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Nonlinear grain–grain forces and the width of the solitary wave in granular chains: a numerical study

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Abstract

Any impulse results in the formation of a solitary wave of time averaged width \(W\) in a granular chain. If the grain–grain interaction potential \(V\sim \delta ^n\), where \(\delta \) is the distance by which the grains approach each other, then it is well established that \(n\ge 2\). Here we present dynamical simulation based results which suggest that \(W-1\propto (n-2)^{-\alpha }\) where \(\alpha =0.3283\) or \(\approx \)1/3. While in qualitative agreement, the result is quantitatively different from the formula for \(W\) proposed earlier by Nesterenko.

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Acknowledgments

This work has been partially supported by the US Army Research Office through a STIR Grant. We thank Yoichi Takato for his role in redoing the figures. Sourish Chakravarty’s help with the figures is also gratefully acknowledged.

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  1. Department of Physics, State University of New York, Buffalo, NY, 14260-1500, USA

    Diankang Sun & Surajit Sen

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  1. Diankang Sun
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  2. Surajit Sen
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Correspondence to Surajit Sen.

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Sun, D., Sen, S. Nonlinear grain–grain forces and the width of the solitary wave in granular chains: a numerical study. Granular Matter 15, 157–161 (2013). https://doi.org/10.1007/s10035-013-0400-5

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