Motion and pinning of discrete interfaces

DOI10.1007/s00205-009-0215-zzbMath1186.82054OpenAlexW1979571634MaRDI QIDQ849240

Maria Stella Gelli, Andrea Braides, Matteo Novaga

Publication date: 25 February 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-009-0215-z

zbMATH Keywords

motion of interfacesdiscrete-continuous analysis

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Particle methods and lattice-gas methods (76M28) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21)

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Cites Work

• Unnamed Item
• Unnamed Item
• Variational analysis of the asymptotics of the \(XY\) model
• On total variation minimization and surface evolution using parametric maximum flows
• Homogenization of contact line dynamics
• Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint
• Convergence of discrete schemes for the Perona-Malik equation
• The heat equation shrinking convex plane curves
• Approximation of free-discontinuity problems
• Quenching and propagation of bistable reaction-diffusion fronts in multidimensional periodic media
• Stability of front solutions in inhomogeneous media
• Effective motion of a curvature-sensitive interface through a heterogeneous medium
• Flat flow is motion by crystalline curvature for curves with crystalline energies
• Propagation failure of traveling waves in a discrete bistable medium
• Pinning and de-pinning phenomena in front propagation in heterogeneous media
• Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications
• Variational description of bulk energies for bounded and unbounded spin systems
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice
• Uniqueness of self-similar solutions for a crystalline flow
• Depinning Transitions in Discrete Reaction-Diffusion Equations
• A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
• Curvature-Driven Flows: A Variational Approach