-
Previous Article
A velocity-based time-stepping scheme for multibody dynamics with unilateral constraints
- DCDS-S Home
- This Issue
-
Next Article
Dual formulation of a viscoplastic contact problem with unilateral constraint
Prolegomena to studies on dynamic materials and their space-time homogenization
1. | Université Pierre et Marie Curie, Institut Jean Le Rond d'Alembert, UMR CNRS 7190, Case 162, Tour 55, 4 place Jussieu, 75252 Paris Cedex 05, France, France |
References:
[1] |
I. I. Blekhman and K. A. Lur'e, On dynamic materials, (Russian) Doklady Akademii Nauk, 371 (2000), 182-185.
doi: 10.1134/1.171720. |
[2] |
V. L. Ginzburg and V. N. Tsytovich, Several problems of the theory of transition radiation and transition scattering, Physics Reports, 49 (1979), 1-89; Original Russian in Usp. Fiz. Nauk, 126 (1978), 553-563.
doi: 10.1016/0370-1573(79)90052-8. |
[3] |
K. A. Lurie, "Introduction to the Mathematical Theory of Dynamic Materials," Advances in Mechanics and Mathematics, 15, Springer, New York, 2007. |
[4] |
K. A. Lurie, On homogenization of activated laminates in 1D-space and time, Zeit. Angew. Math. Mech., 89 (2009), 333-340.
doi: 10.1002/zamm.200800185. |
[5] |
K. A. Lurie, D. Onofrei and S. L. Weekes, Mathematical analysis of the waves propagation through a rectangular material structure in space-time, J. Math. Analysis and Applications, 355 (2009), 180-194.
doi: 10.1016/j.jmaa.2009.01.031. |
[6] |
G. A. Maugin, "Material Inhomogeneties in Elasticity," Applied Mathematics and Mathematical Computation, 3, Chapman & Hall, London, 1993. |
[7] |
G. A. Maugin, "Configurational Forces. Thermomechanics, Physics, Mathematics, and Numerics," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2011. |
[8] |
G. Nadin, Traveling fronts in space-time periodic media, J. Math. Pures Appl. (9), 92 (2009), 232-262.
doi: 10.1016/j.matpur.2009.04.002. |
[9] |
D. E. Neuenschwander, "Emmy Noether's Wonderful Theorem," Johns Hopkins University Press, Baltimore, MD, 2011. |
[10] |
M. Rousseau, G. A. Maugin and M. Berezovski, Elements of study on dynamic materials, Arch. Appl. Mechanics, 81 (2011), 925-942.
doi: 10.1007/s00419-010-0461-4. |
[11] |
E. Sánchez-Palencia and A. Zaoui, eds., "Homogenization Techniques for Composite Media," Papers from the course held in Udine, July 1-5, 1985, Lecture Notes in Physics, 272, Springer-Verlag, Berlin, 1987.
doi: 10.1007/3-540-17616-0. |
[12] |
C. A. Truesdell and R. A. Toupin, Classical theory of fields, in "Handbuch der Physik, Vol. III/1" (ed. S. Flügge), Springer-Verlag, Berlin, 1960. |
[13] |
A. I. Vesnitskii and A. V. Metrikine, Transition radiation in mechanics, Physics-Uspekhi, 39 (1996), 983-1007. |
show all references
References:
[1] |
I. I. Blekhman and K. A. Lur'e, On dynamic materials, (Russian) Doklady Akademii Nauk, 371 (2000), 182-185.
doi: 10.1134/1.171720. |
[2] |
V. L. Ginzburg and V. N. Tsytovich, Several problems of the theory of transition radiation and transition scattering, Physics Reports, 49 (1979), 1-89; Original Russian in Usp. Fiz. Nauk, 126 (1978), 553-563.
doi: 10.1016/0370-1573(79)90052-8. |
[3] |
K. A. Lurie, "Introduction to the Mathematical Theory of Dynamic Materials," Advances in Mechanics and Mathematics, 15, Springer, New York, 2007. |
[4] |
K. A. Lurie, On homogenization of activated laminates in 1D-space and time, Zeit. Angew. Math. Mech., 89 (2009), 333-340.
doi: 10.1002/zamm.200800185. |
[5] |
K. A. Lurie, D. Onofrei and S. L. Weekes, Mathematical analysis of the waves propagation through a rectangular material structure in space-time, J. Math. Analysis and Applications, 355 (2009), 180-194.
doi: 10.1016/j.jmaa.2009.01.031. |
[6] |
G. A. Maugin, "Material Inhomogeneties in Elasticity," Applied Mathematics and Mathematical Computation, 3, Chapman & Hall, London, 1993. |
[7] |
G. A. Maugin, "Configurational Forces. Thermomechanics, Physics, Mathematics, and Numerics," CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2011. |
[8] |
G. Nadin, Traveling fronts in space-time periodic media, J. Math. Pures Appl. (9), 92 (2009), 232-262.
doi: 10.1016/j.matpur.2009.04.002. |
[9] |
D. E. Neuenschwander, "Emmy Noether's Wonderful Theorem," Johns Hopkins University Press, Baltimore, MD, 2011. |
[10] |
M. Rousseau, G. A. Maugin and M. Berezovski, Elements of study on dynamic materials, Arch. Appl. Mechanics, 81 (2011), 925-942.
doi: 10.1007/s00419-010-0461-4. |
[11] |
E. Sánchez-Palencia and A. Zaoui, eds., "Homogenization Techniques for Composite Media," Papers from the course held in Udine, July 1-5, 1985, Lecture Notes in Physics, 272, Springer-Verlag, Berlin, 1987.
doi: 10.1007/3-540-17616-0. |
[12] |
C. A. Truesdell and R. A. Toupin, Classical theory of fields, in "Handbuch der Physik, Vol. III/1" (ed. S. Flügge), Springer-Verlag, Berlin, 1960. |
[13] |
A. I. Vesnitskii and A. V. Metrikine, Transition radiation in mechanics, Physics-Uspekhi, 39 (1996), 983-1007. |
[1] |
Xiongxiong Bao, Wenxian Shen, Zhongwei Shen. Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems. Communications on Pure and Applied Analysis, 2019, 18 (1) : 361-396. doi: 10.3934/cpaa.2019019 |
[2] |
Henri Schurz. Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 353-363. doi: 10.3934/dcdss.2008.1.353 |
[3] |
Arthur Bottois, Nicolae Cîndea. Controllability of the linear elasticity as a first-order system using a stabilized space-time mixed formulation. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022028 |
[4] |
Georgios T. Kossioris, Georgios E. Zouraris. Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1845-1872. doi: 10.3934/dcdsb.2013.18.1845 |
[5] |
Yuming Zhang. On continuity equations in space-time domains. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4837-4873. doi: 10.3934/dcds.2018212 |
[6] |
Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control and Related Fields, 2021, 11 (3) : 601-624. doi: 10.3934/mcrf.2021014 |
[7] |
Vincent Astier, Thomas Unger. Galois extensions, positive involutions and an application to unitary space-time coding. Advances in Mathematics of Communications, 2019, 13 (3) : 513-516. doi: 10.3934/amc.2019032 |
[8] |
Dong-Ho Tsai, Chia-Hsing Nien. On space-time periodic solutions of the one-dimensional heat equation. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3997-4017. doi: 10.3934/dcds.2020037 |
[9] |
Susanne Pumplün, Thomas Unger. Space-time block codes from nonassociative division algebras. Advances in Mathematics of Communications, 2011, 5 (3) : 449-471. doi: 10.3934/amc.2011.5.449 |
[10] |
Dmitry Turaev, Sergey Zelik. Analytical proof of space-time chaos in Ginzburg-Landau equations. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1713-1751. doi: 10.3934/dcds.2010.28.1713 |
[11] |
Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216 |
[12] |
Frédérique Oggier, B. A. Sethuraman. Quotients of orders in cyclic algebras and space-time codes. Advances in Mathematics of Communications, 2013, 7 (4) : 441-461. doi: 10.3934/amc.2013.7.441 |
[13] |
Grégory Berhuy. Algebraic space-time codes based on division algebras with a unitary involution. Advances in Mathematics of Communications, 2014, 8 (2) : 167-189. doi: 10.3934/amc.2014.8.167 |
[14] |
David Grant, Mahesh K. Varanasi. Duality theory for space-time codes over finite fields. Advances in Mathematics of Communications, 2008, 2 (1) : 35-54. doi: 10.3934/amc.2008.2.35 |
[15] |
Montgomery Taylor. The diffusion phenomenon for damped wave equations with space-time dependent coefficients. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5921-5941. doi: 10.3934/dcds.2018257 |
[16] |
Paolo Paoletti. Acceleration waves in complex materials. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 637-659. doi: 10.3934/dcdsb.2012.17.637 |
[17] |
Sung Kyu Choi, Namjip Koo. Stability of linear dynamic equations on time scales. Conference Publications, 2009, 2009 (Special) : 161-170. doi: 10.3934/proc.2009.2009.161 |
[18] |
Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems and Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069 |
[19] |
David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131 |
[20] |
Xiaopeng Zhao. Space-time decay estimates of solutions to liquid crystal system in $\mathbb{R}^3$. Communications on Pure and Applied Analysis, 2019, 18 (1) : 1-13. doi: 10.3934/cpaa.2019001 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]