On the Wave Transmission in a Gently Perturbed Weakly Inhomogeneous Non-Linear Force Chain


  • O.I. Gerasymov Department of General and Theoretical Physics, Odesa State Environmental University
  • A.Ya. Spivak Department of General and Theoretical Physics, Odesa State Environmental University




wave transport, Hertz chain, resonance modes, multiscale analysis, disorder


We have obtained rigorous analytic and numerical solutions of the equations which govern the transport of mechanical perturbations in a gently precompressed 1D Hertz chain. Both finite-length and infinite-length systems have been studied. We examine both discrete and continuous
formulations of the mentioned problem. A few families of analytic solutions of the problem given in the form of quasinormal waves and specific resonance modes have been obtained in the linear approximation for weakly perturbed inhomogeneous systems. Resonance modes are proposed to be interpreted as the Ramsauer–Townsend effect which happens due to the inhomogeneity. The obtained analytic results have been compared with numerical solutions of the discrete equations. We observe a multiscaled scenario of the impulse transport in an inhomogeneous force chain which could happens either asymptotically or at the intermittency between discrete- and continuous limits of the formulated problem. The role of a disorder has been also analyzed with the help of the Dyson concept.


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How to Cite

Gerasymov, O., & Spivak, A. (2020). On the Wave Transmission in a Gently Perturbed Weakly Inhomogeneous Non-Linear Force Chain. Ukrainian Journal of Physics, 65(11), 1008. https://doi.org/10.15407/ujpe65.11.1008



General physics