A numerical approach related to defect-type theories for some weakly random problems in homogenization

We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a rare event at the microscopic level. It however affects the macroscopic properties of the material, and we indeed provide a method to compute the first and second-order corrections. To this end, we formally establish an asymptotic expansion of the macroscopic properties. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated

The Fischler's Proposals for the Common Agricultural Policy: Paving the Way for the Future?

The Mid-Term Review proposals presented by the European Commission in July 2002 and January 2003 correspond no doubt to the most radical CAP reform since the latter was established in the early 1960's. This is not because these proposals include firm commitments on market access and export competition dossiers in the perspective of WTO talks. The proposals are silent on these points. This is because they finally achieve the shift from product to producer support by replacing all existing or newly introduced direct income payments, with a few exceptions, by a single decoupled payment per farm, based on historical references and conditional upon cross-compliance to environmental, animal welfare as well as food security and quality criteria. In addition, they expand the scope of rural development instruments to promote food quality, meet higher standards and foster animal welfare and they increase amounts available for rural development by transferring funds from the first to the second pillar via the introduction of an EU-wide system of degression and modulation. This paper discusses these proposals from both an external and internal point of view. We analyse to what extent the MTR proposals could facilitate the EU negotiation position in the WTO. From a domestic point of view, these proposals correspond to appropriate changes in the right direction with however some important qualifications. We analyse these qualifications. We also discuss to what extent the MTR proposals should be considered as the ultimate reform of the CAP or as the third step, after 1992 and 1999, in the long-term process where public intervention would be mainly reserved for correcting market failures, notably the promotion of positive externalities and public goods as well as the reduction in risk and instability faced by agricultural producers.Common Agricultural Policy (CAP), decoupling, cross-compliance, modulation, WorldTrade Organisation (WTO)

Multilateral Agricultural Negotiations and Multifunctionality: Some Research Issues

International Relations/Trade,

Periodic long-time behaviour for an approximate model of nematic polymers

We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation of the classical Doi closure, at the level of the kinetic equation ; second, we prove the convergence of the solution to the Fokker-Planck equation to periodic solutions in the long-time limit

Special Quasirandom Structures: a selection approach for stochastic homogenization

We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et al, Physical Review B 1990; Zunger et al, Physical Review Letters 1990], consists in selecting random realizations that best satisfy some statistical properties (such as the volume fraction of each phase in a composite material) usually only obtained asymptotically. We study the approach theoretically in some simplified settings (one-dimensional setting, perturbative setting in higher dimensions), and numerically demonstrate its efficiency in more general cases