文档介绍：arXiv:cond-mat/0307080v1 [cond--mech] 3 Jul 2003Pulse Dynamics in a Chain of Granules With FrictionAlexandre Rosas and Katja LindenbergDepartment of Chemistry and Biochemistry, and Institute for NonlinearScience University of California San Diego La Jolla, CA 92093-0340(Dated: February 2, 2008)We study the dynamics of a pulse in a chain of granules with friction. We present theories forchains of cylindrical granules (Hertz potential with exponentn= 2) and of granules with othergeometries (n >2). Our results are supported via numerical simulations forcylindrical and forspherical granules (n= 5/2).PACS numbers: .-n,.-a,.+xI. INTRODUCTIONThe propagation of pulses in granular materials has been a subject of vigorous recent interest. Seminal workon this subject was carried out by Nesterenko [1] two decadesago in his analysis of the propagation of pression pulses along a line of particles. This early work ?rmly established the nonlinear ?avor of the problem:Nesterenko showed that under appropriate assumptions, among them the slow spatial variation of the displacementsof the particles, the equations of motion for granular particles could in most cases be approximated by a continuousnonlinear partial di?erential equation that admits a soliton solution (later shown to actually be a solitary wavesolution [2, 3]) for a propagating perturbation in the chain. The recent revival of interest in the subject [2, 3, 4, 5, 6,7, 8, 9, 10, 11, 12, 13, 14, 15, 16] has been triggered in part bya concern with important technological applicationssuch as the design of e?cient shock absorbers [14], the detection of buried objects [5, 6, 7, 8], and the fragmentationof granular chains [9]. The revival has involved advances inthe modeling, simulation, and solution of the equationsassociated with important features of granular materials such as their discreteness [2, 3, 10, 14], dimensionality [14],disorder [7, 11, 14], and loading provided by gravitationalforces [4, 7