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

Description

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