Nonlinear evolution equations for degenerate transverse waves in anisotropic elastic solids

Transverse elastic waves behave differently in nonlinear isotropic and anisotropic media. Quadratically nonlinear coupling in the evolution equations for wave amplitudes is not possible in isotropic solids, but such a coupling may occur for certain directions in anisotropic materials. We identify the expression responsible for the coupling and we derive coupled canonical evolution equations for transverse wave amplitudes in the case of two-fold and three-fold symmetry acoustic axes. We illustrate our considerations by examples for a cubic crystal.Comment: 4 page

AGROECOLOGIE : LE CHAINON MANQUANT ROLE DE CONSOMMATEURS ET D'ONG DANS LES PROCESSUS EMERGEANT D'APPRENTISSAGES

N° ISBN - 978-2-7380-1284-5International audienceAcademic texts on agro-ecology are often too limited to production systems. When notions of food systems and food value chains are described they introduce the consumer as a choice taker, reflecting neoclassical economic theory. The study of the emergence of two agroecological chains in Benin and Belgium explains how consumer demands are key learning resources for chain co-creation. In the case of the fair trade rice chain an NGO stimulates the cocreation process while in the beef chain in Gaume consumers who are directly involved in a deliberative process bring about this questioning. Agroecology, Food Systems, Participatory Research, Consumers, Learning process, Food Chain, Knowledge's, Biodiversity, Stock Farming, Rice Farmin