.5377 | 16.8548 | 12.3206 | 20.2351 | 27.5396 | |
7.3636 | 0.2834 | 5.6606 | 23.5377 | 16.8548 | 12.3206 | 20.2351 | 27.5396 | |
7.3636 | 0.2744 | 4.8058 | 23.5377 | 16.5640 | 11.0127 | 18.8793 | 27.5109 | |
7.3636 | 0.2834 | 4.7861 | 23.5377 | 16.8464 | 11.0038 | 19.8830 | 27.5013 | |
7.3636 | 0.2737 | 3.3543 | 21.9667 | 16.0233 | 9.4595 | 16.7483 | 27.5012 | |
7.3636 | 0.2393 | 4.6717 | 22.7163 | 14.5723 | 12.1694 | 18.7025 | 27.5396 | |
6.3771 | 0.1943 | 3.7242 | 16.0259 | 11.9319 | 7.7540 | 13.5113 | 27.4629 | |
5.2069 | 0.1938 | 3.7025 | 14.9344 | 11.9319 | 7.7523 | 13.5054 | 27.4629 |
[1] |
Jianxing Zhao, Jincheng Luo. Properties and calculation for C-eigenvalues of a piezoelectric-type tensor. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021162 |
[2] |
Yannan Chen, Antal Jákli, Liqun Qi. The C-eigenvalue of third order tensors and its application in crystals. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021183 |
[3] |
Ruixue Zhao, Jinyan Fan. Quadratic tensor eigenvalue complementarity problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022073 |
[4] |
Wanbin Tong, Hongjin He, Chen Ling, Liqun Qi. A nonmonotone spectral projected gradient method for tensor eigenvalue complementarity problems. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 425-437. doi: 10.3934/naco.2020042 |
[5] |
David Burguet. Examples of $\mathcal{C}^r$ interval map with large symbolic extension entropy. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 873-899. doi: 10.3934/dcds.2010.26.873 |
[6] |
Fan Wu. Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor. Evolution Equations and Control Theory, 2021, 10 (3) : 511-518. doi: 10.3934/eect.2020078 |
[7] |
Ya Li, ShouQiang Du, YuanYuan Chen. Modified spectral PRP conjugate gradient method for solving tensor eigenvalue complementarity problems. Journal of Industrial and Management Optimization, 2022, 18 (1) : 157-172. doi: 10.3934/jimo.2020147 |
[8] |
Yaotang Li, Suhua Li. Exclusion sets in the Δ-type eigenvalue inclusion set for tensors. Journal of Industrial and Management Optimization, 2019, 15 (2) : 507-516. doi: 10.3934/jimo.2018054 |
[9] |
Hao Li, Hai Bi, Yidu Yang. The two-grid and multigrid discretizations of the $ C^0 $IPG method for biharmonic eigenvalue problem. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1775-1789. doi: 10.3934/dcdsb.2020002 |
[10] |
Denis Volk. Almost every interval translation map of three intervals is finite type. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2307-2314. doi: 10.3934/dcds.2014.34.2307 |
[11] |
Wenguo Shen. Unilateral global interval bifurcation for Kirchhoff type problems and its applications. Communications on Pure and Applied Analysis, 2018, 17 (1) : 21-37. doi: 10.3934/cpaa.2018002 |
[12] |
Giovanni Cimatti. Forced periodic solutions for piezoelectric crystals. Communications on Pure and Applied Analysis, 2005, 4 (2) : 475-485. doi: 10.3934/cpaa.2005.4.475 |
[13] |
Eugenia Pérez. On periodic Steklov type eigenvalue problems on half-bands and the spectral homogenization problem. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 859-883. doi: 10.3934/dcdsb.2007.7.859 |
[14] |
Gang Wang, Yiju Wang, Yuan Zhang. Brualdi-type inequalities on the minimum eigenvalue for the Fan product of M-tensors. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2551-2562. doi: 10.3934/jimo.2019069 |
[15] |
Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti. On a conjectured reverse Faber-Krahn inequality for a Steklov--type Laplacian eigenvalue. Communications on Pure and Applied Analysis, 2015, 14 (1) : 63-82. doi: 10.3934/cpaa.2015.14.63 |
[16] |
Qi Li, Hong Xue, Changxin Lu. Event-based fault detection for interval type-2 fuzzy systems with measurement outliers. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1301-1328. doi: 10.3934/dcdss.2020412 |
[17] |
Ramasamy Kavikumar, Boomipalagan Kaviarasan, Yong-Gwon Lee, Oh-Min Kwon, Rathinasamy Sakthivel, Seong-Gon Choi. Robust dynamic sliding mode control design for interval type-2 fuzzy systems. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1839-1858. doi: 10.3934/dcdss.2022014 |
[18] |
Kaiping Liu, Haitao Che, Haibin Chen, Meixia Li. Parameterized S-type M-eigenvalue inclusion intervals for fourth-order partially symmetric tensors and its applications. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022077 |
[19] |
Jiří Neustupa. On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body. Conference Publications, 2007, 2007 (Special) : 758-767. doi: 10.3934/proc.2007.2007.758 |
[20] |
Marius Tucsnak. Control of plate vibrations by means of piezoelectric actuators. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 281-293. doi: 10.3934/dcds.1996.2.281 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]