The emergence of waves in random discrete systems

Pickton, John; Hopcraft, Keith Iain; Jakeman, Eric

Abstract

Essential criteria for the emergence of wave-like manifestations occurring in an entirely discrete system are identified using a simple model for the movement of particles through a network. The dynamics are entirely stochastic and memoryless involving a birth-death-migration process. The requirements are that the network should have at least three nodes, that migration should have a directional bias, and that the particle dynamics have a non-local dependence. Well defined bifurcations mark transitions between amorphous, wave-like and collapsed states with an intermittent regime between the latter two.

Citation

Pickton, J., Hopcraft, K. I., & Jakeman, E. (in press). The emergence of waves in random discrete systems. Scientific Reports, 6(21), https://doi.org/10.1038/s41598-016-0022-3

• Journal Article Type: Article
• Acceptance Date: Oct 24, 2016
• Online Publication Date: Dec 23, 2016
• Deposit Date: Jan 5, 2017
• Publicly Available Date: Jan 5, 2017
• Journal: Scientific Reports
• Electronic ISSN: 2045-2322
• Publisher: Nature Publishing Group
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Issue: 21
• DOI: https://doi.org/10.1038/s41598-016-0022-3
• Public URL: https://nottingham-repository.worktribe.com/output/832458
• Publisher URL: http://www.nature.com/articles/s41598-016-0022-3