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.

livestock grazing is one of the most important kinds of land usage that has a high potential to decrease or increase carbon storage in rangeland ecosystem. this research was investigated the effects of enclosure on soil carbon storage in a rangeland with dominant plants of artemisia aucheri. hence, two rangelands of enclosure (shahtappeh-chah mahmood) and no enclosure (chiro) were chosen in sem...

Numerical study of double-diffusive natural convective heat transfer in a curved cavity filledwith a porous medium has been carried out in the current study. Polar system has beenselected as coordinate system. As a result, all equations have been discredited in r and θdirections. Brinkmann extended Darcy model has been utilized to express fluid flow inporous matrix in the enclosure. Smaller and...

Based on the necessity for enclosure protection of temperature and relative humidity sensors installed in a hostile environment, a wind tunnel was used to quantify the time that the sensors take to reach equilibrium in the environmental conditions to which they are exposed. Two treatments were used: (1) sensors with polyvinyl chloride (PVC) enclosure protection, and (2) sensors with no enclosur...

At present advanced projects of the early XXI century are beginning to develop. These projects include lunar base development and manned missions to Mars. The space suit is one of the basic requirements for successful implementation of future programs. The space suit enclosure enables mobility of crewmembers wearing pressurized space suits which will be required to complete these missions. Requ...

The epiboly of the Caenorhabditis elegans hypodermis involves the bilateral spreading of a thin epithelial sheet from the dorsal side around the embryo to meet at the ventral midline in a process known as ventral enclosure. We present evidence that ventral enclosure occurs in two major steps. The initial migration of the hypodermis is led by a quartet of cells, which exhibit protrusive activity...