Abstract
A one-dimensional reaction–diffusion model was used to study periodic filament formation in a laterally coupled gas discharge. Our results demonstrate three types of pattern formation (localized solitary filaments, small oscillation and intermediate), which deform into one another subject to a control parameter θ(φa/pd) and a boundary condition (where pd is the pressure–distance and φa is the applied voltage). The work shows the same qualitative dependence as the experimental work of Guikema et al (2000 Phys. Rev. Lett. 85 3817).
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