Power-Law in Depth-Dependence of Signal Speed in Vertical Granular Chain**The authors acknowledge the financial support (KRF-2000-DPO106) of the Korea Research Foundation and financial support of the BK21 project of the Ministry of Education, Korea

Abstract

The signal generated by an initial perturbation dispersively propagates in the vertical granular chain under gravity. For the power-law-type contact force, the signal speed follows power-law with the depth. When the perturbation is very weak, the exponent is . When the perturbation is very strong, the exponent approaches zero. The transition of the exponent from oscillatory regime with weak nonlinearity to quasi-solitary regime with strong nonlinearity is smooth.