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Tenuous structures from disorderly growth processes.

T A Witten, M E Cates

    Science (New York, N.Y.)
    |June 27, 1986
    PubMed
    Summary
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    Random growth processes create fractal structures with unique properties. These aggregates, unlike ordinary matter, exhibit scale invariance and are understood through statistical principles and models.

    Area of Science:

    • Physics
    • Materials Science
    • Statistical Mechanics

    Background:

    • Colloidal aggregation and random growth processes yield structures with unique properties.
    • These structures exhibit scale invariance, behaving as fractals.

    Purpose of the Study:

    • To explore the mechanisms behind fractal aggregate formation.
    • To relate fractal structures to other irreversible processes in physics.

    Main Methods:

    • Qualitative understanding of cluster-by-cluster aggregation using a solvable schematic model.
    • Discussion of diffusion-limited aggregation (DLA) and particle deposition.
    • Application of statistical principles to understand disorderly growth.

    Main Results:

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  • Fractal aggregates display invariance under spatial length scale changes.
  • Two primary mechanisms for fractal aggregate formation are identified: cluster-by-cluster and diffusion-limited aggregation.
  • Fractal properties can be understood using simple statistical principles.

    • Conclusions:

    • Disorderly growth mechanisms produce structures with unique, fractal properties.
    • Fractal aggregates differ significantly from ordinary bulk matter.
    • Further understanding of diffusion-limited aggregation is needed, though it relates to other physical processes.