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Modelling and Simulation

Working Group 8.41

Publications 8.41

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Title: Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system
Author(s): K. John, S. Alonso and M. Bär
Journal: Phys. Rev. E
Year: 2014
Volume: 90
Issue: 5-1
Pages: 052913
DOI: 10.1103/PhysRevE.90.052913
ISSN: 1550-2376
Web URL: http://www.ncbi.nlm.nih.gov/pubmed/25493864
Keywords: pattern formation
Tags: 8.41, exc-media
Abstract: During pattern formation in spatially extended systems, different mechanisms with different characteristic length scales, e.g., reaction-diffusion processes or molecular interactions, can be active. Such multiscale effects may generate new phenomena, which are not observed in systems where pattern formation occurs on a single scale. Here, we derive and analyze a reaction-diffusion model of the FitzHugh-Nagumo type with short-range attractive molecular interactions of the activator species. The model exhibits a wave instability. Simulations in one and two dimensions show traveling waves with a wavelength set by the parameters of the molecular interaction in the model. In two dimensions, simulations reveal a labyrinthine arrangement of the waves in systems with isotropic diffusion, whereas parallel bands of counterpropagating waves are formed in simulations of a model with anisotropic diffusion. The latter findings are in good qualitative agreement with experimental observation in the catalytic NO+H\_{{}2} reaction on an anisotropic Rh(110) surface. In addition we have identified a transition regime in the simulations, where a short scale instability triggers global oscillations in an excitable regime.

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