Mathematical theory of solids: from quantum mechanics to continuum models

DOI10.3934/DCDS.2014.34.5085zbMath1305.35120OpenAlexW2317076630MaRDI QIDQ476600

E. Weinan, Jian-feng Lu

Publication date: 2 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.5085

zbMATH Keywords

density functional theoryatomistic modelmultiscale modelingCauchy-Born rule

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of solids (82D20)

Cites Work

• Unnamed Item
• The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule
• Cauchy-Born rule and the stability of crystalline solids: Static problems
• Sufficient conditions for the validity of the Cauchy-Born rule close to \(\mathrm{SO}(n)\)
• The dielectric permittivity of crystals in the reduced Hartree-Fock approximation
• Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
• From molecular models to continuum mechanics
• Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice
• A mathematical formulation of the random phase approximation for crystals
• Effective Maxwell equations from time-dependent density functional theory
• Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model
• Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes
• The Kohn-Sham equation for deformed crystals

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