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See supplementary material at http://link.aps.org/supplemental/10.1103/ PhysRevE.82.050301 for Movie 1: A movie that shows the evolution of the packing during tapping at Γ = 7.0 followed by tapping at Γ = 1.5. Movie 2: A movie that shows the dynamics of a single tap at three very different values of Γ.
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We have seen that the two invariants of Σ (i.e. the trace and the determinant in 2D) are proportional to one another [i.e., Det (Σ) =aTr (Σ) +b]. Moreover a and b are independent of the amplitude and duration of the taps used to reach a given Σ. Therefore, Tr (Σ) suffices to characterize Σ for our purposes.
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We have seen that the two invariants of Σ (i.e. the trace and the determinant in 2D) are proportional to one another [i.e., D e t (Σ) = a T r (Σ) + b]. Moreover a and b are independent of the amplitude and duration of the taps used to reach a given Σ. Therefore, T r (Σ) suffices to characterize Σ for our purposes.
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Cambridge University Press, Cambridge, England
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A. Mehta, Granular Physics (Cambridge University Press, Cambridge, England, 2007), Chap..
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Granular Physics
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