Free access
Issue
ESAIM: M2AN
Volume 45, Number 5, September-October 2011
Page(s) 873 - 899
DOI http://dx.doi.org/10.1051/m2an/2010106
Published online 23 February 2011
  1. R. Alicandro, A. Braides and M. Cicalese, Continuum limits of discrete films with superlinear growth densities. Calc. Var. Par. Diff. Eq. 33 (2008) 267–297. [CrossRef]
  2. S. Aubry, The twist map, the extended Frenkel-Kontorova model and the devil's staircase. Physica D 7 (1983) 240–258. [CrossRef] [MathSciNet]
  3. X. Blanc, C. Le Bris and P.L. Lions, From molecular models to continuum mechanics. Arch. Rat. Mech. Anal. 164 (2002) 341–381. [CrossRef] [MathSciNet]
  4. A. Braides and M. Cicalese, Surface energies in nonconvex discrete systems. Math. Models Meth. Appl. Sci. 17 (2007) 985–1037. [CrossRef]
  5. A. Braides and A. DeFranchesi, Homogenisation of multiple integrals. Oxford University Press (1998).
  6. A. Braides and M. Gelli, Continuum limits of discrete systems without convexity hypotheses. Math. Mech. Solids 7 (2002) 41–66. [CrossRef] [MathSciNet]
  7. A. Braides, M. Solci and E. Vitali, A derivation of linear alastic energies from pair-interaction atomistic systems. Netw. Heterog. Media 9 (2007) 551–567.
  8. J. Cahn, J. Mallet-Paret and E. Van Vleck, Travelling wave solutions for systems of ODEs on a two-dimensional spatial lattice. SIAM J. Appl. Math. 59 (1998) 455–493. [CrossRef]
  9. M. Charlotte and L. Truskinovsky, Linear elastic chain with a hyper-pre-stress. J. Mech. Phys. Solids 50 (2002) 217–251. [CrossRef] [MathSciNet]
  10. W. E and P. Ming, Cauchy-Born rule and the stability of crystalline solids: static problems. Arch. Rat. Mech. Anal. 183 (2005) 241–297.
  11. I. Fonseca and S. Müller, A uniqueness proof for the Wulff theorem. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991) 125–136. [MathSciNet]
  12. G. Friesecke and F. Theil, Validitity and failure of the Cauchy-Born rule in a two-dimensional mass-spring lattice. J. Nonlinear Sci. 12 (2002) 445–478. [CrossRef] [MathSciNet]
  13. G. Friesecke, R. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461–1506. [CrossRef] [MathSciNet]
  14. D. Gérard-Varet and N. Masmoudi, Homogenization and boundary layer. Preprint available at www.math.nyu.edu/faculty/masmoudi/homog_Varet3.pdf (2010).
  15. P. Lancaster and L. Rodman, Algebraic Riccati Equations. Oxford University Press (1995).
  16. J.L. Lions, Some methods in the mathematical analysis of systems and their controls. Science Press, Beijing, Gordon and Breach, New York (1981).
  17. J.A. Nitsche, On Korn's second inequality. RAIRO Anal. Numér. 15 (1981) 237–248. [MathSciNet]
  18. C. Radin, The ground state for soft disks. J. Stat. Phys. 26 (1981) 367–372.
  19. B. Schmidt, A derivation of continuum nonlinear plate theory from atomistic models. Multiscale Mod. Sim. 5 (2006) 664–694. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  20. B. Schmidt, On the passage from atomic to continuum theory for thin films. Arch. Rat. Mech. Anal. 190 (2008) 1–55. [CrossRef] [MathSciNet]
  21. B. Schmidt, On the derivation of linear elasticity from atomistic models. Net. Heterog. Media 4 (2009) 789–812. [CrossRef]
  22. E. Sonntag, Mathematical Control Theory. Second edition, Springer (1998).
  23. L. Tartar, The general theory of homogenization. Springer (2010).
  24. F. Theil, A proof of crystallization in a two dimensions. Comm. Math. Phys. 262 (2006) 209–236. [CrossRef] [MathSciNet]

Recommended for you