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Dissipative structures in two dimensions.

T Erneux, M Herschkowitz-Kaufman

    Biophysical Chemistry
    |October 1, 1975
    PubMed
    Summary
    This summary is machine-generated.

    This study explores dissipative structures in bounded chemical systems. Results show system dimensions significantly influence pattern formation and solution multiplicity.

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    Area of Science:

    • Chemical kinetics
    • Non-equilibrium thermodynamics
    • Pattern formation

    Background:

    • Dissipative structures are key to understanding complex systems far from equilibrium.
    • Previous research has explored these structures in simpler systems.

    Purpose of the Study:

    • To investigate dissipative structures in one- and two-dimensional bounded chemical systems.
    • To analyze the impact of boundary conditions, geometry, and system size on pattern formation.

    Main Methods:

    • Modeling a chemical network with reactions and diffusion.
    • Numerical simulations to observe pattern evolution.
    • Comparison with bifurcation theory.

    Main Results:

    • Demonstrated influence of boundary conditions (no fluxes, fixed concentrations), geometry (circular, rectangular), and system size on pattern variety.

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  • Observed a sharp increase in the multiplicity of stable ordered solutions from one to two dimensions.

    • Conclusions:

    • System dimensionality is a critical factor in dissipative structure formation.
    • The complexity of stable patterns significantly increases with dimensionality, impacting chemical system behavior.