TY - JOUR A1 - Pikovsky, Arkady T1 - Scaling of energy spreading in a disordered Ding-Dong lattice JF - Journal of statistical mechanics: theory and experiment N2 - 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. KW - connections between chaos and statistical physics KW - nonlinear dynamics KW - transport properties Y1 - 2020 U6 - https://doi.org/10.1088/1742-5468/ab7e30 SN - 1742-5468 VL - 2020 IS - 5 PB - IOP Publishing Ltd. CY - Bristol ER - TY - JOUR A1 - Pikovskij, Arkadij T1 - First and second sound in disordered strongly nonlinear lattices: numerical study JF - Journal of statistical mechanics: theory and experiment N2 - 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. KW - disordered systems (theory) KW - connections between chaos and statistical physics Y1 - 2015 U6 - https://doi.org/10.1088/1742-5468/2015/08/P08007 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol ER -