Subharmonic wave transition in a quasi-one-dimensional noisy fluidized shallow granular bed
Abstract
We present an experimental and theoretical study of the pattern formation process of standing subharmonic waves in a fluidized quasi-one-dimensional shallow granular bed. The fluidization process is driven by means of a time-periodic air flow, analogous to a tapping type of forcing. Measurements of the amplitude of the critical mode close to the transition are in quite good agreement with those inferred from a universal stochastic amplitude equation. This allows us to determine both the bifurcation point of the deterministic system and the corresponding noise intensity. We also show that the probability density distribution is well described by a generalized Rayleigh distribution, which is the stationary solution of the corresponding Fokker-Planck equation of the universal stochastic amplitude equation that describes our system.
Description
The authors would like to thank to S. Rica and specially C. Orellana for fruitful discussions of the preliminary results of this study. M.G.C., N.M., and C.F. acknowledge the financial support of FONDECYT Grant Nos. 1090045, 1090188, and 11090049, respectively. M.G.C. and N.M. acknowledge the financial support of FONDAP Grant No. 11980002. C.F. acknowledges the financial support of Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile.
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