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...

In the present study, adsorption of Co(tsPc)-4 using γ-Alumina was investigated. γ-Alumina was prepared by gel combustion method. The XRD pattern revealed that the synthesized γ-Alumina is amorphous and SEM image showed its nanosize scale while BET surface area about 501 m2/g and pore size of 7 nm implies highly porous surface which is a characteristic property of a high-quality adsorbent. In t...

Nickel-based superalloys have been widely used for elevated temperature applications such as turbine disc of jet engines due to their excellent mechanical properties. The typical microstructure of these alloys primarily consists of dispersed precipitates of the ordered γ’ phase with L12 structure within a disordered face-centered cubic γ matrix. The γ -γ’ microstructure in these alloys can be c...

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...

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via Γ-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

the concept of  -semihyperring is a generalization of semiring, a generalization of semihyperring and a generalization of      -semiring. since the theory of ideals plays an important role in the theory of  - semihyperring, in this paper, we will make an intensive study of the notions of noetherian, artinian, simple and   regular      -semihyperrings. the bulk of this paper...