arXiv subjects

Heekyong Kim

Publications and source records attributed to Heekyong Kim.

2 recordsLinked to original sources

arXiv1999

Power-Laws in Nonlinear Granular Chain under Gravity

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by $h^{-1/4(1-1/p)}$ where $h$ and $p$ denote depth and the exponent of contact force, and the power-law for the grain velocity is $h^{-1/4({1/3}+1/p)}$. Other depth-dependent power-laws for oscillation frequency, wavelength, and period are given by combining above two and the phase velocity power-law $h^{1/2(1-1/p)}$. We verify above power-laws by comparing with the data obtained by numerical simulations.

cond-mat.stat-mech↗

arXiv1998

Power-Law Behaviors in Nonlinearly Coupled Granular Chain under Gravity

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 $d^{-α}$, 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 $d_i^{-β}$, 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 $d_i^{-(α+β)}$. We find $α=0.250$ and $β=0.167$ for the Hertzian contact force.

patt-sol↗