Tuning the range of spatial coupling in electrochemical systems: From local via nonlocal to global coupling

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Abstract
A specific feature of pattern formation in electrochemical systems is the occurrence of accelerated fronts; they can be attributed to long-range spatial coupling. In this paper we demonstrate that different coupling functions can be realized by tuning easily accessible parameters: The range of the coupling crucially depends on the length scales of the system, and the strength of the coupling is proportional to the conductivity of the electrolyte. Simulations in the bistable regime are presented which illustrate how the front behavior changes qualitatively when length scales or conductivity are varied.