1. Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective
- Author
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A. N. Sekar Iyengar, Prasanta K. Panigrahi, and Abhinna Kumar Behera
- Subjects
Physics ,Hurst exponent ,Applied Mathematics ,General Physics and Astronomy ,Wavelet transform ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Phase synchronization ,Nonlinear Sciences - Chaotic Dynamics ,symbols.namesake ,Fourier transform ,Wavelet ,Morlet wavelet ,symbols ,Detrended fluctuation analysis ,Statistical physics ,Chaotic Dynamics (nlin.CD) ,Bouncing ball dynamics ,Mathematical Physics - Abstract
The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations., Comment: 17 pages, 10 figures, 1 table
- Published
- 2013
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