Applications of time-scale methods to linear and nonlinear wave propagation in a one-dimensional disordered lattice

David Hughes

doi:10.1117/12.255435

22 October 1996 Applications of time-scale methods to linear and nonlinear wave propagation in a one-dimensional disordered lattice

David Hughes

Author Affiliations +

Proceedings Volume 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI; (1996) https://doi.org/10.1117/12.255435
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Displacement events of nearest neighbor spring coupled mass points, embedded in a semi-infinite, periodic 1D lattice, which is driven at constant velocity at one end, are studied. The displacements of the mass points are due to small amplitude, linear oscillations, and large amplitude, low frequency translations due to nonlinear waves, or solitons, propagating on the lattice. The translational symmetry of the underlying rigid periodic lattice is broken by defect sites whose positions and amplitudes are random. Because of intermittent reflections and transmissions of the solitons at the impurity defect sites, there results stick- slip motions of the mass points of varying magnitudes and durations. The joint distribution for these events, of magnitude (delta) x and duration (delta) t, is approximated by way of the zero crossings of the wavelet transform of the displacement time series of a tracer atom in the complex flow. There follows estimates of the scaling laws of statistical quantities characterizing the motion.

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David Hughes "Applications of time-scale methods to linear and nonlinear wave propagation in a one-dimensional disordered lattice", Proc. SPIE 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, (22 October 1996); https://doi.org/10.1117/12.255435

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