Volume fluctuations and linear response in a simple model of compaction

By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and explicit expressions for the average and the variance are provided. Experimental and molecular dynamics results are analyzed and qualitatively compared with the model predictions. The relevance of considering open or closed systems is discussed, as well as the meaning and properties of the Edwards compactivity and the effective (configurational) temperature introduced by some authors. Finally, the linear response to a change in the vibration intensity is also investigated. A KWW decay of the volume response function is clearly identified. This seems to confirm some kind of similarity between externally excited granular systems and structural glasses.