Peyresq lectures on nonlinear phenomena : [lectures of two summer schools, the INLN Summer Schools on Nonlinear Phenomena, in June 1998 and June 1999]

This monograph presents a concept of constitutive modelling of a wide variety of materials that are microscopically and macroscopically homogeneous. From one point of view it is a generalization of the fictitious classical "series" and "parallel" models; the author's model covers as special cases real structures of two-phase materials with inclusions in a matrix, or with both substructures being continuous or discontinuous. From another point of view it is a special case of a model with tensorial internal variables. Concrete structures are characterized by specific structural parameters that can be determined by simple macroscopic tests. Examples of applications to plasticity, rheology, shape memory and continuum damage, as well as to metallic polycrystalline materials and concrete and fibre-reinforced materials, are demonstrated Elasticity and geometry, B. Audoly and Y. Pomeau; quantum chaos, D. Delande; the water-wave problem as a spatial dynamical system, G. Iooss; cold atoms and multiple scattering, R. Kaiser; an introduction to Zakharov theory of weak turbulence, M.L. Bellac; phenomena beyond all orders and bifurcations of reversible homoclinic connections near higher resonances, E. Lombardi; mathematical modelling in the life sciences - applications in pattern formation and wound healing, P.K. Maini; relative equilibria and conserved quantities in symmetric Hamiltonian system, J. Montaldi Annotation Nonlinear science has a very broad scope and the aim of this volume of lectures is to introduce different aspects of this vast domain to research students whose studies are necessarily concentrated on only one. The lectures given at summer schools in France between 1997 and 1999, describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and the tripping of atoms Nonlinear science has a very broad scope and the aim of this volume of lectures is to introduce different aspects of this vast domain to research students whose studies are necessarily concentrated on only one. The lectures given at summer schools in France between 1997 and 1999, describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and the laser cooling of atoms. " ... a compilation of lecture notes on various topics in nonlinear physics delivered by specialists during the summer schools organized by the Institut Non Linéaire de Nice (INLN) in Peyresq (French Alps of Provence) since 1998. The first volume, edited by R. Kaiser and J. Montaldi, contains courses from the years 1998 and 1999. This volume collects notes of the lectures given from the summers of 2000, 2001 and 2002"--Preface, v. 2 A collection of lectures on nonlinear science, given at summer schools in France between 1997 and 1999. They describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and more. This paper follows from a set of lectures by the two authors given in the beautiful setting of the Rencontres de Peyresq, in the high country, north of Nice in late Spring 1999.