Surface tension and \(\Gamma\)-convergence of Van der Waals-Cahn-Hilliard phase transitions in stationary ergodic media

DOI10.1007/s10955-020-02662-5zbMath1483.53119arXiv1910.07682OpenAlexW3094400935WikidataQ114225342 ScholiaQ114225342MaRDI QIDQ2659344

Peter S. Morfe

Publication date: 26 March 2021

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.07682

zbMATH Keywords

phase transitionsstochastic homogenization\(\Gamma\)-convergenceAllen-Cahn functionaldeterministic Finsler normstationary ergodic Finsler metric

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Phase transitions (general) in equilibrium statistical mechanics (82B26) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (6)

A variational principle for pulsating standing waves and an Einstein relation in the sharp interface limit ⋮ Comparison principles for second-order elliptic/parabolic equations with discontinuities in the gradient compatible with Finsler norms ⋮ \(\Gamma\)-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals ⋮ Gradient Damage Models for Heterogeneous Materials ⋮ Γ-convergence and stochastic homogenisation of phase-transition functionals ⋮ Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions

Cites Work

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• Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
• Domain formation in magnetic polymer composites: an approach via stochastic homogenization
• Scaling limits in statistical mechanics and microstructures in continuum mechanics
• Surface tension in the dilute Ising model. The Wulff construction
• Convexity properties of the surface tension and equilibrium crystals
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Approximation of free-discontinuity problems
• An introduction to \(\Gamma\)-convergence
• A new approach to front propagation problems: theory and applications
• Isoperimetry in supercritical bond percolation in dimensions three and higher
• The gradient theory of phase transitions and the minimal interface criterion
• Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media
• Stochastic homogenisation of free-discontinuity problems
• Motion by curvature by scaling nonlocal evolution equations
• Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field
• A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies
• The Diffuse Interface Approach in Materials Science
• Gradient theory of phase transitions in composite media
• Planelike minimizers in periodic media
• Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals
• Free Energy of a Nonuniform System. I. Interfacial Free Energy

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