We study, by means of Γ-convergence, the asymptotic behaviour of a variational problem modeling a dislocation ensemble moving on a slip plane through a discrete array of obstacles. The variational problem is a two dimensional phase transition type energy given by a non local term and a non linear potential which penalizes non integer values. In this paper we consider a regime corresponding to a...

One-dimensional γ-Al2O3 nanofibers were modified with Nb2O5 to be used as an efficient heterogeneous catalyst to catalyze biomass into 5-hydroxymethylfurfural (5-HMF). At low Nb2O5 loading, the niobia species were well dispersed on γ-Al2O3 nanofiber through Nb-O-Al bridge bonds. The interaction between Nb2O5 precursor and γ-Al2O3 nanofiber results in the niobia species with strong Lewis acid si...

The convenient, high yielding and diastereoselective synthesis of α-amino-β-substituted-γ,γ-disubstituted butyric acid derivatives was carried out by a three-component tandem reaction of a chiral equivalent of nucleophilic glycine. The reaction was performed smoothly under mild conditions and enabled the construction of two or three adjacent chiral centers in one step, thus affording a novel an...

This note completely resolves the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional, by showing that one of the critical assumptions of the authors’ previous work [10] is unnecessary.

Γ-convergence results for power-law functionals with variable exponents are obtained. The main motivation comes from the study of (first-failure) dielectric breakdown. Some connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. 2000 Mathematics Subject Classification:

We study variational problems with volume constraints (also called level set constraints) of the form

We consider a thin curved film made of a martensitic material. The behavior of the film is governed by a free energy composed of a bulk energy term and an interfacial energy term. We show that the minimizers of the free energy converge to the minimizers of an energy depending on a two-dimensional deformation and one Cosserat vector field when the thickness of the curved film goes to zero. using...

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all L and certain Orlicz spaces for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher [1] for the coercive two-well case. The theorem has applications to a certain thin-f...