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Self similar formation of an inverse cascade in vibrating elastic plates

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FIG. 1. (Color online) Snapshots of the out-of-plate displacement ζ (x,y,t) obtained by the numerical simulation of the F¨oppl–von K´arm´an equations (1) and (2) at six different times: (a) t = 22 × 10 3 , (b) t = 50 × 10 3 , (c) t = 62 × 10 3 , (d) t = 82
FIG. 3. (Color online) (a) Angular average of the spectra, n k , as a function of wave number k in log-log scale, at different time steps starting at t = 35 × 10 3
FIG. 6. (Color online) (a) Self-similar universal function φ ∞ (s) as a function of the self-similar variable, s, in linear scale
FIG. 7. (Color online) (a) The ratio E 4 /E 2 vs t, under the same conditions as in Fig
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