Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials

Chaos
I B Shiroky, O V Gendelman

Abstract

We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition fr...Continue Reading

References

Jun 21, 2001·Physical Review Letters·A Carpio, L L Bonilla
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A CarpioG Dell'Acqua
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Carpio, L L Bonilla
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V V SmirnovL I Manevitch
Jul 2, 2016·Physical Review Letters·Neel NadkarniChiara Daraio

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Citations

Sep 6, 2018·Chaos·Juan F R ArchillaYusuke Doi
Aug 17, 2018·Physical Review. E·I B Shiroky, O V Gendelman

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