The process of global economic integration is justified by the primary goal of inclusive and balanced growth for all economies, so it is relevant to identify the extent to which this goal has been ...achieved. This research evaluates whether the member economies of the Asia-Pacific Economic Cooperation (APEC) have experienced economic convergence during the 1960–1990 (pre-APEC) and 1990–2020 (post-APEC) periods. For this purpose, beta, sigma and gamma convergence are estimated, which are methodological approaches proposed by Barro and Sala-i-Martin (1991, Brookings Papers on Economic Activity, 1991(1), 170–182) and Marchante et al. (2006, Fundación de Estudios de Economía Aplicada Working Papers No. 2006-05), for APEC as a region and for the high- and middle-income economies that conform it. The results show that the process of economic convergence among APEC members intensified after its formation in 1989 and that the region can be categorized as an ‘economic convergence club’. As well as that, the high- and middle-income groups are converging towards their respective stationary state.
In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study ...can be written as gradient flows of functionals at different levels: in the set of probability measures, in the set of symmetric probability measures on N variables, and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to complete the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the confining and interaction potentials is crucial for the unique identification of the limits and for deriving the EVIs at each description level of the interacting particle system.
We derive a dimensionally-reduced limit theory for an n-dimensional nonlinear elastic body that is slender along k dimensions. The starting point is to view an elastic body as an n-dimensional ...Riemannian manifold together with a not necessarily isometric W1,2-immersion in n-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally-reduced limit theory views the elastic body as a k-dimensional Riemannian manifold along with an isometric W2,2-immersion in n-dimensional Euclidean space and linear data in the normal directions. The equilibrium configuration minimizes a functional depending on the average covariant derivatives of the linear data. The dimensionally-reduced limit is obtained using a Γ-convergence approach. The limit includes as particular cases plate, shell, and rod theories. It applies equally to “standard” elasticity and to “incompatible” elasticity, thus including as particular cases so-called non-Euclidean plate, shell, and rod theories.
Some nonlocal optimal design problems Fernández Bonder, Julián; Spedaletti, Juan F.
Journal of mathematical analysis and applications,
03/2018, Volume:
459, Issue:
2
Journal Article
Peer reviewed
Open access
In this paper we study two optimal design problems associated to fractional Sobolev spaces Ws,p(Ω). Then we find a relationship between these two problems and finally we investigate the convergence ...when s↑1.
•Convergence analysis in order to assess the value of the approximated fracture energy that is numerically estimated ruling out the discretization error.•Comparison between the approximated fracture ...energy and the expected value from the Griffith theory for fixed value of the internal length parameter.•Study of the internal length parameter influence at the initiation process.•Energetic comparison between the sharp and the smeared approaches during crack propagation.•Analysis of fracture energy value in 3d setups.
The phase field approach to brittle fracture is based on smeared energetic representation of sharp fracture into surface. The passage between damaged and undamaged zones is influenced by an internal length scale parameter. In the present paper the approximation of fracture energy in phase field models is studied. Firstly, the diffusion equation of the phase field is numerically investigated. It is demonstrated through simple paradigmatic 2d and 3d cases that the fracture energy during crack initiation and propagation phenomena, such as crack branching and bifurcation, is strictly correlated with the internal length parameter. Moreover, it is shown that for finite value of the internal length parameter the dissipated energy does not depend only on the crack extension but on the geometrical configuration of fracture differently from the Griffith sharp approach. In particular, it is demonstrated that 3d cracks with same area may be characterized by different values of approximated fracture energy.
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