Related papers: Higher-order singular perturbation models for phas…
We discuss a model for phase transitions in which a double-well potential is singularly perturbed by possibly several terms involving different, arbitrarily high orders of derivation. We study by $\Gamma$-convergence the asymptotic…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
We investigate the $\limsup$ inequality in the double gradient model for phase transitions governed by a Modica--Mortola functional with a double-well potential in two dimensions. Specifically, we consider energy functionals of the form \[…
A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…
We study the asymptotic behaviour of double-well energies perturbed by a higher-order fractional term, which, in the one-dimensional case, take the form $$ \frac{1}{\varepsilon}\int_I…
In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…
We study the limit behavior of Cahn--Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the…
In 2023, Cristoferi, Fonseca and Ganedi proved that Cahn-Hilliard type energies with spatially inhomogeneous potentials converge to the usual (isotropic and homogeneous) perimeter functional if the length-scale $\delta$ of spatial…
A vectorial Modica--Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain…
By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the Gamma limit of a single-well Modica-Mortola functional. The…
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the…
The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularization designed to balance bulk and…
An explicit representation of the Gamma limit of a single-well Modica--Mortola functional is given for one-dimensional space under the graph convergence which is finer than conventional $L^1$-convergence or convergence in measure. As an…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on…
This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…
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 systems. Specifically, we study the asymptotic behavior, as…
A variational model for the interaction between homogenization and phase separation is considered in the regime where the former happens at a finer scale than the latter. The first order $\Gamma-$limit is proven to exhibit a separation of…