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Travelling waves in a reaction-diffusion model for electrodeposition

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  • Bozzini, Benedetto
  • Lacitignola, Deborah
  • Sgura, Ivonne

Abstract

In this paper we consider an analytical and numerical study of a reaction-diffusion system for describing the formation of transition front waves in some electrodeposition (ECD) experiments. Towards this aim, a model accounting for the coupling between morphology and composition of one chemical species adsorbed at the surface of the growing cathode is addressed. Through a phase-space analysis we prove the existence of travelling waves, moving with specific wave speed. The numerical approximation of the PDE system is performed by the Method of Lines (MOL) based on high order space semi-discretization by means of the Extended Central Difference Formulae (D2ECDF) introduced in [1]. First of all, to show the advantage of the proposed schemes, we solve the well-known Fisher scalar equation, focusing on the accurate approximation of the wave profile and of its speed. Hence, we provide numerical simulations for the electrochemical reaction-diffusion system and we show that the results obtained are qualitatively in good agreement with experiments for the electrodeposition of Au–Cu alloys.

Suggested Citation

  • Bozzini, Benedetto & Lacitignola, Deborah & Sgura, Ivonne, 2011. "Travelling waves in a reaction-diffusion model for electrodeposition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1027-1044.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:5:p:1027-1044
    DOI: 10.1016/j.matcom.2010.10.008
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    1. R. D. Benguria & M. C. Depassier & M. Loss, 2008. "Upper and lower bounds for the speed of pulled fronts with a cut-off," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 331-334, February.
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    Cited by:

    1. Yadav, Vivek S. & Maurya, Vikas & Rajpoot, Manoj K. & Jaglan, Jyoti, 2022. "Spatiotemporal pattern formations in stiff reaction-diffusion systems by new time marching methods," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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