Gradient damage models for heterogeneous materials
A Bach, T Esposito, R Marziani, CI Zeppieri - SIAM Journal on Mathematical …, 2023 - SIAM
In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and
Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse …
Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse …
-Convergence and Stochastic Homogenization of Second-Order Singular Perturbation Models for Phase Transitions
AF Donnarumma - Journal of Nonlinear Science, 2025 - Springer
We study the effective behavior of random, heterogeneous, anisotropic, second-order phase
transitions energies that arise in the study of pattern formations in physical–chemical …
transitions energies that arise in the study of pattern formations in physical–chemical …
A note on spatially inhomogeneous Cahn-Hilliard energies
S Wojtowytsch - arXiv preprint arXiv:2408.02154, 2024 - arxiv.org
In 2023, Cristoferi, Fonseca and Ganedi proved that Cahn-Hilliard type energies with
spatially inhomogeneous potentials converge to the usual (isotropic and homogeneous) …
spatially inhomogeneous potentials converge to the usual (isotropic and homogeneous) …
Diffuse Interface Energies with Microscopic Heterogeneities: Homogenization and Rare Events
PS Morfe, C Wagner - arXiv preprint arXiv:2408.14914, 2024 - arxiv.org
We analyze Allen-Cahn functionals with stationary ergodic coefficients in the regime where
the length scale $\delta $ of the heterogeneities is much smaller (microscopic) than the …
the length scale $\delta $ of the heterogeneities is much smaller (microscopic) than the …
From discrete to continuum in the helical XY-model: emergence of chirality transitions in the to limit
M Cicalese, D Reggiani, F Solombrino - arXiv preprint arXiv:2412.15994, 2024 - arxiv.org
We analyze the discrete-to-continuum limit of a frustrated ferromagnetic/anti-ferromagnetic
$\mathbb {S}^ 2$-valued spin system on the lattice $\lambda_n\mathbb {Z}^ 2$ as …
$\mathbb {S}^ 2$-valued spin system on the lattice $\lambda_n\mathbb {Z}^ 2$ as …
[PDF][PDF] Γ-Convergence and Applications to Phase Transitions
I Fonseca - math.utk.edu
In this series of lectures, we will study the notion of Γ-convergence, as introduced by De
Giorgi in 1975 (see [13]), to rigorously derive the classical model for phase transitions …
Giorgi in 1975 (see [13]), to rigorously derive the classical model for phase transitions …