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

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

Professor Panos Kevrekidis

In this talk, Professor Kevrikidis will provide an overview of results in the setting of granular crystals, consisting of beads interacting through Hertzian contacts.

In 1d he will show that there exist three prototypical types of coherent nonlinear waveforms: shock waves, travelling solitary waves and discrete breathers. The latter are time-periodic, spatially localised structures.

For each one, Professor Kevrikidis will analyse 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. He 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, Professor Kevrikidis will complement the mathematical theory and numerical computations with state-of-the-art experiments, allowing their quantitative identification and visualisation. Finally, time permitting, ongoing extensions of these themes will be briefly touched upon, most notably in higher dimensions, in heterogeneous or disordered chains and in the presence of damping and driving; associated open questions will also be outlined.

Speaker

Professor Panos Kevrikidis is a professor at the Department of Mathematics & Statistics at the University of Massachusetts Amherst.