Elisa Davoli

Wulff shape emergence in graphene

Graphene samples are identified as minimizers of configurational energies featuring both two- and three-body atomic-interaction terms. This variational viewpoint allows for a detailed description of ground-state geometries as connected subsets of a regular hexagonal lattice. We investigate here how these geometries evolve as the number n of carbon atoms in the graphene sample increases. By means of an equivalent characterization of minimality via a discrete isoperimetric inequality, we prove that ground states converge to the ideal hexagonal Wulff shape as n →∞. Precisely, ground states deviate from such hexagonal Wulff shape by at most Kn3/4 + o(n3/4) atoms, where both the constant K and the rate n3/4 are sharp.

Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity

In this paper we deduce by {\Gamma}-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order {\epsilon}^ (2{\alpha}-2), with {\alpha}>=3. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on {\alpha}.

Homogenization of integral energies under periodically oscillating differential constraints

A homogenization result for a family of integral energies

Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity

\begin{aligned} u_{\varepsilon }\mapsto \int _\Omega f(u_{\varepsilon }(x))\,dx,\quad \varepsilon \rightarrow 0^+, \end{aligned}

Sharp N^{3/4} Law for the Minimizers of the Edge-Isoperimetric Problem on the Triangular Lattice

uε↦∫Ωf(uε(x))dx,ε→0+,is presented, where the fields

Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints

u_{\varepsilon }