A 3D-2D dimensional reduction analysis for supremal functionals is performed in the realm of Γ-convergence. We show that the limit functional still admits a supremal representation, and we provide a precise identification of its density in some particular cases. Our results rely on an abstract representation theorem for the Γ-limit of a family of supremal functionals. Mathematics Subject Classi...

This paper deals with the passage from discrete to continuous in modeling the static elastic properties, in the setting of anti-planar linear elasticity, of vertical screw dislocations in a cylindrical crystal. We study, in the framework of Γ-convergence, the asymptotic behavior of the elastic stored energy induced by dislocations as the atomic scale ε tends to zero, in the regime of dilute dis...

We deal with a class of reaction-diffusion equations, in space dimension d > 1, perturbed by a Gaussian noise ∂wδ/∂t which is white in time and colored in space. We assume that the noise has a small correlation radius δ, so that it converges to the white noise ∂w/∂t, as δ ↓ 0. By using arguments of Γ-convergence, we prove that, under suitable assumptions, the quasi-potential Vδ converges to the...

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Γ-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either ho...

We prove the stability of a large class of unilateral minimality properties which arise naturally in the theory of crack propagation proposed by Francfort and Marigo in [22]. Then we give an application to the quasistatic evolution of cracks in composite materials.

We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus non-convex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

This report describes a low cost, shielded enclosure that was developed to contain the electromagnetic radiation generated by electronic equipment in order to reduce the potential for radio frequency interference (RFI). The enclosure is made from thin wire mesh screening that is attached to a wooden framework for support. Allowances are made at both ends of the enclosure for large cable bulkhea...

—We present the results of systematic comparison of 2D and 3D numerical models of mass transfer in semidetached binaries. It is shown that only for case of γ ∼ 1 (near-isothermal case) the obtained 2D and 3D solutions are qualitatively similar. For higher value of γ the 3D flow structure is drastically changed and for γ = 1.2 the accretion disk is not formed in the system. Numerical results sho...