EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 41 / No 2 (March-April 2007) ESAIM: M2AN, 41 2 (2007) 391-426 References
Free Access
Issue
ESAIM: M2AN
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
Page(s) 391 - 426
DOI https://doi.org/10.1051/m2an:2007018
Published online 16 June 2007
  1. R. Alicandro and M. Cicalese, A general integral representation result for continuum limits of discrete energies with superlinear growth. SIAM J. Math. Anal. 36 (2004) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Anitescu, D. Negrut, P. Zapol and A. El-Azab, A note on the regularity of reduced models obtained by nonlocal quasi-continuum-like approach. Technical report ANL/MCS-P1303-1105, Argonne National Laboratory, Argonne, Illinois (2005). Available at http://www-unix.mcs.anl.gov/~anitescu/PUBLICATIONS/quasicont.pdf. [Google Scholar]
  3. N. Antonic, C.J. van Duijn, W. Jäger and A. Mikelic, Multiscale problems in science and technology. Challenges to mathematical analysis and perspectives. Springer (2002). [Google Scholar]
  4. M. Arndt and M. Griebel, Derivation of higher order gradient continuum models from atomistic models for crystalline solids. SIAM J. Multiscale Model. Simul. 4 (2005) 531–562. [CrossRef] [Google Scholar]
  5. M. Arroyo and T. Belytshko, A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes. Mech. Mater. 35 (2003) 175–622. [CrossRef] [Google Scholar]
  6. N.W. Ashcroft and N.D. Mermin, Solid-State Physics. Saunders College Publishing (1976). [Google Scholar]
  7. A. Askar, Lattice dynamical foundations of continuum theories. World Scientific, Philadelphia (1985). [Google Scholar]
  8. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977) 337–403. [Google Scholar]
  9. J.M. Ball, Singularities and computation of miminizers for variational problems, in Foundations of Computational Mathematics, R. DeVore, A. Iserles and E. Suli Eds., Cambridge University Press London Mathematical Society Lecture Note Series 284 (2001) 1–20. [Google Scholar]
  10. J.M. Ball, Some open problems in elasticity, in Geometry, Mechanics, and Dynamics. Springer (2002) 3–59. [Google Scholar]
  11. J.M. Ball and R.D. James, Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100 (1987) 13–52. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.M. Ball and R.D. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. Royal Soc. London A 338 (1992) 389–450. [Google Scholar]
  13. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  14. T.J. Barth, T. Chan and R. Haimes Eds., Multiscale and multiresolution methods, Lecture notes in computational science and engineering 20. Springer (2002). [Google Scholar]
  15. P. Bénilan, H. Brezis and M. Crandall, A semilinear equation in Formula . Ann. Sc. Norm. Sup. Pisa 2 (1975) 523–555. [Google Scholar]
  16. A. Bensoussan, J.-L. Lions and G. Papnicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications 5. North-Holland (1978). [Google Scholar]
  17. F. Bethuel, G. Huisken, S. Müller and K. Steffen, Variational models for microstructures and phase transition, in Calculus of Variations and Geometric Evolution Problems, Lecture Notes in Mathematics 1713. Springer (1999) 85–210. [Google Scholar]
  18. K. Bhattacharya, Microstructure of Martensite: Why It Forms and How It Gives Rise to the Shape-Memory Effect. Oxford Series on Materials Modelling, Oxford University Press (2003). [Google Scholar]
  19. K. Bhattacharya and G. Dolzmann, Relaxation of some multi-well problems. Proc. Royal Soc. Edinburgh A 131 (2001) 279–320. [CrossRef] [Google Scholar]
  20. X. Blanc, A mathematical insight into ab initio simulations of solid phase, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, M. Defranceschi and C. Le Bris Eds., Lect. Notes Chem. 74. Springer (2000) 133–158. [Google Scholar]
  21. X. Blanc, Geometry optimization for crystals in Thomas-Fermi type theories of solids. Comm. P.D.E. 26 (2001) 651–696. [CrossRef] [Google Scholar]
  22. X. Blanc, Unique solvability for system of nonlinear elliptic PDEs arising in solid state physics. SIAM J. Math. Anal. 38 (2006) 1235–1248. [CrossRef] [MathSciNet] [Google Scholar]
  23. X. Blanc and C. Le Bris, Optimisation de géométrie dans le cadre des théories de Thomas-Fermi pour les cristaux périodiques [Geometry optimization for Thomas-Fermi type theories of solids]. Note C.R. Acad. Sci. Sér. 1 329 (1999) 551–556. [Google Scholar]
  24. X. Blanc and C. Le Bris, Thomas-Fermi type models for polymers and thin films. Adv. Diff. Equ. 5 (2000) 977–1032. [Google Scholar]
  25. X. Blanc and C. Le Bris, Periodicity of the infinite-volume ground-state of a one-dimensional quantum model. Nonlinear Anal., T.M.A 48 (2002) 791–803. [Google Scholar]
  26. X. Blanc and C. Le Bris, Définition d'énergies d'interfaces à partir de modèles atomiques. Note C.R. Acad. Sci. Sér. 1 340 (2005) 535–540. [Google Scholar]
  27. X. Blanc, C. Le Bris and F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. ESAIM: M2AN 39 (2005) 797–826. [Google Scholar]
  28. X. Blanc, C. Le Bris and F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics: the convex case. Acta Math. Appl. Sinica (to appear). [Google Scholar]
  29. X. Blanc, C. Le Bris and P.-L. Lions, Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus [From molecular models to continuum mechanics]. Note C.R. Acad. Sci. Sér. 1 332 (2001) 949–956. [Google Scholar]
  30. X. Blanc, C. Le Bris and P.-L. Lions, From molecular models to continuum mechanics. Arch. Rat. Mech. Anal. 164 (2002) 341–381. [Google Scholar]
  31. X. Blanc, C. Le Bris and P.-L. Lions, A definition of the ground state energy for systems composed of infinitely many particles. Comm. P.D.E 28 (2003) 439–475. [Google Scholar]
  32. X. Blanc, C. Le Bris and P.-L. Lions, Du discret au continu pour des modèles de réseaux aléatoires d'atomes [Discrete to continuum limit for some models of stochastic lattices of atoms]. Note C.R. Acad. Sci. Sér. 1. 342 (2006) 627–633. [Google Scholar]
  33. X. Blanc, C. Le Bris and P.-L. Lions, On the energy of some microscopic stochastic lattices. Arch. Rat. Mech. Anal. 184 (2007) 303–339. [CrossRef] [Google Scholar]
  34. X. Blanc, C. Le Bris and P.-L. Lions (in preparation). [Google Scholar]
  35. A. Braides, Γ-convergence for beginners, Oxford Lecture Series in Mathematics and its Applications 22. Oxford University Press, Oxford (2002). [Google Scholar]
  36. A. Braides, Non-local variational limits of discrete systems. Commun. Contemp. Math. 2 (2000) 285–297. [CrossRef] [MathSciNet] [Google Scholar]
  37. A. Braides and M.S. Gelli, Continuum limits of discrete systems without convexity hypotheses. Math. Mech. Solids 7 (2002) 41–66. [CrossRef] [MathSciNet] [Google Scholar]
  38. A. Braides and M.S. Gelli, Limits of discrete systems with long-range interactions. J. Convex Anal. 9 (2002) 363–399. [MathSciNet] [Google Scholar]
  39. A. Braides and M.S. Gelli, The passage from discrete to continuous variational problems: a nonlinear homogenization process. Preprint of the Scuola Normale Superiore di Pisa (2003). Available at http://cvgmt.sns.it/cgi/get.cgi/papers/bragel03/ [Google Scholar]
  40. A. Braides, G. Dal Maso and A. Garroni, Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case. Arch. Rat. Mech. Anal. 146 (1999) 23–58. [Google Scholar]
  41. A. Braides, M.S. Gelli and M. Sigalotti, The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case. Proc. Steklov Inst. Math. 236 (2002) 395–414. [Google Scholar]
  42. L. Breimana, Probability, Classics in Applied Mathematics. SIAM, Philadelphia (1992). [Google Scholar]
  43. H. Brezis, Semilinear equations in Formula without condition at infinity. Appl. Math. Optim. 12 (1984) 271–282. [CrossRef] [MathSciNet] [Google Scholar]
  44. V.V. Bulatov and T. Diaz de la Rubia, Multiscale modelling of materials. MRS Bulletin 26 (2001). [Google Scholar]
  45. D. Caillerie, A. Mourad and A. Raoult, Discrete homogenization in graphene sheet modeling, J. Elasticity 84 (2006) 33–68. [Google Scholar]
  46. C. Carstensen, Numerical Analysis of Microstructure, in Theory and Numerics of Differential Equations, J.F. Blowey, J.P. Coleman and A.W. Craig Eds., Springer (2001) 59–126. [Google Scholar]
  47. C. Carstensen and T. Roubíček, Numerical approximation of young measuresin non-convex variational problems. Numer. Math. 84 (2000) 395–415. [CrossRef] [MathSciNet] [Google Scholar]
  48. I. Catto, C. Le Bris and P.-L. Lions, Limite thermodynamique pour des modèles de type Thomas-Fermi. Note C.R.A.S. Sér. 1 322 (1996) 357–364. [Google Scholar]
  49. I. Catto, C. Le Bris and P.-L. Lions, Sur la limite thermodynamique pour des modèles de type Hartree et Hartree-Fock [On the thermodynamic limit for Hartree and Hartree-Fock type models]. Note C.R.A.S. Sér. 1 327 (1998) 259–266. [Google Scholar]
  50. I. Catto, C. Le Bris and P.-L. Lions, Mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford University Press (1998). [Google Scholar]
  51. I. Catto, C. Le Bris and P.-L. Lions, On the thermodynamic limit for Hartree-Fock type models. Ann. Inst. H. Poincaré, Anal. Non Linéaire 18 (2001) 687–760. [Google Scholar]
  52. I. Catto, C. Le Bris and P.-L. Lions, On some periodic Hartree-type models for crystals. Ann. Inst. H. Poincaré, Anal. Non Linéaire 19 (2002) 143–190. [Google Scholar]
  53. I. Catto, C. Le Bris and P.-L. Lions, From atoms to crytals: a mathematical journey. Bull. Amer. Math. Soc. 42 (2005) 291–363. [CrossRef] [MathSciNet] [Google Scholar]
  54. M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rat. Mech. Anal. 103 (1988) 237–277. [Google Scholar]
  55. P.G. Ciarlet, Mathematical elasticity, Vol. 1. North Holland (1993). [Google Scholar]
  56. G. Csányi, T. Albaret, G. Moras, M.C. Payne and A. De Vita, Multiscale hybrid simulation methods for material systems J. Phys. Condens. Matt. 17 (2005) R691. [Google Scholar]
  57. R. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag Berlin (1989). [Google Scholar]
  58. G. Dal Maso, An introduction to Γ-convergence, Progress in Nonlinear Differential Equations and their Applications 8. Birkhäuser Boston, Inc., Boston, MA (1993). [Google Scholar]
  59. P. Deák, T. Frauenheim and M.R. Pederson, Eds., Computer simulation of materials at atomic level. Wiley (2000). [Google Scholar]
  60. B.N. Delaunay, N.P. Dolbilin, M.I. Shtogrin and R.V. Galiulin, A local criterion for regularity of a system of points. Sov. Math. Dokl. 17 (1976) 319–322. [Google Scholar]
  61. G. Dolzmann, Variational Methods for Crystalline Microstructure – Analysis and Computation. Springer-Verlag (2003). [Google Scholar]
  62. W. E and B. Engquist, The Heterogeneous Multi-Scale Methods. Comm. Math. Sci. 1 (2003) 87–132. [Google Scholar]
  63. W. E and Z. Huang, Matching conditions in atomistic-continuum modeling of materials. Phys. Rev. Lett. 87 (2001) 135501. [CrossRef] [PubMed] [Google Scholar]
  64. W. E and Z. Huang, A dynamic atomistic-continuum method for the simulation of crystalline materials. J. Comp. Phys. 182 (2002) 234–261. [CrossRef] [Google Scholar]
  65. W. E and P.B. Ming, Atomistic and continuum theory of solids, I. Preprint (2003). [Google Scholar]
  66. W. E and P.B. Ming, Analysis of multiscale methods. J. Comp. Math. 22 (2004) 210–219. [Google Scholar]
  67. W. E and P.B. Ming, Cauchy-Born rule and stability of crystals: static problems. Arch. Rat. Mech. Anal. 183 (2007) 241–297. [CrossRef] [MathSciNet] [Google Scholar]
  68. M. Fago, R.L. Hayes, E.A. Carter and M. Ortiz, Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation. Phys. Rev. B 70 (2004) 100102(R). [Google Scholar]
  69. I. Fonseca, Variational methods for elastic crystals. Arch. Rat. Mech. Anal. 97 (1987) 187–220. [Google Scholar]
  70. I. Fonseca, The lower quasiconvex envelope of the stored energy function for an elastic crystal. J. Math. Pures Appl. 67 (1988) 175–195. [MathSciNet] [Google Scholar]
  71. G. Friesecke and R.D. James, A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. J. Mech. Phys. Solids 48 (2000) 1519–1540. [CrossRef] [MathSciNet] [Google Scholar]
  72. G. Friesecke, R.D. James and S. Müller, Rigorous derivation of nonlinear plate theory and geometric rigidity. C.R. Acad. Sci. Paris Sér. I 334 (2002) 173–178. [Google Scholar]
  73. G. Friesecke and F. Theil, Validity and failure of the Cauchy-Born hypothesis in a Two-Dimensional Mass-Spring Lattice. J. Nonlinear Sci. 12 (2002) 445–478. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  74. C.S. Gardner and C. Radin, The infinite-volume ground state of the Lennard-Jones potential. J. Stat. Phys. 20 (1979) 719–724. [CrossRef] [Google Scholar]
  75. G. Geymonat, F. Krasucki and S. Lenci, Analyse asymptotique du comportement d'un assemblage collé [Asymptotic analysis of the behaviour of a bonded joint]. C.R. Acad. Sci. Paris Sér. I 322 (1996) 1107–1112. [Google Scholar]
  76. G. Geymonat, F. Krasucki and S. Lenci, Mathematical analysis of a bonded joint with a soft thin adhesive. Math. Mech. Solids 4 (1999) 201–225. [CrossRef] [MathSciNet] [Google Scholar]
  77. WJ. Hehre, L. Radom, P.V.R. Shleyer and J. Pople, Ab initio molecular orbital theory. Wiley (1986). [Google Scholar]
  78. O. Iosifescu, C. Licht and G. Michaille, Variational limit of a one dimensional discrete and statistically homogeneous system of material points. Asymptot. Anal. 28 (2001) 309–329. [MathSciNet] [Google Scholar]
  79. O. Iosifescu, C. Licht and G. Michaille, Variational limit of a one-dimensional discrete and statistically homogeneous system of material points. C.R. Acad. Sci. Paris Sér. I Math. 332 (2001) 575–580. [Google Scholar]
  80. F. John, Rotation and strain. Comm. Pure Appl. Math. 14 (1961) 391–413. [CrossRef] [MathSciNet] [Google Scholar]
  81. F. John, Bounds for deformations in terms of average strains, in Inequalities III, O. Shisha Ed. (1972) 129–144. [Google Scholar]
  82. D. Kinderlehrer, Remarks about equilibrium configurations of crystals, in Material instabilities in contiuum mechanics and related mathematical problems, J.M. Ball Ed., Oxford University Press (1998) 217–242. [Google Scholar]
  83. D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rat. Mech. Anal. 115 (1991) 329–365. [Google Scholar]
  84. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [Google Scholar]
  85. O. Kirchner, L.P. Kubin and V. Pontikis Eds., Computer simulation in materials science, Kluwer (1996). [Google Scholar]
  86. H. Kitagawa, T. Aihara Jr. and Y. Kawazoe Eds., Mesoscopic dynamics of fracture, Advances in Materials Research. Springer (1998). [Google Scholar]
  87. C. Kittel, Introduction to Solid State Physics. 7th edn. Wiley (1996). [Google Scholar]
  88. J. Knap and M. Ortiz, An Analysis of the QuasiContinuum Method. J. Mech. Phys. Solids 49 (2001) 1899. [CrossRef] [Google Scholar]
  89. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems. I-II-III. Comm. Pure Appl. Math. 39 (1986) 113–137, 139–182, 353–377. [CrossRef] [MathSciNet] [Google Scholar]
  90. U. Krengel, Ergodic theorems, Studies in Mathematics 6. de Gruyter (1985). [Google Scholar]
  91. J. Kristensen, On the non-locality of quasiconvexity. Ann. Inst. H. Poincaré, Anal. Non Linéaire 16 (1999) 1–13. [Google Scholar]
  92. C. Le Bris, Computational Chemistry, in Handbook of numerical analysis, Vol. X, P.G. Ciarlet Ed., North-Holland (2003). [Google Scholar]
  93. C. Le Bris, Computational chemistry from the perspective of numerical analysis, Acta Numer. 14 (2005) 363–444. [Google Scholar]
  94. J. Li, K.J. Van Vliet, T. Zhu, S. Suresh and S. Yip, Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418 (2002) 307. [CrossRef] [PubMed] [Google Scholar]
  95. C. Licht, Comportement asymptotique d'une bande dissipative mince de faible rigidité [Asymptotic behaviour of a thin dissipative layer with low stiffness]. C.R. Acad. Sci. Paris Sér. I 317 (1993) 429–433. [Google Scholar]
  96. C. Licht and G. Michaille, Une modélisation du comportement d'un joint collé élastique [A modelling of elastic adhesively bonding joints]. C.R. Acad. Sci. Paris Sér. I 322 (1996) 295–300. [Google Scholar]
  97. E.H. Lieb, Thomas-Fermi and related theories of atoms and molecules. Rev. Modern Phys. 53 (1981) 603–641 . [Google Scholar]
  98. E.H. Lieb and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids. Adv. Math. 23 (1977) 22–116. [CrossRef] [Google Scholar]
  99. P. Lin, A nonlinear wave equation of mixed type for fracture dynamics. Research report No. 777, Department of Mathematics, The National University of Singapore, August 2000. Available at http://www.math.nus.edu.sg/ matlinp/WWW/linsiap.pdf [Google Scholar]
  100. P. Lin, Theoretical and numerical analysis of the quasi-continuum approximation of a material particle model. Math. Comput. 72 (2003) 657–675. [Google Scholar]
  101. P. Lin, Convergence analysis of a quasi-continuum approximation for a two-dimensional material. Preprint 2005-80 of the Institute for mathematical sciences, National University of Singapore (2005). Available at http://www.ims.nus.edu.sg/preprints/2005-80.pdf [Google Scholar]
  102. P. Lin and C.W. Shu, Numerical solution of a virtual internal bond model for material fracture. Physica D 167 (2002) 101–121. [CrossRef] [MathSciNet] [Google Scholar]
  103. W.K. Liu, D. Qian and M.F. Horstemeyer, Special Issue on Multiple Scale Methods for Nanoscale Mechanics and Materials. Comp. Meth. Appl. Mech. Eng. 193 (2004) 17–20. [Google Scholar]
  104. M. Luskin, On the computation of crystalline microstructure. Acta Numer. 5 (1996) 191–258. [Google Scholar]
  105. M. Luskin, Computational modeling of microstructure, in Proceedings of the International Congress of Mathematicians, ICM, Beijing (2002) 707–716. [Google Scholar]
  106. R. Miller and E.B. Tadmor, The Quasicontinuum Method: Overview, applications and current directions. J. Computer-Aided Materials Design 9 (2002) 203–239. [Google Scholar]
  107. R. Miller, E.B. Tadmor, R. Phillips and M. Ortiz, Quasicontinuum simulation of fracture at the atomic scale. Modelling Simul. Mater. Sci. Eng. 6 (1998) 607. [Google Scholar]
  108. C.B. Morrey Jr., Quasi-convexity and the lower semi-continuity of multiple integrals. Pacific J. Math. 2 (1952) 25–53. [CrossRef] [MathSciNet] [Google Scholar]
  109. S. Müller, Variational models for microstructure and phase transitions, in Calculus of Variations and Geometric Evolution Problems. Lect. Notes Math. 1713. Springer Verlag, Berlin (1999) 85–210. [Google Scholar]
  110. B.R.A. Nijboer and W.J. Ventevogel, On the configuration of systems of interacting particles with minimum potential energy per particle. Physica 98A (1979) 274. [Google Scholar]
  111. B.R.A Nijboer and W.J. Ventevogel, On the configuration of systems of interacting particles with minimum potential energy per particle. Physica 99A (1979) 569. [Google Scholar]
  112. C. Ortner, Continuum limit of a one-dimensional atomistic energy based on local minimization. Technical report 05/11, Oxford University Computing Laboratory (2005). [Google Scholar]
  113. S. Pagano and R. Paroni, A simple model for phase transitions: from the discrete to the continuum problem. Quart. Appl. Math. 61 (2003) 89–109. [MathSciNet] [Google Scholar]
  114. P. Pedregal, Parametrized Measures and Variational Principles. Birkhäuser (1997). [Google Scholar]
  115. P. Pedregal, Variational Methods in Nonlinear Elasticity. SIAM (2000). [Google Scholar]
  116. C. Pisani Ed., Quantum mechanical ab initio calculation of the properties of crystalline materials, Lecture Notes in Chemistry 67. Springer (1996). [Google Scholar]
  117. D. Raabe, Computational Material Science. Wiley (1998). [Google Scholar]
  118. C. Radin, Ground states for soft disks. J. Stat. Phys. 26 (1981) 365. [CrossRef] [Google Scholar]
  119. Y.G. Reshetnyak, Liouville's theory on conformal mappings under minimal regularity assumptions. Sibirskii Math. 8 (1967) 69–85. [Google Scholar]
  120. M.O. Rieger and J. Zimmer, Young measure flow as a model for damage, SIAM J. Math. Anal. (2005) (to appear). [Google Scholar]
  121. R.E. Rudd and J.Q. Broughton, Concurrent coupling of length scales in solid state system, in [59] 251–291. [Google Scholar]
  122. B. Schmidt, On the passage form atomic to continuum theory for thin films. Preprint 82/2005 of the Max Planck Institute of Leipzig (2005). Available at http://www.mis.mpg.de/preprints/2005/prepr2005_82.html [Google Scholar]
  123. B. Schmidt, Qualitative properties of a continuum theory for thin films. Preprint 83/2005 of the Max Planck Institute of Leipzig (2005). Available at http://www.mis.mpg.de/preprints/2005/prepr2005_83.html [Google Scholar]
  124. B. Schmidt, A derivation of continuum nonlinear plate theory form atomistic models. Preprint 90/2005 of the Max Planck Institute of Leipzig (2005). Available at http://www.mis.mpg.de/preprints/2005/prepr2005_90.html [Google Scholar]
  125. V.B. Shenoy, R. Miller, E.B. Tadmor, R. Phillips and M. Ortiz, Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80 (1998) 742. [CrossRef] [Google Scholar]
  126. V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips and M. Ortiz, An adaptative finite element approach to atomic-scale mechanics – the QuasiContinuum Method. J. Mech. Phys. Solids 47 (1999) 611. [CrossRef] [MathSciNet] [Google Scholar]
  127. J.P. Solovej, Universality in the Thomas-Fermi-von Weizsäcker model of atoms and molecules. Comm. Math. Phys. 129 (1990) 561–598. [CrossRef] [MathSciNet] [Google Scholar]
  128. V. Šveràk, On regularity for Monge-Ampère equations. Preprint, Heriott-Watt University (1991). [Google Scholar]
  129. V. Šveràk, Rank-one convexity does not imply quasiconvexity. Proc. Roy. Soc. Edinburgh A 120 (1992) 185–189. [Google Scholar]
  130. V. Šveràk, On the problem of two wells, in Microstructure and phase transition, IMA Vol. Math. Appl. 54. Springer, New York, (1993) 183–189. [Google Scholar]
  131. A. Szabo and N.S. Ostlund, Modern quantum chemistry: an introduction. Macmillan (1982). [Google Scholar]
  132. E.B. Tadmor and R. Phillips, Mixed atomistic and continuum models of deformation in solids. Langmuir 12 (1996) 4529. [CrossRef] [Google Scholar]
  133. E.B. Tadmor, M. Ortiz and R. Phillips, Quasicontinuum analysis of defects in solids. Phil. Mag. A. 73 (1996) 1529–1563. [Google Scholar]
  134. E.B. Tadmor, G.S. Smith, N. Bernstein and E. Kaxiras, Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B 59 (1999) 235. [CrossRef] [Google Scholar]
  135. F. Theil, A proof of crystallization in two dimensions. Comm. Math. Phys. 262 (2006) 209–236. [Google Scholar]
  136. L. Truskinovsky, Fracture as a phase transformation, in Contemp. Res. in Mech. and Math. of Materials, Ericksen's symposium, R. Batra and M. Beatty Eds., CIMNE, Barcelone (1996) 322–332. [Google Scholar]
  137. W.J. Ventevogel, On the configuration of a one-dimensional system of interacting particles with minimum potential energy per particle. Physica 92A (1978) 343. [Google Scholar]
  138. S. Yip, Synergistic materials science. Nature Mater. 2 (2003) 3–5. [CrossRef] [Google Scholar]
  139. L.C. Young, Lectures on the calculus of variations and optimal control theory. W.B. Saunders Co., Philadelphia-London-Toronto (1969). [Google Scholar]
  140. F. Zaittouni, F. Lebon and C. Licht, Étude théorique et numérique du comportement d'un assemblage de plaques [Theoretical study of the behaviour of bonded plates]. C.R. Mécanique 330 (2002) 359–364. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you