Objective
Within the framework of the project it is proposed to perform a cycle of theoretical and experimental investigations of new wave effects in media with complex structure with account of their discreteness, and also of nonlinearity and nonlocality of interatomic interactions.
First of all, one has to reveal new wave effects and the scale-dependent phenomena that have no analogs in the classical theory, cannot be described by traditional method and can be put into the basis of methods for diagnostics and identification of microstructured materials. These investigations will be used for theoretical justification of experiments on the study of physical properties of media with microstructure.
The specific goals of the project are: Elaboration of new mathematical models describing nonlinear dynamical processes in media with microstructure within the scope of the both strongly and weakly nonlocal theory of elasticity (nonlinear waves in the Cosserat continuum, models of acousticorientational interactions in nematic and smectic liquid crystals). Construction of 1D and 2D lattice models of elastic media with complex lattice which take account of nonlocality and nonlinearity of interatomic and intermollar interactions. Comparison of the quasicontinuum approximation of these models with models of the nonlocal theory of elasticity. Numerical and analytical investigations of the nonlinear dynamics of spatiotemporal structures: phase transformations, formation and decay of bound states of solitons, modulated instabilities and nonlinear resonant interactions of wave trains in solids.
Elaboration of an approximate analytical theory adequately describing the processes of a collision of 1D and 2D solitons, when a strong overlap of their fields and a stantial energy exchange between them take place. Consideration of the processes of soliton collision, emission and scattering described by both integrable equations and their non-integrable generalisations. Experimental investigations of nonlinear strain waves in microstructured and microdamaged solids and development of acoustic methods for testing microstructured and microdamaged materials.
Topic(s)
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75252 Paris
France