Objective
The proposed interdisciplinary programme which critically approaches a problem of both theoretical and engineering interests, gathers experienced specialists of condensed-matter physics, applied mathematics and theoretical mechanics, and numerical simulations, in order to attack simultaneously the complementary facets of a single general problem: the guided propagation of non-linear localized and periodic waves in solids and structures. These waves may be of purely elastic, purely magnetic or mixed magneto-mechanical nature. They are generally guided by a slender structure (rod, plate) or a substrate or environment, having appropriate properties (e.g. non linearity, dissipation). The problem of contact of the wave-guide element (rod, plate, thin film) embedded into or layered on a medium is essential for further study. Dispersion is inherent in these physical systems and non-linearity is involved via the component members. The research aims at a precise understanding of both physical processes and mathematical treatment with the perspective of delineating regimes and choice of new material components that yield potentially useful applications, such as in new non-destructive testing approaches, and in magnetic or magneto-elastic dynamic devices.
This area is more practical and should be one of the fruitful consequences of the whole programme that includes the refinement of lattice/discrete models, the better foundation of the long-wave continuum limit, and the application of powerful mathematical techniques of investigation adapted to non-exactly integrable systems in non-linear science. A generic formal approach based on solutions using the Weierstrass-function representation, group-invariant analysis, high-performance computing based on accurate finite-difference schemes for stiff problems, and spectral analysis, will provide precise estimates necessary for the pioneering experiments developed for capturing localized strain waves in solids (laser optical holography).
This clearly means the common focus on one specific object of study through the exploitation of tools developed successfully by all involved teams, separately or already in common via informal co-operative programmes. From the point of view of non-linear science, the assessment of characteristic properties (e.g. formation of stable soliton complexes) of highly dispersive non-linear systems such as those that naturally emerge from the considered physical situations - whether of magnetic, mechanical, or mixed origin - is the most important point, the experimental observation being also an inevitable asset. Based on relevant discretization of two-dimensional continuous and original discrete models, high-performance numerical simulation is necessary and complementary for a comprehensive study of non-stationary complex non-linear wave processes, that cannot be solved analytically.
It is expected that numerous joint scientific papers of a high calibre will result from a constructive interaction between the participating teams, the overall project being conceived so as to avoid a simple juxtaposition of individual endeavours, although each of the teams may naturally push forward a specific aspect but it should inspires the other teams too. In addition to individual visits, a mid-term workshop of all participants is envisaged. It will be pertinent to conclude the co-operation with a dissemination of results to a larger community of scientists in the form of an international colloquium. In the mean time, participating teams plan to share ideas and results at various scientific meetings of common interest.
Among the prospects resulting from this joint programme one should underline a new comprehensive understanding of non-linear mechanical and magnetic wave-guides and new trends to applications in engineering and geophysics, of new non-destructive testing methods and impact and magnetic devices (multi-layered systems), as well as a better grasp of the various mechanisms of the synergetic of physical and/or geometrical properties.
Call for proposal
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75252 Paris
France