this discrete model can be approximated by a continuous energy defined on special functions with bounded variation. In fact, if we limit the interactions in the sum to the nearest neighbors in the portion of εZ contained in some fixed Ω, and we interpret the values ui as the discretization of a function defined in Ω, then these energies can be studied using the methods of Γ-convergence, and the...

We study the asymptotic behavior of functionals associated to the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness (proportional to a small parameter) ε and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The transition shell-membr...

In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indic...

We present the second of two articles on the small volume-fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. After having established the results for the sharp-interface version of the functional [SIAM J. Math. Anal., 42 (2010), pp. 1334–1370], we consider here the full diffuse-interface functional and address the limit in whic...

A weak transverse static magnetic field (WTSMF, 0–0.5 T) is applied to the directional solidification process of a DD3 Ni-based SX superalloy, aiming tailor microstructure and microsegregation alloys. The mechanisms microstructural refinement distribution caused by WTSMF during are discussed. It shown that primary dendrite arm spacing rapidly reduced from 181 143 μm, average size γ′ phase signi...

We point out that a simple test of the mechanism of CP violation can be performed by a measurement of the CP asymmetries in exclusive and inclusive radiative rare decays. We show that the rate asymmetries ∆Γ = Γ(B → fγ)− Γ(B+ → f̄γ) for certain final states f can be predicted in a theoretically clean way. Some implications for b → sl+l− decays are discussed.

A mild, green and highly efficient route for regio-selective amination of oxiranes was developed via incorporation of Mn(II), Fe(II), Co(II), Ni(II), Cu(II) and Zn(II) cations onto the surface of hydroxyapatite-encapsulated γ-Fe2O3 nanoparticles (γ-Fe2O3@HAp). Among six magnetically recoverable catalytic systems denoted as [γ-Fe2O3@HAp-MII], the catalyst in which M designated as Fe(II) showed t...

Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Γ(G) the fundamental group of X(G). We show that Γ(G) is a limit of colored braid groups over the poset of simplices of G. When G = GT is the comparability graph associated with a rooted tree T , a case recently investigated by the first author, the result takes the following very simple form: Γ(GT ) is a li...

If Γ is any finite graph, then the unlabelled configuration space of n points on Γ, denoted UCΓ, is the space of n-element subsets of Γ. The braid group of Γ on n strands is the fundamental group of UC Γ. We apply a discrete version of Morse theory to these UCΓ, for any n and any Γ, and provide a clear description of the critical cells in every case. As a result, we can calculate a presentation...