1,720,972 research outputs found
A bridging mechanism in the homogenization of brittle composites with soft inclusions
Full text linkWe provide a homogenization result for the energy-functional associated with a purely brittle composite whose microstructure is characterized by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale to obtain, in the limit as tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack
Γ-convergence of free-discontinuity problems
No full textWe study the Γ-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Γ-convergence, representation of the Γ-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper
New results on Gamma-limits of integral functionals
Full text linkFor Psi is an element of W-1,W-p (Omega; R-m) and g is an element of W--1,W-p (Omega;R-d), 1 [0, +infinity] of the form F-k(Psi,g) (u, v) = {integral(Omega) f(k)(x, del u, v) if u - Psi is an element of W-0(1,p) (Omega; R-m) and div upsilon = g, where the integrands f(k) satisfy growth conditions of order p, uniformly in k. We prove a Gamma-compactness result for F-k(Psi,g) with respect to the weak topology of W-1,W-P (Omega; R-m) x L-p (Omega; R-dxn) and we show that under suitable assumptions the integrand of the Gamma-limit is continuously differentiable. We also provide a result concerning the convergence of momenta for minimizers of F-k(Psi,g) (C) 2013 Elsevier Masson SAS. All rights reserved
Quantitative analysis of finite-difference approximations of free-discontinuity problems
Full text linkMotivated by applications to image reconstruction, in this paper we analyse a finite-difference discretisation of the Ambrosio–Tortorelli functional. Denoted by " the elliptic-approximation parameter and by i the discretisation step-size, we fully describe the relative impact of " and i in terms of limits for the corresponding discrete functionals, in the three possible scaling regimes. We show, in particular, that when " and i are of the same order, the underlying lattice structure affects the -limit which turns out to be an anisotropic free-discontinuity functional
Asymptotic analysis of a second-order singular perturbation model for phase transitions
No full textWe study the asymptotic behavior, as tends to zero, of the functionals introduced by Coleman and Mizel in the theory of nonlinear second-order materials.
By proving a new nonlinear interpolation inequality, we show a Γ-convergence result. Moreover, in the special case of the classical potential, we provide an upper bound on the values of k such that the minimizers of the functional cannot develop oscillations on some fine scale and a lower bound on the values for which oscillations occur, the latter improving a previous estimate by Mizel, Peletier and Troy
Discrete-to-continuum limits for strain-alignment-coupled systems: magnetostrictive solids, ferroelectric crystals and nematic elastomers
Full text linkpreprint (download@http://cvgmt.sns.it
A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation
Full text linkIn this note we formulate a sufficient condition for the quasiconvexity at x ____mapsto ____l x of certain functionals which model the stored-energy of elastic materials subject to a deformation . The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to M'{u}ller and Spector, on admissible deformations. Deformations obey the condition u(x)= ____lambda x whenever belongs to the boundary of the domain initially occupied by the material. In terms of the parameters of the models, our analysis provides an explicit ____lambda_0>0 such that for every ____lambda____in (0,____lambda_0] it holds that I(u) ____geq I(u_{____lambda}) for all admissible , where u_{____lambda} is the linear map x ____mapsto ____lambda x applied across the entire domain. This is the quasiconvexity condition referred to above
Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations
Full text linkIn this paper we study the convergence of integral functionals with
-growth in a randomly perforated domain of , with .
Under the assumption that the perforations are small balls whose centres and
radii are generated by a \emph{stationary short-range marked point process}, we
obtain in the critical-scaling limit an averaged analogue of the nonlinear
capacitary term obtained by Ansini and Braides in the deterministic periodic
case \cite{Ansini-Braides}. In analogy to the random setting introduced by
Giunti, H\"ofer, and Vel\'azquez \cite{Giunti-Hofer-Velasquez} to study the
Poisson equation, we only require that the random radii have finite
-moment. This assumption on the one hand ensures that the expectation of
the nonlinear -capacity of the spherical holes is finite, and hence that the
limit problem is well defined. On the other hand, it does not exclude the
presence of balls with large radii, that can cluster up. We show however that
the critical rescaling of the perforations is sufficient to ensure that no
percolating-like structures appear in the limit.Comment: 51 pages, 3 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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