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.

هدف: سرطان از جمله مهمترین بیماری­های قرن حاضر است که افراد بسیاری در سراسر جهان به آن مبتلا می­باشند و ضمن افزایش شیوع این بیماری، هنوز درمان مناسبی برای پیدا نشده است. بین پستان شایع­ترین همچنین علت اصلی مرگ میر ناشی زنان محققان بدنبال یافتن راهکارهای درمانی سرطان، ترکیبات دارویی را علیه سرطان­های مختلف سنتز کرده اثرات آ­نها مورد مطالعه قرار می­دهند. سورافنیب یک مهار کننده­ی اوره مولتی­کیناز ...