Stability of densely branched growth in dissipative diffusion-controlled systems

Juan K. Lin, David G. Grier

    Research output: Contribution to journalArticle

    Abstract

    The dense branching morphology appears in a number of pattern-forming systems. Neither ordered nor fractal, this pattern is characterized by a large number of branches advancing at constant areal density behind a smooth envelope. We propose a two-sided model which accounts for the stability of the dense branching morphology (DBM) through dissipative and anisotropic current transport in the evolving pattern. Confinement of currents to slightly resistive branches suffices to stabilize radially symmetric DBM growth in two and three dimensions Stability of the planar DBM, on the other hand, is found to require, in addition, the introduction of a characteristic length scale, such as a short diffusion length.

    Original languageEnglish (US)
    Pages (from-to)2690-2695
    Number of pages6
    JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
    Volume54
    Issue number3
    StatePublished - 1996

    Fingerprint

    Controlled Diffusions
    Branching
    Branch
    diffusion length
    Length Scale
    Envelope
    Three-dimension
    Fractal
    fractals
    Two Dimensions
    envelopes

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Condensed Matter Physics
    • Statistical and Nonlinear Physics

    Cite this

    Stability of densely branched growth in dissipative diffusion-controlled systems. / Lin, Juan K.; Grier, David G.

    In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 54, No. 3, 1996, p. 2690-2695.

    Research output: Contribution to journalArticle

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