Power—Law in Depth—Dependence of Signal Speed in Vertical Granular Chain

The signalgenerated by an initial perturbation dispersively propagates in the vertical granular chain under gravity. For the power-law-type contact force, the signalspeed follows power-law with the depth. When the perturbation is very weak, the exponent is (1 - 1/p). 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.