dorsal/arxiv
View SchemaPower-Law Behaviors in Nonlinearly Coupled Granular Chain under Gravity
| Authors | Jongbae Hong, Heekyong Kim |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9808008 |
| URL | https://arxiv.org/abs/patt-sol/9808008 |
Abstract
We find power-law behaviors of grain velocity in both propagation and backscattering in a gravitationally compacted granular chain with nonlinear contact force. We focus on the leading peak of the velocity signal which decreases in a power-law $d^{-\alpha}$, where $d$ is the location of the peak, as the signal goes down. The ratio of backscattered to incident leading velocity also follows a power-law $d_i^{-\beta}$, where $d_i$ is the depth of impurity. The up-going backscattered signal is nearly solitary. Therefore, the overall change of the leading velocity peak is given by the power-law $d_i^{-(\alpha+\beta)}$. We find $\alpha=0.250$ and $\beta=0.167$ for the Hertzian contact force.
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"date_created": "2026-03-02T18:00:28.657000Z",
"date_modified": "2026-03-02T18:00:28.657000Z",
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"abstract": "We find power-law behaviors of grain velocity in both propagation and\nbackscattering in a gravitationally compacted granular chain with nonlinear\ncontact force. We focus on the leading peak of the velocity signal which\ndecreases in a power-law $d^{-\\alpha}$, where $d$ is the location of the peak,\nas the signal goes down. The ratio of backscattered to incident leading\nvelocity also follows a power-law $d_i^{-\\beta}$, where $d_i$ is the depth of\nimpurity. The up-going backscattered signal is nearly solitary. Therefore, the\noverall change of the leading velocity peak is given by the power-law\n$d_i^{-(\\alpha+\\beta)}$. We find $\\alpha=0.250$ and $\\beta=0.167$ for the\nHertzian contact force.",
"arxiv_id": "patt-sol/9808008",
"authors": [
"Jongbae Hong",
"Heekyong Kim"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Power-Law Behaviors in Nonlinearly Coupled Granular Chain under Gravity",
"url": "https://arxiv.org/abs/patt-sol/9808008"
},
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