We study the asymptotic behaviour in terms of Γ-convergence of the following one dimensional energy

Let Γ be a finitely generated group having the property that any action of any finite-index subgroup of Γ by homeomorphisms of the circle must have a finite orbit. (By a theorem of É. Ghys, lattices in simple Lie groups of real rank at least 2 have this property.) Suppose that such a Γ acts on a compact manifold M by automorphisms of a codimension-one C foliation, F . We show that if F has a co...

In this paper, we consider the derivation of the modified Wenzel’s and Cassie’s equations for wetting phenomena on rough surfaces from a three-dimensional phase field model. We derive an effective boundary condition by asymptotic two-scale homogenization technique when the size of the roughness is small. The modified Wenzel’s and Cassie’s equations for the apparent contact angles on the rough s...

We investigate, using the framework of Γ-convergence, a phase-field model proposed in [Torabi et al, Proc. R. Soc. A, 2009] for strongly anisotropic systems; in particular, we prove a full Γ-convergence result for an anisotropic Modica-Mortolatype energy.

We show that every word hyperbolic, surface-by-(noncyclic) free group Γ is as rigid as possible: the quasi-isometry group of Γ equals the abstract commensurator group Comm(Γ), which in turn contains Γ as a finite index subgroup. As a corollary, two such groups are quasi-isometric if and only if they are commensurable, and any finitely generated group quasi-isometric to Γ must be weakly commensu...

Let Γ < SLn(Z) be a subgroup of finite index, where n≥5. Suppose Γ acts continuously on a manifold M , where π1(M) = Z n, preserving a measure that is positive on open sets. Further assume that the induced Γ action on H(M) is non-trivial. We show there exists a finite index subgroup Γ′ < Γ and a Γ′ equivariant continuous map ψ :M→Tn that induces an isomorphism on fundamental group. We prove mor...

In this paper we study the set Γn of nth-powers in certain finitely generated groups Γ. We show that, if Γ is soluble or linear, and Γn contains a finite index subgroup, then Γ is nilpotent-by-finite. We also show that, if Γ is linear and Γn has finite index (i.e. Γ may be covered by finitely many translations of Γn), then Γ is soluble-by-finite. The proof applies invariant measures on amenable...

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γ-convergence.

We introduce new definitions of convergence, based on adding stability criteria to Γ-convergence, that are suitable in many cases for studying convergence of local minimizers.

We study the Γ-convergence of the power-law functionals