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Updated: Mar 9, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
The emergence of waves in random discrete systems
John Pickton1, Keith Iain Hopcraft2, Eric Jakeman2
1University of Nottingham, School of Mathematical Sciences, Nottingham, NG7 2RD, UK. pmxjp5@nottingham.ac.uk.
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.
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