@article{Pikovsky2020,
  author    = {Pikovsky, Arkady},
  title     = {Scaling of energy spreading in a disordered Ding-Dong lattice},
  series = {Journal of statistical mechanics: theory and experiment},
  volume    = {2020},
  journal   = {Journal of statistical mechanics: theory and experiment},
  number    = {5},
  publisher = {IOP Publishing Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/ab7e30},
  pages     = {12},
  year      = {2020},
  abstract  = {We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to the appearance of chaos, and subdiffusive. For a range of energies and of weak and moderate levels of disorder, we focus on the macroscopic statistical characterization of spreading. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence of energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.},
  language  = {en}
}
@article{Pikovskij2015,
  author    = {Pikovskij, Arkadij},
  title     = {First and second sound in disordered strongly nonlinear lattices: numerical study},
  series = {Journal of statistical mechanics: theory and experiment},
  journal   = {Journal of statistical mechanics: theory and experiment},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/2015/08/P08007},
  pages     = {10},
  year      = {2015},
  abstract  = {We study numerically secondary modes on top of a chaotic state in disordered nonlinear lattices. Two basic models are considered, with or without a local on-site potential. By performing periodic spatial modulation of displacement and kinetic energy, and following the temporal evolution of the corresponding spatial profiles, we reveal different modes which can be interpreted as first and second sound.},
  language  = {en}
}