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Momentum and energy propagation in tapered granular chains

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Abstract

We study momentum and energy propagation in 1D tapered chains of spherical granules which interact according to a Hertz potential. In this work we apply the binary collision approximation, which is based on the assumption that transfer of energy along the chain occurs via a succession of two-particle collisions. Although the binary theory correctly captures the trends of increase or decrease of kinetic energy and momentum, the actual values of these quantities are not in good quantitative agreement with those obtained by numerically integrating the full equations of motion. To address this difficulty we have developed a mixed numerical/analytical correction algorithm to provide an improved estimate of the velocity of the particles during pulse propagation. With this corrected velocity we are in turn able to correctly predict the momentum and kinetic energy along the chain for several tapering configurations, specifically for forward linear, forward exponential, backward linear and backward exponential tapering.

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Notes

  1. The shape of the granules does not really matter as they are treated as point masses with an interaction determined by their radius of curvature and their mass. We talk about spherical granules for convenience, as is done in a great deal of the relevant literature.

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Acknowledgments

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research (K. L.). A. R. acknowledges support from Bionanotec-CAPES and CNPq. L. P. M. acknowledges support by CAPES. The authors acknowledge helpful discussions with A. H. Romero and U. Harbola.

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Authors and Affiliations

  1. Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, 58059-900, Brazil

    L. P. Machado & Alexandre Rosas

  2. Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, La Jolla, CA, 92093-0340, USA

    Katja Lindenberg

Authors
  1. L. P. Machado
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  2. Alexandre Rosas
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  3. Katja Lindenberg
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Correspondence to Alexandre Rosas.

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Machado, L.P., Rosas, A. & Lindenberg, K. Momentum and energy propagation in tapered granular chains. Granular Matter 15, 735–746 (2013). https://doi.org/10.1007/s10035-013-0444-6

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  • DOI: https://doi.org/10.1007/s10035-013-0444-6

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