On nonlinear dynamics of neutral modes in elastic waves in granular media

Strunin, D. V. and Ali, A. A. (2016) On nonlinear dynamics of neutral modes in elastic waves in granular media. Journal of Coupled Systems and Multiscale Dynamics, 4 (3). ISSN 2330-152X

Abstract

We analyse a passive system featuring a neutrally stable short-wavelength mode. The system is modelled by the Nikolaevskiy equation relevant to certain type of elastic waves, reaction-diffusion systems and convection. Due to the nonlinear coupling between the time-dependent Fourier modes, the system exhibits asymptotically slow evolution towards either zero or non-zero steady state depending on the initial condition and the neutral wave number. Using the centre manifold technique, we deduced that the decay law is that of inverse square root of time. The result is confirmed by the computations of the dynamical system for the Fourier modes.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 22 Feb 2017 03:27
Last Modified: 19 Dec 2017 04:53
Uncontrolled Keywords: mathematical, physical & engineering sciences, life, climate, environmental sciences
Fields of Research : 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1166/jcsmd.2016.1105
URI: http://eprints.usq.edu.au/id/eprint/30154

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