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Title: A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
Award ID(s):
2011444 1953535
NSF-PAR ID:
10320560
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Volume:
387
Issue:
C
ISSN:
0045-7825
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’. 
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