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Brazilian Journal of Physics

, Volume 47, Issue 2, pp 231–238 | Cite as

Diffusion-Driven Instability on a Curved Surface: Spherical Case Revisited

  • M. Núñez-López
  • G. Chacón-Acosta
  • J. A. Santiago
General and Applied Physics

Abstract

In this manuscript, we review the reaction-diffusion systems when these processes occur on curved surfaces. We show a general overview, from the original manuscripts by Turing, to the most recent developments with thick curved surfaces. We use the classical Schnakenberg model to present in a self-contained way the instability conditions of pattern formation in a flat surface; next, we give the basic elements of differential geometry of surfaces. With these tools, we study the reaction-diffusion system on a curved surface particularly on the sphere. When comparing the dispersion relations of both geometries, we found a modification in the range of the wavenumber due solely to the geometry of the substrate where the species diffuses.

Keywords

Turing patterns Reaction-diffusion Curved surfaces 

Notes

Acknowledgments

The authors would like to thank the partial support provided by the project “Programa de fortalecimiento de la interdisciplina en los CA de la DCNI” of the UAMC.

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Copyright information

© Sociedade Brasileira de Física 2017

Authors and Affiliations

  • M. Núñez-López
    • 1
  • G. Chacón-Acosta
    • 1
  • J. A. Santiago
    • 1
  1. 1.Departamento de Matemáticas Aplicadas y SistemasUniversidad Autónoma Metropolitana-CuajimalpaCiudad de MéxicoMexico

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