Some Vignettes of Nonlinear Waves in Granular Crystals: From Modeling and Analysis to Computations and Experiments

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• Panayotis Kevrekidis (University of Massachusetts)
• Wednesday 07 December 2022, 10:30-11:00
• Seminar Room 1, Newton Institute.

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HY2W05 - Physical applications

In this talk, we will provide an overview of some results in the setting of granular crystals, consisting of beads interacting through Hertzian contacts. In 1d we show that there exist three prototypical types of coherent nonlinear waveforms: shock waves, traveling solitary waves and discrete breathers. The latter are time-periodic, spatially localized structures. For each one, we will discuss the existence theory, presenting connections to prototypical models of nonlinear wave theory, such as the Burgers equation, the Korteweg-de Vries equation and the nonlinear Schrodinger (NLS) equation, respectively. We will also explore the stability of such structures, presenting some explicit stability criteria analogous to the famous Vakhitov-Kolokolov criterion in the NLS model. Finally, for each one of these structures, we will complement the mathematical theory and numerical computations with recent experiments, allowing their quantitative identification and visualization. Finally, time permitting, ongoing extensions of these themes will be briefly touched upon, most notably towards the study of dispersive shock waves in discrete systems, in higher dimensions, in heterogeneous or disordered chains and in the presence of damping and driving; associated open questions will also be outlined. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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