GEOMETRY OPTIMIZATION FOR CRYSTALS IN THOMAS–FERMI TYPE THEORIES OF SOLIDS

DOI10.1081/PDE-100001767zbMath1022.82017MaRDI QIDQ2747890

Xavier Blanc

Publication date: 2 November 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

stabilityexistence of minimumpolymers and thin filmsTFW energyThomas-Fermi-von Weizsäcker solid-state setting

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Statistical mechanics of polymers (82D60) Statistical mechanics of crystals (82D25) Molecular physics (81V55) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (6)

Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms ⋮ Optimal lattice configurations for interacting spatially extended particles ⋮ Atomistic to Continuum limits for computational materials science ⋮ Optimal and non-optimal lattices for non-completely monotone interaction potentials ⋮ From atoms to crystals: a mathematical journey ⋮ Minimal soft lattice theta functions

Cites Work

• Unnamed Item
• Universality in the Thomas-Fermi-von Weizsäcker model of atoms and molecules
• The Thomas-Fermi-von Weizsäcker theory of atoms and molecules
• The Thomas-Fermi theory of atoms, molecules and solids
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Schauder estimates by scaling
• Sharp condition on the decay of the potential for the absence of a zero-energy ground state of the Schrodinger equation
• A ecessary and Sufficient Condition for The Stability of General molecular Systems
• Optimisation de géométrie dans le cadre des théories de type Thomas—Fermi pour les cristaux périodiques

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