Mariapia Palombaro

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We prove that for any connected open set Ω ⊂ Rn and for any set of matrices K = {A1, A2, A3} ⊂ M m×n, with m ≥ n and rank(Ai − Aj) = n for i 6= j, there is no non-constant solution B ∈ L∞(Ω,Mm×n), called exact solution, to the problem DivB = 0 in D(Ω,R) and B(x) ∈ K a.e. in Ω . In contrast, A. Garroni and V. Nesi [10] exhibited an example of set K for which(More)
Abstract. We study the homogenization and singular perturbation of the wave equation in a periodic media for long times of the order of the inverse of the period. We consider inital data that are Bloch wave packets, i.e., that are the product of a fast oscillating Bloch wave and of a smooth envelope function. We prove that the solution is approximately(More)
We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of(More)
We study, for times of order 1/ε, solutions of wave equations which are O(ε2) modulations of an ε periodic wave equation. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order ε. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity(More)
We discuss an atomistic model for heterogeneous nanowires, allowing for dislocations at the interface. We study the limit as the atomic distance converges to zero, considering simultaneously a dimension reduction and the passage from discrete to continuum. Employing the notion of Gamma-convergence, we establish the minimal energies associated to defect-free(More)
Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By employing the notion of Gamma-convergence and a geometric rigidity estimate, we perform a discrete to continuum limit and a(More)
In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit(More)