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Related Experiment Videos

Dissipative pattern formation in ternary non-linear reaction-electrodiffusion systems with concentration-dependent

H Malchow1

  • 1Department of Biophysics, Faculty of Science, Kyoto University, Japan.

Journal of Theoretical Biology
|December 7, 1988
PubMed
Summary

Ionic dissipative structures can emerge from Turing instability in reaction systems. Concentration-dependent diffusion influences spatial distribution amplitudes, controlling pattern formation in ionic systems.

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Area of Science:

  • Chemical kinetics
  • Physical chemistry
  • Non-equilibrium thermodynamics

Background:

  • Turing instability can lead to pattern formation in reaction-diffusion systems.
  • Electroneutral ternary ionic systems exhibit complex dynamics.
  • Concentration-dependent diffusion affects spatial pattern evolution.

Purpose of the Study:

  • Derive conditions for ionic dissipative structure emergence.
  • Analyze the role of concentration-dependent diffusion.
  • Investigate pattern formation in ionic reaction systems.

Main Methods:

  • Analysis of Turing instability in ionic systems.
  • Derivation of conditions for bifurcating inhomogeneous solutions.
  • Series expansion using eigenfunctions of the Laplace operator.

Related Experiment Videos

  • Modeling with polynomial concentration dependence of diffusion.

    • Main Results:

    • Conditions for ionic dissipative structure formation are established.
    • The bifurcating solution branch is characterized by eigenfunctions.
    • Concentration dependence of diffusion is shown to control spatial distribution amplitudes.
    • Model system with polynomial diffusion dependence analyzed.

    Conclusions:

    • Concentration-dependent diffusion is a key factor in controlling spatial patterns in ionic dissipative structures.
    • The study provides a theoretical framework for understanding pattern formation in complex ionic systems.
    • Results are applicable to various chemical and physical systems exhibiting similar instabilities.