Theory of fractures in disordered media


    Fracture
    Bilaplacian fracture patterns
    • Two-dimensional fracturing can be investigated with conformal complex functions.
    • These analytically available functions provide inside into the fracturing process.

    Publications

    Bilaplacian fracture patterns
    A. Levermann and I. Procaccia
    Bi-Laplacian Growth Patterns in Disordered Media
    Physical Review Letters  89 (2002),  234501.
    » Highlighted in Nature 421 (2003), 124 by L.P. Kadanoff .
    bibtex entry

    F. Barra, A. Levermann, I. Procaccia
    Quasi-Static Brittle Fractures in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III
    Physical Review E  66 (2002),  066122.
    bibtex entry

    F. Barra, H.G. Hentschel, A. Levermann, I. Procaccia
    Quasistatic fractures in brittle media and iterated conformal maps
    Physical Review E  65 (2002),  R045101 (Rapid Comm.).
    bibtex entry

    The theoretically related problem of Diffusion Limited Aggregation
    A. Levermann and I. Procaccia
    Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
    Physical Review E  69 (2004),  031401.
    bibtex entry

    H.G. Hentschel, A. Levermann, I. Procaccia
    Transition in the Fractal Properties from Diffusion Limited Aggregation to Laplacian Growth via their Generalization
    Physical Review E  66 (2002),  016308.
    bibtex entry

    M.H. Jensen, A. Levermann, J. Mathiesen, I. Procaccia
    Multifractal structure of the harmonic measure of diffusion-limited aggregates
    Physical Review E  65 (2002),  046109.
    bibtex entry

    B. Davidovitch, M.H. Jensen, A. Levermann, J. Mathiesen, I. Procaccia
    Thermodynamic Formalism of the Harmonic Measure of Diffusion Limited Aggregates: Phase Transition and Converged f(α)
    Physical Review Letters  87 (2001),  164101.
    bibtex entry

    F. Barra, B. Davidovitch, A. Levermann, I. Procaccia
    Laplacian Growth and Diffusion Limited Aggregation: Different universality classes
    Physical Review Letters  87 (2001),  134501.
    bibtex entry

    B. Davidovitch, A. Levermann, I. Procaccia,
    Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters,
    Physical Review E  62 (2000),  R5919 (Rapid Comm.).
    bibtex entry