Breathers and thermal relaxation in Fermi–Pasta–Ulam arrays

Abstract

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1537090͔Breathers are highly localized oscillatory excitations in discrete nonlinear lattices that have been invoked as a possible way to store and transport vibrational energy in a large variety of physical and biophysical contexts. A particular scenario where the robustness and longevity of breathers has been a matter of considerable debate involves nonlinear arrays subject to thermal relaxation via the connection of surface sites to a cold environment. The important questions are these: Can breathers "created spontaneously or by design… survive for a long time in such a relaxing environment? If they can survive, can they move? We detail answers to these questions, one of which is rather unequivocal: Breathers that move do not live very long. So is another: Breathers are quite robust when they do not move. The more complicated question then deals with the conditions that allow breathers to remain stationary and undisturbed for a long time in a relaxing environment. We detail some conditions that lead to this outcome, and others that definitely do not.

Discrete breathers — Advances in theory and applications

“…Cooling at the boundaries (see previous chapter), kicking the system with strong local kicks, and perhaps other nonstationary lattice evolutions can be used to generate discrete breathers along such transients. We will not focus on the growing amount of numerical data available in the literature [388,38,390,313,330,241,318]. The interested reader may check a collection of results on all these aspects in Ref.…”

Early time evolution of a localized nonlinear excitation in the β-FPUT chain

“…2 Energy dispersion in this model can be slow or fast depending upon the initial conditions. [3][4][5][6][7][8] The system accommodates phonons (for ↵ > 0). 2 For ↵ = 0 and > 0, solitary waves and metastable localized nonlinear excitations (LNEs) 9-13 are commonly encountered.…”

Highly nonlinear solitary waves in periodic dimer granular chains

“…Moreover, chains of granular media have been shown to be highly tunable [1,2,3] and have the potential to be used in many engineering applications -including shock and energy absorbing layers [9,10,11,12], sound focusing devices (tunable acoustic lenses and delay lines), sound absorption layers, and sound scramblers [13,14].A class of phenomena for which 1D chains of granular media provide an ideal setting concerns the interplay between nonlinearity and periodicity. The study of nonlinear oscillator chains has a time-honored history, originat-ing with the Fermi-Pasta-Ulam problem [18,19,20]. Its applications arise in numerous areas of physics, including coupled waveguide arrays and photorefractive crystals in nonlinear optics [21,22], Bose-Einstein condensates in optical lattices in atomic physics [23], and DNA double-strand dynamics in biophysics [24].…”