DynSyst_Special_Topics:Collaborative Research: Fundamental and Applied Dynamics of Granular Crystals: Disorder, Localization and Energy Harvesting

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The research objective of the present proposal is to study nonlinear waveforms that may arise in granular crystals, including traveling waves, defect modes, and discrete breathers. It also intends to provide a roadmap for identifying when these different structures will arise, systematically building up in complexity, from monomer lattices, to dimmer, trimmer and heterogeneous ones, and from one- to multiple-defect chains and even random lattices. Granular crystals consist of chains of interacting particles that deform elastically when they collide. Their properties (material types, sizes, shapes) are extremely tunable and their dynamic response may be modified to be weakly or strongly nonlinear. The project will involve a fruitful cross-pollination of tools and methods from dynamical systems, nonlinear ordinary and partial differential equations, asymptotic analysis and numerical computation on the theoretical side. These will be interwoven with physical experiments that will attempt to excite and identify the relevant nonlinear waves and to investigate their properties (amplitude, width, energy, lifetime, interactions, higher-dimensional analogs etc.). A continuous feedback loop between mathematical theory, numerical simulation and physical experimentation will be the driving force of the study.It is anticipated that this project will have a significant societal impact due to the potential discovery of mechanical systems that may affect aspects of everyday life. In particular, localized modes will be studied for potential use in energy harvesting systems, delay lines and shock protective or vibration absorption materials. Additionally, the relevant effort will involve student researchers with a vigorous educational component including both formal (associated with coursework and research conferences) and informal (inter-group exchanges and visits) educational opportunities. It will bring together students from fundamentally different backgrounds (mathematics and aeronautical/aerospace engineering) providing them with a rich interdisciplinary experience that will offer an excellent framework for learning and scientific exchange/collaboration. The program will also foster collaborations between the two institutions, but also with other Universities (Oxford University in the UK, Princeton University and the University of Athens). We expect that several conference presentations, journal articles and patent applications will emerge from this study.