Discrete-to-Continuum Limits of Multibody Systems with Bulk and Surface Long-Range Interactions
From MaRDI portal
Publication:5116575
DOI10.1137/19M1289212zbMath1446.49009arXiv1910.00346OpenAlexW3047065793MaRDI QIDQ5116575
Annika Bach, Marco Cicalese, Andrea Braides
Publication date: 18 August 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.00346
homogenization\(\Gamma\)-convergencemultibody interactionsdiscrete-to-continuumfree-discontinuity functionals
Methods involving semicontinuity and convergence; relaxation (49J45) Discrete approximations in optimal control (49M25) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)
Related Items
From atomistic systems to linearized continuum models for elastic materials with voids ⋮ Homogenisation of dynamical optimal transport on periodic graphs ⋮ A Bending-Torsion Theory for Thin and Ultrathin Rods as a \(\boldsymbol{\Gamma}\)-Limit of Atomistic Models ⋮ Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems ⋮ Discrete-to-continuum limits of long-range electrical interactions in nanostructures ⋮ Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy ⋮ The antiferromagnetic \(XY\) model on the triangular lattice: chirality transitions at the surface scaling ⋮ Homogenization of ferromagnetic energies on Poisson random sets in the plane
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Continuum limit of total variation on point clouds
- Domain formation in magnetic polymer composites: an approach via stochastic homogenization
- Interfaces, modulated phases and textures in lattice systems
- Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity
- Cauchy-Born rule and the stability of crystalline solids: Static problems
- The variational approach to fracture
- Continuum limits of discrete thin films with superlinear growth densities
- Approximation of free-discontinuity problems
- Variational methods in image segmentation with 7 image processing experiments
- An introduction to \(\Gamma\)-convergence
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- Continuum limit and stochastic homogenization of discrete ferromagnetic thin films
- On Lennard-Jones systems with finite range interactions and their asymptotic analysis
- Quasistatic crack growth in nonlinear elasticity
- From molecular models to continuum mechanics
- From statistical polymer physics to nonlinear elasticity
- Homogenization of free discontinuity problems
- Discrete stochastic approximations of the Mumford-Shah functional
- \(\Gamma\)-convergence of free-discontinuity problems
- On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth
- Effective cohesive behavior of layers of interatomic planes
- Local and Nonlocal Continuum Limits of Ising-Type Energies for Spin Systems
- Finite-differences discretizations of the mumford-shah functional
- Analysis of Concentration and Oscillation Effects Generated by Gradients
- NON-LOCAL VARIATIONAL LIMITS OF DISCRETE SYSTEMS
- An Integral-Representation Result for Continuum Limits of Discrete Energies with MultiBody Interactions
- A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
- A density result in SBV with respect to non-isotropic energies
- Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
- Mumford–Shah functionals on graphs and their asymptotics
- Analysis of $p$-Laplacian Regularization in Semisupervised Learning
- Atomistic to Continuum limits for computational materials science
- $Q$-Tensor Continuum Energies as Limits of Head-to-Tail Symmetric Spin Systems