The energy of some microscopic stochastic lattices
From MaRDI portal
Publication:877818
DOI10.1007/s00205-006-0028-2zbMath1173.82308OpenAlexW2027769455MaRDI QIDQ877818
Pierre-Louis Lions, Xavier Blanc, Claude Le Bris
Publication date: 3 May 2007
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-006-0028-2
Related Items
Homogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting), Stochastic homogenization and random lattices, On the crystal ground state in the Schrödinger-Poisson model with point ions, Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions, Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions, A variant of stochastic homogenization theory for elliptic operators., Non-local energetics of random heterogeneous lattices, Aperiodic fractional obstacle problems, Mean-field models for disordered crystals, Continuum limit and stochastic homogenization of discrete ferromagnetic thin films, On null-homology and stationary sequences, Discrete stochastic approximations of the Mumford-Shah functional, Asymptotic behavior of the Dirichlet energy on Poisson point clouds, Variance reduction for effective energies of random lattices in the Thomas–Fermi–von Weizsäcker model, Atomic to continuum passage for nanotubes: a discrete Saint-Venant principle and error estimates, Mathematical derivation of a rubber-like stored energy functional, ELASTIC LIMIT OF SQUARE LATTICES WITH THREE-POINT INTERACTIONS, Discrete to continuum limit for some models of stochastic lattices of atoms, Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity, Thermodynamic limit of crystal defects with finite temperature tight binding, Atomistic to Continuum limits for computational materials science, The reduced Hartree-Fock model for short-range quantum crystals with nonlocal defects, Homogenization of random convolution energies, QM/MM Methods for Crystalline Defects. Part 1: Locality of the Tight Binding Model, From statistical polymer physics to nonlinear elasticity, Point defects in tight binding models for insulators, The reduced Hartree-Fock model with self-generated magnetic fields, Homogenization of ferromagnetic energies on Poisson random sets in the plane, On the Crystal Ground State in the Schrödinger--Poisson Model, MATHEMATICAL MODELING OF POINT DEFECTS IN MATERIALS SCIENCE, Existence of the thermodynamic limit for disordered quantum Coulomb systems
Cites Work
- A proof of crystallization in two dimensions
- Universality in the Thomas-Fermi-von Weizsäcker model of atoms and molecules
- Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
- Ergodic theorems. With a supplement by Antoine Brunel
- The Thomas-Fermi theory of atoms, molecules and solids
- Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
- On some periodic Hartree-type models for crystals
- From molecular models to continuum mechanics
- A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods
- Discrete to continuum limit for some models of stochastic lattices of atoms
- Variational limit of a one-dimensional discrete and statistically homogeneous system of material points
- Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus
- Thomas-fermi and related theories of atoms and molecules
- Sur la limite thermodynamique pour des modèles de type Hartree et Hartree-Fock
- A simple model for phase transitions: from the discrete to the continuum problem
- NON-LOCAL VARIATIONAL LIMITS OF DISCRETE SYSTEMS
- A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
- A Definition of the Ground State Energy for Systems Composed of Infinitely Many Particles
- On the thermodynamic limit for Hartree-Fock type models
- Periodicity of the infinite-volume ground state of a one-dimensional quantum model
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item